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    <id>https://guide.ihamodel.com/blog</id>
    <title>环安软件帮助中心 Blog</title>
    <updated>2026-02-02T00:00:00.000Z</updated>
    <generator>https://github.com/jpmonette/feed</generator>
    <link rel="alternate" href="https://guide.ihamodel.com/blog"/>
    <subtitle>环安软件帮助中心 Blog</subtitle>
    <icon>https://guide.ihamodel.com/img/huanan-favicon.png</icon>
    <entry>
        <title type="html"><![CDATA[建设项目大气一级预测所需资料准备攻略]]></title>
        <id>https://guide.ihamodel.com/blog/air-eia-level1-data-prep-guide</id>
        <link href="https://guide.ihamodel.com/blog/air-eia-level1-data-prep-guide"/>
        <updated>2026-02-02T00:00:00.000Z</updated>
        <summary type="html"><![CDATA[按污染源、评价范围、保护目标、现状数据与气象资料等要点，整理建设项目大气一级预测的资料清单与注意事项。]]></summary>
        <content type="html"><![CDATA[<p>本文从污染源整理、评价范围确定、环境保护目标、环境质量现状数据、气象资料、模型参数设置等九个方面便阐述大气一级预测的资料准备（规划项目亦可参照）。</p>
<h4 id="1工程分析与污染源整理">1、工程分析与污染源整理</h4>
<p>需要收集污染源的相关参数：</p>
<ul>
<li>项目位置：项目基准点经度和纬度</li>
<li>污染源信息，</li>
<li>点源：位置、源高、内径、烟温、烟气量（流速）、污染物排放速率；</li>
<li>面源：位置、边长（X、Y）、源高、污染物排放速率。</li>
<li>预测因子，确定大气预测的污染物（有标准值的污染物）。</li>
</ul>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/%E5%BE%AE%E4%BF%A1%E5%9B%BE%E7%89%87_20200826124122.jpg" alt=""></p>
<h4 id="2评价范围确定价范围确定">2、评价范围确定价范围确定</h4>
<p>利用Aerscreen计算出各污染物的D10%，根据项目排放污染物的最远影响距离（D10%）按照导则5.4的规定确定大气环境影响评价范围。</p>
<ul>
<li>注：1、当最远D10%小于2.5km时，评价范围是以厂址为中心、边长5km。</li>
<li>2、规划项目以规划区边界为起点，外延最远D10%的区域。</li>
</ul>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/%E5%BE%AE%E4%BF%A1%E5%9B%BE%E7%89%87_20200826124132.jpg" alt=""></p>
<p>图1评价范围</p>
<h4 id="3环境空气保护目标">3、环境空气保护目标</h4>
<p>确定评价范围内的环境空气保护目标，包括村庄、学校、医院等。</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/%E5%BE%AE%E4%BF%A1%E5%9B%BE%E7%89%87_20200826124138.png" alt=""></p>
<p>注：建议调查项目周边是否自然保护区、风景名胜区等一类功能区</p>
<h4 id="4环境质量现状数据">4、环境质量现状数据</h4>
<p>A.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;基本污染物（SO2、NO2、PM10、PM2.5、O3、CO）连续一年的逐日监测数据。采用生态环境主管部门发布的环境质量现状数据。B.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;其他污染物（除上述六种基本污染物）。可收集评价范围内进三年与项目排放有关的历史监测资料或进行7天补充监测。</p>
<h4 id="5背景图辅助">5、背景图（辅助）</h4>
<p>背景图主要用来表征污染源、敏感点位置、作为网格浓度的图的底图。</p>
<p>需要根据项目位置及预测范围截取卫星图、厂区CAD平面布置图、规划项目的规划区编辑SHP图。</p>
<h4 id="6气象数据">6、气象数据</h4>
<p>导则对气象数据的相关规定：</p>
<ul>
<li>地面气象数据选择距离项目最近或气象特征基本一致的气象站的逐时地面气象数据，要素至少包括风速、风向、总云量和干球温度。</li>
<li>高空气象数据选择模型所需观测或模拟的气象数据，要素至少包括一天早晚两次不同等压面上的气压、离地高度和干球温度等，其中离地高度3000m以内的有效数据层数应不少于10层。</li>
</ul>
<p>注：气象资料的时间为连续一个基准年</p>
<h4 id="7模型参数">7、模型参数</h4>
<ul>
<li>地表参数：从项目正北方向开始顺时针根据项目周边土地利用类型对项目周 边进行分区（可参考项目所在地的土地利用规划），再对每个分区设置，地表参数频率、土地利用类型、干湿情况。如果周边土地利用类型单一，则不需要分区。</li>
<li>SO2化学衰变：衰减系数（S-1）=0.693/半衰期（S）。AERMOD模型中缺省设置的SO2指数衰减的半衰期为14400s。</li>
<li>氮氧化物转化：需有效环境中O3浓度、烟道内NO2/NOx比率等参数。（在 能准确获得烟道内NO2/NOx比率时可以用模型内置的转化机制来考虑氮氧化物的转化）</li>
<li>沉积计算：湿沉降需要地面气象数据中包含降雨量数据。</li>
<li>干沉降需要在控制选项和污染源设置中输入相关沉积参数。</li>
</ul>
<h4 id="8预测基准年的选择">8、预测基准年的选择</h4>
<p>选择近3年中环境空气质量现状、气象资料数据相对完整且数据可靠的一个完整日历年作为基准年。</p>
<h4 id="9区域削减源">9、区域削减源</h4>
<p>在进行区域削减调查时要明确削减源的拟替代时间（拟替代时间要在所选取的预测基准年之后），区域削减源相关参数整理可以参照新建源，以保证削减源可以进行模型扩散模拟。</p>
<h2 id="大气一级预测注意事项">大气一级预测注意事项</h2>
<h4 id="1污染源源强整理单位问题">1、污染源源强整理单位问题</h4>
<ul>
<li>烟气流速：单位最好转换为m/s，更加直观看出流速是否合理。</li>
<li>温度：环安在线平台大气估算模式单位为℃及K，进一步估算模式Aermod只有K，预测时注意单位与数值是否对应。</li>
<li>排放速率：常用单位为kg/h与g/s，预测时注意单位与数值是否对应。</li>
</ul>
<h4 id="2报告中源强表格格式问题">2、报告中源强表格格式问题</h4>
<ul>
<li>导则要求的坐标为UTM坐标或者经纬度，适用于点源、面源、体源、线源。</li>
<li>注意单位要与导则格式一致最好</li>
</ul>
<h4 id="3预测范围">3、预测范围</h4>
<ul>
<li>预测范围应覆盖评价范围，导则推荐，Aermod网格间距可以采用等间距或近密远疏法进行设置，距离源中心5km的网格间距不超过100m，5~15km的网格间距不超过250m，大于15km的网格间距不超过500m。</li>
</ul>
<h4 id="4环境空气保护目标">4、环境空气保护目标</h4>
<ul>
<li>导则中未给出环境空气保护目标的xy应用什么坐标，单位是m,这里我们用的是相对坐标（相对于模型预测范围中心）。</li>
<li>保护对象：评价范围内一类区的自然保护区、风景名胜区和其他特殊保护的区域；二类区的村庄、居住区、医院、学校等。</li>
</ul>
<h4 id="5环境空气现状达标分析">5、环境空气现状达标分析</h4>
<ul>
<li>首先搜集有无项目所在地官方的环境质量公报，若没有官方环境质量公报，通过评价基准年监测点常规监测数据进行判断。（年均质量浓度和相应百分位数日均浓度均达标，才能判断为达标区）</li>
<li>如果质量公报数据只有年均值，没有日均值，则需要使用逐日空气质量数据进行补充，并注明数据来源；两个数据来源在同一项上不能同时存在，优先采用公报数据。例如：</li>
</ul>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/%E5%BE%AE%E4%BF%A1%E5%9B%BE%E7%89%87_20200826124143.jpg" alt=""></p>]]></content>
        <author>
            <name>杨工</name>
            <email>sjzhakj@163.com</email>
        </author>
        <category label="aermod" term="aermod"/>
    </entry>
    <entry>
        <title type="html"><![CDATA[帕斯奎尔稳定度计算方法]]></title>
        <id>https://guide.ihamodel.com/blog/pasquill-stability-class-calculation</id>
        <link href="https://guide.ihamodel.com/blog/pasquill-stability-class-calculation"/>
        <updated>2026-01-29T00:00:00.000Z</updated>
        <summary type="html"><![CDATA[对比93导则修订算法与原版帕斯奎尔稳定度分类方法，并说明统计分级处理方式。]]></summary>
        <content type="html"><![CDATA[<p>帕斯奎尔稳定度软件有两种算法，一种是93大气导则算法，一种是原版的帕斯奎尔稳定度算法。</p>
<h2 id="1193导则修订算法">1.1、93导则修订算法</h2>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/%E8%A1%A8B1.jpg" alt=""></p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/%E8%A1%A8B2.jpg" alt=""></p>
<h2 id="12原版帕斯奎尔稳定度分类">1.2、原版帕斯奎尔稳定度分类</h2>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/%E7%A8%B3%E5%AE%9A%E5%BA%A62.jpg" alt=""></p>
<p>根据修正的太阳辐射强度R，计算辐射强度</p>
<ul>
<li>strong (&gt; 700 W m−2)</li>
<li>moderate (350-700 W m−2)</li>
<li>slight (&lt; 350 W m−2)</li>
<li>夜间（太阳辐射为负值）</li>
</ul>
<h2 id="13统计分析结果">1.3统计分析结果</h2>
<p>在进行稳定度统计时，有A-B，B-C，C-D这三个半稳定度分级，而在SLAB模型和AFTOX模型中不存在该稳定度，因此软件有两个选项：</p>
<ul>
<li>向不稳定方向提半级：此时A-B取A，B-C取B，C-D取C</li>
<li>向稳定方向提半级：此时A-B取B，B-C取C，C-D取D</li>
</ul>
<p>用户可根据区域的土地利用类型提级，如果位于城区区域则大气趋向于不稳定，在农村区域大气趋向于稳定。</p>]]></content>
        <author>
            <name>杨工</name>
            <email>sjzhakj@163.com</email>
        </author>
        <category label="aermod" term="aermod"/>
    </entry>
    <entry>
        <title type="html"><![CDATA[CALPUFF并行版若干CPU测试]]></title>
        <id>https://guide.ihamodel.com/blog/calpuff-parallel-cpu-benchmarks</id>
        <link href="https://guide.ihamodel.com/blog/calpuff-parallel-cpu-benchmarks"/>
        <updated>2026-01-28T00:00:00.000Z</updated>
        <summary type="html"><![CDATA[记录CALPUFF并行版在不同CPU平台下的运行速度测试结果。]]></summary>
        <content type="html"><![CDATA[<p>CALPUFF并行版支持并行计算，在MPI环境下支持多个CPU或者一个CPU多个核心进行计算。</p>
<p>软件的程序经过了Intel fortran的优化，运行速度相比原版快很多，本次测试单核心为intel优化的程序的运行速度。</p>
<p>测试平台1-AMD Ryzen 1700</p>
<p>CPU： AMD Ryzen 1700 @3.0GHz内存：金士顿 DDR4 8Gx2 @ 2400</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/1700-2.png" alt=""></p>
<p>测试平台2-AMD Ryzen2600</p>
<p>CPU： AMD Ryzen 2600 @3.6GHz内存：芝奇DDR4 8Gx2 @ 2666</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/2600-2.png" alt=""></p>
<p>测试平台3-i5-8400</p>
<p>CPU： Intel i5-8400 @2.8GHz内存：金士顿DDR4 8Gx2 @2666</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/8400-1.png" alt=""></p>
<p>测试平台4-i7-8700</p>
<p>CPU： Intel i7-8700 @3.2GHz内存：威刚XMP DDR4 8Gx2 @2666</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/8700-1.png" alt=""></p>
<p>测试平台5 -志强2673 V3</p>
<p>CPU：志强2673 V3 X2 @2.4GHz内存：三星 DDR4-ECC 16Gx4 @2133</p>
<p>1、各平台所有核心满载时的成绩如下，运行时间越短代表运行速度越快，其中双路E5-2673最快，i7-8700次之，i5-8400最慢，ryzen 2600x次慢。</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/%E6%88%90%E7%BB%A91.png" alt=""></p>
<p>2、各平台单线程运行速度如下，其中i7-8700运行最快，i5-8400次之，双路E5-2673最慢，AMD 1700次慢。</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/%E6%88%90%E7%BB%A92.png" alt=""></p>
<p>3、各平台加速比</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/1700-3-1.png" alt=""></p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/2600-3.png" alt=""></p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/8400-2.png" alt=""></p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/8700-2.png" alt=""></p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/2673-1.png" alt=""></p>
<p>总结：</p>
<p>桌面CPU中现在以i7 8700最佳，单核性能最高，在6c/12t的加持下，并行性能不错，在中等计算量（60个源，1万个点）下计算一年需要近9个小时，勉强可以接受。E5-2673 v3这个老平台，受限于较低的cpu频率@2.4HGhz，单核性能不高，但核心数多，运行速度最快，运行一年需要6个小时。</p>
<p>对于更高的计算量，请购买更高的平台。比如intel i9-9980xe，18核36线程@4.4GHz，应该可以满足要求。</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/9900.png" alt=""></p>
<p>或者AMD的 线程撕裂者 <a href="mailto:2990wx@3.0GHz">2990wx@3.0GHz</a> 32核64线程睿频4.2GHz。</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/2990wx-1024x421.png" alt=""></p>]]></content>
        <author>
            <name>杨工</name>
            <email>sjzhakj@163.com</email>
        </author>
        <category label="calpuff" term="calpuff"/>
    </entry>
    <entry>
        <title type="html"><![CDATA[土壤环境评价中的大气沉降影响预测问题]]></title>
        <id>https://guide.ihamodel.com/blog/soil-eia-atmospheric-deposition-forecast</id>
        <link href="https://guide.ihamodel.com/blog/soil-eia-atmospheric-deposition-forecast"/>
        <updated>2026-01-28T00:00:00.000Z</updated>
        <summary type="html"><![CDATA[结合HJ 964-2018附录E与案例，梳理土壤环境评价中大气沉降影响预测的关键参数与实现路径。]]></summary>
        <content type="html"><![CDATA[<p>土壤环境评价中涉及大气沉降影响的预测问题，在《环境影响评价技术导则-土壤环境》（HJ 964-2018）附录E中推荐了预测方法。根据导则推荐的方法，我们具体需要做哪些工作？有哪些技术难点？环安土壤环境影响评价系统能带来哪些实用性的功能？这篇文章我们用实际案例来具体分析一下。</p>
<p>首先看一下导则附录E推荐的预测公式：</p>
<p>ΔS=n(Is-Ls-Rs)/(ρb×A×D)</p>
<p>式中：ΔS—单位质量表层土壤中某种物质的增量，g/kg；</p>
<p>Is—预测评价范围内单位年份表层土壤中某种物质的输入量，g；</p>
<p>Ls—预测评价范围内单位年份表层土壤中某种物质经淋溶排出量，g；</p>
<p>Rs—预测评价范围内单位年份表层土壤中某种物质经径流排出量，g；</p>
<p>ρb—表层土壤容重，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi><mi>g</mi><mi mathvariant="normal">/</mi><msup><mi>m</mi><mn>3</mn></msup></mrow><annotation encoding="application/x-tex">kg/m^3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em"></span><span class="mord mathnormal" style="margin-right:0.03148em">k</span><span class="mord mathnormal" style="margin-right:0.03588em">g</span><span class="mord">/</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span></span></span></span>；</p>
<p>A—预测评价范围，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>m</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">m^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141em"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>；</p>
<p>D—表层土壤深度，一般取0.2m，可根据实际情况适当调整；</p>
<p>n—持续年份，a。</p>
<p>这些参数中，物质输出量Ls和Rs根据导则推荐可以不考虑，ρb&nbsp;为现状监测测定，D导则有推荐值，n根据项目实际情况可得。因此关键点便在于如何获取物质输入量和预测评价范围，得到这两个参数问题便迎刃而解。</p>
<p>Is物质输入量实际属于大气沉降预测问题，在用AERMOD软件做大气环境影响预测时可计算得出，具体做法可参考《AERMOD沉积参数设置说明及相关参数取值参考》，在此文中我们不做过多阐述。</p>
<p>A预测评价范围的计算，可以用ArcGIS绘制并计算得出，或者使用地图软件绘制、测量并计算得出。无论使用哪种方法，这项工作都比较繁琐。针对这一问题，环安土壤环境影响评价系统给出了一个轻松便捷的解决方法，我们下面用实际案例来演示一下。</p>
<p>例：某化工企业年产1000&nbsp;吨对氯邻硝基乙酰乙酰苯胺技改项目，预计运营50年。项目占地面积为1.57公顷，评价等级为二级，评价范围为占地范围内及占地范围外0.2km范围内。污染土壤的途径主要为废气污染物沉降至地面，导致土壤环境污染。根据土壤理化性质调查和现状监测，项目所在地土壤容重为1210<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi><mi>g</mi><mi mathvariant="normal">/</mi><msup><mi>m</mi><mn>3</mn></msup></mrow><annotation encoding="application/x-tex">kg/m^3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em"></span><span class="mord mathnormal" style="margin-right:0.03148em">k</span><span class="mord mathnormal" style="margin-right:0.03588em">g</span><span class="mord">/</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span></span></span></span>，甲苯现状值为0.000002g/kg。废气污染物沉降至地面的源强见下表。</p>
<p>项目土壤环境影响源及影响因子识别表</p>
<p>针对以上案例，软件具体操作如下：</p>
<p>第一步：绘制厂界，输入项目信息。</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/%E5%8E%82%E7%95%8C%E5%92%8C%E4%BF%A1%E6%81%AF-1536x728.gif" alt=""></p>
<p>第二步：设置敏感目标，软件自动计算评价等级并生成评价范围。</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/image-72.png" alt=""></p>
<p>第三步：选择要预测的监测因子。</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/image-73.png" alt=""></p>
<p>第四步：设置监测点并输入现状值。</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/image-74.png" alt=""></p>
<p>第五步：输入参数，计算沉降影响预测值。</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/image-75.png" alt=""></p>
<p>在此过程中，软件会自动计算评价范围的面积（A），并应用于计算沉降影响预测中，无需用户手动绘制评价范围并测量计算面积，省时省力。</p>]]></content>
        <author>
            <name>杨工</name>
            <email>sjzhakj@163.com</email>
        </author>
        <category label="水文地质" term="水文地质"/>
    </entry>
    <entry>
        <title type="html"><![CDATA[最完整的（截止到2009年）全球30米分辨率地形数据（ASTER GDEM）]]></title>
        <id>https://guide.ihamodel.com/blog/aster-gdem-30m-dem-data</id>
        <link href="https://guide.ihamodel.com/blog/aster-gdem-30m-dem-data"/>
        <updated>2026-01-28T00:00:00.000Z</updated>
        <summary type="html"><![CDATA[介绍ASTER GDEM 30m全球地形数据的来源、覆盖范围与获取方式。]]></summary>
        <content type="html"><![CDATA[<p>简介：</p>
<p>2009 年 6 月 30 日，美国航天局（NASA）与日本经济产业省（METI）共 同推出了最新的地球电子地形数据 ASTER GDEM（先进星载热发射和反射辐射 仪全球数字高程模型），该数据是根据 NASA 的新一代对地观测卫星 TERRA 的详尽观测结果制作完成的。这一全新地球数字高程模型包含了先进星载热发射 和反辐射计（ASTER）搜集的 130 万个立体图像。 ASTER 测绘数据覆盖范围为北纬 83°到南纬 83°之间的所有陆地区域，比 以往任何地形图都要广得多，达到了地球陆地表面的 99%。此前，最完整的地 形数据是由 NASA 的航天飞机雷达地形测绘任务（SRTM）提供的，此项任务对 位于北纬 60°和南纬 57°间地球 80%的陆地进行了测绘。</p>
<p>（目前，SRTM 90 米分辨率地形数据可以通过中国科学院计算机网络信息 中心国际科学数据服务平台免费获得（<a href="http://srtm.datamirror.csdb.cn/%EF%BC%89%EF%BC%89">http://srtm.datamirror.csdb.cn/））</a> 备注：现在已不可下载。</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/aster-1024x569.jpg" alt=""></p>
<p>生产流程 ：</p>
<p>ASTER GDEM 是采用全自动化的方法对 150 万景的 ASTER存档数据进行 处理生成的，其中包括通过立体相关生成的 1264118 个基于独立场景的 ASTER DEM 数据，再经过去云处理，除去残余的异常值，取平均值，并以此作为 ASTER GDEM 对应区域的最后像素值。纠正剩余的异常数据，再按 1°×1°分片，生 成全球 ASTER GDEM 数据。 基本流程如下：</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/aster2-1024x566.jpg" alt=""></p>
<p>数据获得</p>
<p>目前，ASTER GDEM 数据可以在网上免费获取。用户通过日本的 ERSDAC （Earth Remote Sensing Data Analysis Center，地球遥感数据分析中心） （<a href="http://www.gdem.aster.ersdac.or.xn--jp)-rk6ei12cjw5b/">http://www.gdem.aster.ersdac.or.jp）或美国</a> NASA 的 LP DAAC（Land Processes Distributed Active Archive Center，美国陆地过程分布式活动档案中 心）（<a href="http://www.gdem.aster.ersdac.or.jp/index.jsp%EF%BC%89%E5%85%8D%E8%B4%B9%E4%B8%8B%E8%BD%BD%E8%BF%99%E4%BA%9B%E6%95%B0%E6%8D%AE%E3%80%82%E5%BD%93%E7%84%B6%EF%BC%8C">http://www.gdem.aster.ersdac.or.jp/index.jsp）免费下载这些数据。当然，</a> 拥有数据下载权限之前都需要进行相关网站的用户注册和所需数据的申请。</p>
<p>更多信息请下载以下PDF文件</p>
<p>ASTER-GDEM-1下载</p>
<p>现在ASTER已经更新到V3版本，可从以下网站下载&nbsp;Earthdata Search (nasa.gov)</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/earthdata-1024x610.jpg" alt=""></p>
<p>更多关于ASGER DEMV3的信息，请阅读ASTGTM_User_Guide_V3下载</p>]]></content>
        <author>
            <name>杨工</name>
            <email>sjzhakj@163.com</email>
        </author>
        <category label="aermod" term="aermod"/>
    </entry>
    <entry>
        <title type="html"><![CDATA[如何为AERMOD/AERSCREEN模型处理地形数据]]></title>
        <id>https://guide.ihamodel.com/blog/guide-processing-terrain-data-aermod-aerscreen-models</id>
        <link href="https://guide.ihamodel.com/blog/guide-processing-terrain-data-aermod-aerscreen-models"/>
        <updated>2025-11-10T00:00:00.000Z</updated>
        <summary type="html"><![CDATA[AERSCREEN使用地形是通过调取AERMAP地形预处理程序进行的，因此AERSCREEN对地形数据的要求和AERMAP是一样的。系统中会自动获取污染源为中心点，半径25km的地形数据，如果用户需要手动处理地形数据，可按以下步骤处理。]]></summary>
        <content type="html"><![CDATA[<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/%E5%9C%B0%E5%BD%A24.jpg" alt="img"></p>
<p>AERSCREEN使用地形是通过调取AERMAP地形预处理程序进行的，因此AERSCREEN对地形数据的要求和AERMAP是一样的。</p>
<p>系统中会自动获取污染源为中心点，半径25km的地形数据，如果用户需要手动处理地形数据，可按以下步骤处理。</p>
<p>1.下载地形数据</p>
<h2 id=""></h2>
<h3 id="11下载网站">1.1下载网站</h3>
<p>下载这个数据，有很多网址，这里提供的为：</p>
<ul>
<li><a href="http://srtm.csi.cgiar.org/SELECTION/inputCoord.asp">http://srtm.csi.cgiar.org/SELECTION/inputCoord.asp</a></li>
</ul>
<h3 id="12下载srtm-90数据">1.2下载SRTM 90数据</h3>
<p><strong>（1</strong>**）格式说明**</p>
<p>首先要注意，可以选择GeoTiff 和 ArcInfo ASCII 两种格式。这两种格式arcgis（arcinfo、arcview）和Global mapper都可以打开，但surfer不能打开。问题的关键是下一步。</p>
<ul>
<li>选择服务器，随便选择一个即可，在数据下载缓慢时建议更换服务器</li>
<li>三种选择下载数据区域的方式，这里选择Multiple Selection</li>
<li>选择数据区域，鼠标选取即可</li>
<li>蓝色框框-Click here to Begin Search</li>
</ul>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/%E5%9C%B0%E5%BD%A21.jpg" alt="img"> <img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/%E5%9C%B0%E5%BD%A22.jpg" alt="img"></p>
<p><strong>（2</strong>**）格式选择**</p>
<p>网站上的数据有两种不同的格式，一个是带mask的，还有一个不是：如下图。注意，前两个下载地址下载的文件格式可用arcinfo 等软件进行处理。红色框内是带mask的，蓝色框内是不带mask的。可用多种下载工具下载数据.</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/%E5%9C%B0%E5%BD%A23-1024x335.jpg" alt="img"></p>
<p><strong>（3</strong>**）命名规范**</p>
<p>全国的SRTM 90数据还是比较大的，如果不是做全国项目的话，大多地形数据是用不到的，可以只下载包含预测区域的地形数据。</p>
<p>数据说明：</p>
<ul>
<li>从第一节中网站下载的数据，一个文件包含5o×5o的区域。</li>
<li>文件命名格式tif，srtm表示数据来源，54_03表示数据块为经度方向第53块，纬度方向为第三块，如下图示。</li>
<li>根据下图可以下载对应数据，解压缩放到aermodsystem的相应目录下面</li>
</ul>
<p>注：每个颜色块代表一个数据文件，底图为中国行政区划图，四周的编号，可以组合起来可以查文件所包含的经纬度范围。</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/%E5%9C%B0%E5%BD%A24-1024x728.jpg" alt="img"></p>
<h2 id="2地形数据处理">2.地形数据处理</h2>
<p>（1）数据下载后解压缩，解压缩后为tif格式。用global mapper打开。打开时有询问，选yes to all</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/global1-1024x632.png" alt="img"></p>
<p>（2）打开后如下图：</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/global2-1024x634.png" alt="img"></p>
<p>（3）打开菜单file中的导出dem格式对话框，见下图。</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/global3-1024x629.png" alt="img"></p>
<p>选择DEM格式</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/global5.png" alt="img"></p>
<p>（4）根据污染源坐标，设置导出的DEM的经纬度范围，范围50km。</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/global5-1.png" alt="img"></p>
<p>（5）将数据放置到AERSCREEN文件夹下， 并在demlist.txt中指定格式为DEM，并指定文件的路径。</p>
<blockquote>
<p>DEM :
—————————————————-
NADGRIDS: .<br>
tif\terrain.dem</p>
</blockquote>
<p>（6）根据导则要求需要采用NAD83的基准面，用户也可以在gl中设定。</p>]]></content>
        <author>
            <name>杨工</name>
            <email>sjzhakj@163.com</email>
        </author>
        <category label="aerscreen" term="aerscreen"/>
        <category label="aermod" term="aermod"/>
    </entry>
    <entry>
        <title type="html"><![CDATA[声功率级与声压级之间的关系]]></title>
        <id>https://guide.ihamodel.com/blog/relationship-between-lw-and-lp</id>
        <link href="https://guide.ihamodel.com/blog/relationship-between-lw-and-lp"/>
        <updated>2025-11-06T00:00:00.000Z</updated>
        <summary type="html"><![CDATA[AERSCREEN输入文件编写规则。]]></summary>
        <content type="html"><![CDATA[<p><strong>在靠近大型面声源（如墙面、大型机器表面）的位置，单位面积的声功率级（本质上是声强级）与声压级之间在数值上近似相等。</strong></p>
<p>以下是具体的推导过程。</p>
<h2 id="1-单位面积的声功率级l_w-声强级l_i">1. 单位面积的声功率级（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mi>W</mi></msub></mrow><annotation encoding="application/x-tex">L_W</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em">W</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span>）= 声强级（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mi>I</mi></msub></mrow><annotation encoding="application/x-tex">L_I</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span>）</h2>
<p>声功率是声源在单位时间内辐射的总声能量（单位：瓦特 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">W</mi></mrow><annotation encoding="application/x-tex">\mathrm{W}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathrm" style="margin-right:0.01389em">W</span></span></span></span>）。<br>
单位面积的声功率就是声强 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi><mtext>&nbsp;</mtext><mo stretchy="false">(</mo><mrow><mi mathvariant="normal">W</mi><mi mathvariant="normal">/</mi><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup></mrow><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">I\ (\mathrm{W/m^2})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em"></span><span class="mord mathnormal" style="margin-right:0.07847em">I</span><span class="mspace">&nbsp;</span><span class="mopen">(</span><span class="mord"><span class="mord mathrm">W/</span><span class="mord"><span class="mord mathrm">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span>，表示单位时间内通过垂直于声波传播方向的单位面积的声能量。</p>
<p>声功率与声强之间的关系为：</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>W</mi><mo>=</mo><mi>I</mi><mo>×</mo><mi>S</mi></mrow><annotation encoding="application/x-tex">W = I \times S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.13889em">W</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.7667em;vertical-align:-0.0833em"></span><span class="mord mathnormal" style="margin-right:0.07847em">I</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.05764em">S</span></span></span></span></span>
<p>其中，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>W</mi></mrow><annotation encoding="application/x-tex">W</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.13889em">W</span></span></span></span> 是声功率（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">W</mi></mrow><annotation encoding="application/x-tex">\mathrm{W}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathrm" style="margin-right:0.01389em">W</span></span></span></span>），<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi></mrow><annotation encoding="application/x-tex">I</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span></span></span> 是声强（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">W</mi><mi mathvariant="normal">/</mi><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">\mathrm{W/m^2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathrm">W/</span><span class="mord"><span class="mord mathrm">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span>），<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi></mrow><annotation encoding="application/x-tex">S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.05764em">S</span></span></span></span> 是透声面积（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">\mathrm{m^2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141em"></span><span class="mord"><span class="mord mathrm">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span>）。</p>
<p>根据声功率级计算公式，可得<strong>总声功率级</strong> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mrow><mi>W</mi><mo separator="true">,</mo><mtext>tot</mtext></mrow></msub></mrow><annotation encoding="application/x-tex">L_{W,\text{tot}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em">W</span><span class="mpunct mtight">,</span><span class="mord text mtight"><span class="mord mtight">tot</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span></span></span></span> 与声强级 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mi>I</mi></msub></mrow><annotation encoding="application/x-tex">L_I</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span> 的关系：</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>L</mi><mrow><mi>W</mi><mo separator="true">,</mo><mtext>tot</mtext></mrow></msub><mo>=</mo><msub><mi>L</mi><mi>I</mi></msub><mo>+</mo><mn>10</mn><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mn>10</mn></msub><mi>S</mi></mrow><annotation encoding="application/x-tex">L_{W,\text{tot}} = L_I + 10\log_{10} S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em">W</span><span class="mpunct mtight">,</span><span class="mord text mtight"><span class="mord mtight">tot</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.9386em;vertical-align:-0.2441em"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.207em"><span style="top:-2.4559em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal" style="margin-right:0.05764em">S</span></span></span></span></span>
<p>等价地：</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>L</mi><mi>I</mi></msub><mo>=</mo><msub><mi>L</mi><mrow><mi>W</mi><mo separator="true">,</mo><mtext>tot</mtext></mrow></msub><mo>−</mo><mn>10</mn><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mn>10</mn></msub><mi>S</mi></mrow><annotation encoding="application/x-tex">L_I = L_{W,\text{tot}} - 10\log_{10} S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em">W</span><span class="mpunct mtight">,</span><span class="mord text mtight"><span class="mord mtight">tot</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.9386em;vertical-align:-0.2441em"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.207em"><span style="top:-2.4559em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal" style="margin-right:0.05764em">S</span></span></span></span></span>
<p>因此，<strong>单位面积的声功率级</strong>（即面元处的 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mi>W</mi></msub></mrow><annotation encoding="application/x-tex">L_W</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em">W</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span>）与该处的声强级 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mi>I</mi></msub></mrow><annotation encoding="application/x-tex">L_I</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span> 数值相同：</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>L</mi><mi>W</mi></msub><mtext>&nbsp;</mtext><mo stretchy="false">(</mo><mtext>单位面积</mtext><mo stretchy="false">)</mo><mo>=</mo><msub><mi>L</mi><mi>I</mi></msub></mrow><annotation encoding="application/x-tex">L_W\ (\text{单位面积}) = L_I</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em">W</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace">&nbsp;</span><span class="mopen">(</span><span class="mord text"><span class="mord cjk_fallback">单位面积</span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>
<blockquote>
<p>注：<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mrow><mi>W</mi><mo separator="true">,</mo><mtext>tot</mtext></mrow></msub></mrow><annotation encoding="application/x-tex">L_{W,\text{tot}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em">W</span><span class="mpunct mtight">,</span><span class="mord text mtight"><span class="mord mtight">tot</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span></span></span></span> 是对整个辐射面的积分结果，<strong>不等于</strong>任一局部点的 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mi>I</mi></msub></mrow><annotation encoding="application/x-tex">L_I</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span>；只有将“每个面元上的声强”换算成“该面元的单位面积声功率级”时，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mi>W</mi></msub><mo stretchy="false">(</mo><mtext>单位面积</mtext><mo stretchy="false">)</mo><mo>≡</mo><msub><mi>L</mi><mi>I</mi></msub></mrow><annotation encoding="application/x-tex">L_W(\text{单位面积})\equiv L_I</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em">W</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord text"><span class="mord cjk_fallback">单位面积</span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">≡</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span> 才成立。</p>
</blockquote>
<hr>
<h2 id="2-声压级l_p">2. 声压级（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">L_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span></span></span></span>）</h2>
<p>声压级定义为：</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>L</mi><mi>p</mi></msub><mo>=</mo><mn>20</mn><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mn>10</mn></msub><mtext> ⁣</mtext><mrow><mo fence="true">(</mo><mfrac><mi>p</mi><msub><mi>p</mi><mn>0</mn></msub></mfrac><mo fence="true">)</mo></mrow><mtext>&nbsp;</mtext><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></mrow></mrow><annotation encoding="application/x-tex">L_p = 20\log_{10}\!\left(\frac{p}{p_0}\right)\ \mathrm{dB}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:2.4em;vertical-align:-0.95em"></span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.207em"><span style="top:-2.4559em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:-0.1667em"></span><span class="mspace" style="margin-right:0.1667em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1076em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathnormal">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="mspace">&nbsp;</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord"><span class="mord mathrm">dB</span></span></span></span></span></span>
<p>其中，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi></mrow><annotation encoding="application/x-tex">p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em"></span><span class="mord mathnormal">p</span></span></span></span> 为有效声压，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mn>0</mn></msub><mo>=</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup><mtext>&nbsp;</mtext><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">a</mi></mrow></mrow><annotation encoding="application/x-tex">p_0 = 2\times10^{-5}\ \mathrm{Pa}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.8141em"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">5</span></span></span></span></span></span></span></span></span><span class="mspace">&nbsp;</span><span class="mord"><span class="mord mathrm">Pa</span></span></span></span></span> 为空气中常用的基准声压。</p>
<hr>
<h2 id="3-关键关系声强-i-与-声压-p">3. 关键关系：声强 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi></mrow><annotation encoding="application/x-tex">I</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span></span></span> 与 声压 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi></mrow><annotation encoding="application/x-tex">p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em"></span><span class="mord mathnormal">p</span></span></span></span></h2>
<p>在自由声场中，对于行波（远离反射面的传播波），有：</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>I</mi><mo>=</mo><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mi>ρ</mi><mtext> </mtext><mi>c</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">I = \frac{p^2}{\rho\,c}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.07847em">I</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:2.3715em;vertical-align:-0.8804em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.4911em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathnormal">ρ</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">c</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>
<p>其中，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ρ</mi></mrow><annotation encoding="application/x-tex">\rho</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em"></span><span class="mord mathnormal">ρ</span></span></span></span> 是介质密度（空气约 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1.2</mn><mtext>&nbsp;</mtext><mrow><mi mathvariant="normal">k</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">/</mi><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup></mrow></mrow><annotation encoding="application/x-tex">1.2\ \mathrm{kg/m^3}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em"></span><span class="mord">1.2</span><span class="mspace">&nbsp;</span><span class="mord"><span class="mord mathrm">kg/</span><span class="mord"><span class="mord mathrm">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">3</span></span></span></span></span></span></span></span></span></span></span></span>），<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>c</mi></mrow><annotation encoding="application/x-tex">c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">c</span></span></span></span> 是声速（空气约 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>343</mn><mtext>&nbsp;</mtext><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">/</mi><mi mathvariant="normal">s</mi></mrow></mrow><annotation encoding="application/x-tex">343\ \mathrm{m/s}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">343</span><span class="mspace">&nbsp;</span><span class="mord"><span class="mord mathrm">m/s</span></span></span></span></span>），<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ρ</mi><mi>c</mi></mrow><annotation encoding="application/x-tex">\rho c</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em"></span><span class="mord mathnormal">ρ</span><span class="mord mathnormal">c</span></span></span></span> 为特性阻抗（空气约 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>415</mn><mtext>&nbsp;</mtext><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">y</mi><mi mathvariant="normal">l</mi></mrow><mo>=</mo><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">a</mi><mo>⋅</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">/</mi><mi mathvariant="normal">m</mi></mrow></mrow><annotation encoding="application/x-tex">415\ \mathrm{Rayl}=\mathrm{Pa\cdot s/m}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em"></span><span class="mord">415</span><span class="mspace">&nbsp;</span><span class="mord"><span class="mord mathrm">Rayl</span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathrm">Pa</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mord mathrm">s/m</span></span></span></span></span>）。</p>
<hr>
<h2 id="4-靠近面声源的特殊情况">4. 靠近面声源的特殊情况</h2>
<p>当测量点非常靠近一个大型、均匀辐射的面声源（远大于波长）时，声波在该点附近近似为平面波。<br>
平面波同样满足：</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>I</mi><mo>=</mo><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mi>ρ</mi><mtext> </mtext><mi>c</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">I = \frac{p^2}{\rho\,c}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.07847em">I</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:2.3715em;vertical-align:-0.8804em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.4911em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathnormal">ρ</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">c</span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span>
<hr>
<h2 id="5-推导声强级l_i与声压级l_p的关系">5. 推导声强级（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mi>I</mi></msub></mrow><annotation encoding="application/x-tex">L_I</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span>）与声压级（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">L_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span></span></span></span>）的关系</h2>
<p>由定义：</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>L</mi><mi>I</mi></msub><mo>=</mo><mn>10</mn><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mn>10</mn></msub><mtext> ⁣</mtext><mrow><mo fence="true">(</mo><mfrac><mi>I</mi><msub><mi>I</mi><mn>0</mn></msub></mfrac><mo fence="true">)</mo></mrow><mo>=</mo><mn>10</mn><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mn>10</mn></msub><mtext> ⁣</mtext><mrow><mo fence="true">(</mo><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mi>ρ</mi><mtext> </mtext><mi>c</mi><mtext> </mtext><msub><mi>I</mi><mn>0</mn></msub></mrow></mfrac><mo fence="true">)</mo></mrow><mo>=</mo><mn>20</mn><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mn>10</mn></msub><mi>p</mi><mo>−</mo><mn>10</mn><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mn>10</mn></msub><mo stretchy="false">(</mo><mi>ρ</mi><mtext> </mtext><mi>c</mi><mo stretchy="false">)</mo><mo>−</mo><mn>10</mn><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mn>10</mn></msub><msub><mi>I</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">L_I = 10\log_{10}\!\left(\frac{I}{I_0}\right)
= 10\log_{10}\!\left(\frac{p^2}{\rho\,c\,I_0}\right)
= 20\log_{10} p - 10\log_{10}(\rho\,c) - 10\log_{10} I_0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:2.4em;vertical-align:-0.95em"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.207em"><span style="top:-2.4559em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:-0.1667em"></span><span class="mspace" style="margin-right:0.1667em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3603em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:-0.0785em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em">I</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.836em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:2.4411em;vertical-align:-0.95em"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.207em"><span style="top:-2.4559em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:-0.1667em"></span><span class="mspace" style="margin-right:0.1667em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.4911em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathnormal">ρ</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">c</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:-0.0785em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.9386em;vertical-align:-0.2441em"></span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.207em"><span style="top:-2.4559em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.207em"><span style="top:-2.4559em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">ρ</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">c</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.9386em;vertical-align:-0.2441em"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.207em"><span style="top:-2.4559em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:-0.0785em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>
<p>而：</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>L</mi><mi>p</mi></msub><mo>=</mo><mn>20</mn><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mn>10</mn></msub><mtext> ⁣</mtext><mrow><mo fence="true">(</mo><mfrac><mi>p</mi><msub><mi>p</mi><mn>0</mn></msub></mfrac><mo fence="true">)</mo></mrow><mo>=</mo><mn>20</mn><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mn>10</mn></msub><mi>p</mi><mo>−</mo><mn>20</mn><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mn>10</mn></msub><msub><mi>p</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">L_p = 20\log_{10}\!\left(\frac{p}{p_0}\right)
= 20\log_{10} p - 20\log_{10} p_0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:2.4em;vertical-align:-0.95em"></span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.207em"><span style="top:-2.4559em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:-0.1667em"></span><span class="mspace" style="margin-right:0.1667em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1076em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathnormal">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.9386em;vertical-align:-0.2441em"></span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.207em"><span style="top:-2.4559em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.9386em;vertical-align:-0.2441em"></span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.207em"><span style="top:-2.4559em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span></span>
<p>联立得：</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>L</mi><mi>I</mi></msub><mo>=</mo><msub><mi>L</mi><mi>p</mi></msub><mo>+</mo><mn>10</mn><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mn>10</mn></msub><mtext> ⁣</mtext><mrow><mo fence="true">(</mo><mfrac><msubsup><mi>p</mi><mn>0</mn><mn>2</mn></msubsup><mrow><mi>ρ</mi><mtext> </mtext><mi>c</mi><mtext> </mtext><msub><mi>I</mi><mn>0</mn></msub></mrow></mfrac><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">L_I = L_p + 10\log_{10}\!\left(\frac{p_0^2}{\rho\,c\,I_0}\right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:2.4411em;vertical-align:-0.95em"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.207em"><span style="top:-2.4559em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:-0.1667em"></span><span class="mspace" style="margin-right:0.1667em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.4911em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathnormal">ρ</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">c</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:-0.0785em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-2.4519em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2481em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em"><span class="delimsizing size3">)</span></span></span></span></span></span></span>
<p>在空气中，若取 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mn>0</mn></msub><mo>=</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup><mtext>&nbsp;</mtext><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">a</mi></mrow></mrow><annotation encoding="application/x-tex">p_0 = 2\times10^{-5}\ \mathrm{Pa}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.8141em"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">5</span></span></span></span></span></span></span></span></span><span class="mspace">&nbsp;</span><span class="mord"><span class="mord mathrm">Pa</span></span></span></span></span>、<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>I</mi><mn>0</mn></msub><mo>=</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>12</mn></mrow></msup><mtext>&nbsp;</mtext><mrow><mi mathvariant="normal">W</mi><mi mathvariant="normal">/</mi><msup><mi mathvariant="normal">m</mi><mn>2</mn></msup></mrow></mrow><annotation encoding="application/x-tex">I_0 = 10^{-12}\ \mathrm{W/m^2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:-0.0785em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">12</span></span></span></span></span></span></span></span></span><span class="mspace">&nbsp;</span><span class="mord"><span class="mord mathrm">W/</span><span class="mord"><span class="mord mathrm">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathrm mtight">2</span></span></span></span></span></span></span></span></span></span></span></span>，且标准条件下 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ρ</mi><mi>c</mi><mo>≈</mo><mn>400</mn><mtext>–</mtext><mn>415</mn><mtext>&nbsp;</mtext><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">y</mi><mi mathvariant="normal">l</mi></mrow></mrow><annotation encoding="application/x-tex">\rho c \approx 400\text{–}415\ \mathrm{Rayl}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6776em;vertical-align:-0.1944em"></span><span class="mord mathnormal">ρ</span><span class="mord mathnormal">c</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em"></span><span class="mord">400</span><span class="mord text"><span class="mord">–</span></span><span class="mord">415</span><span class="mspace">&nbsp;</span><span class="mord"><span class="mord mathrm">Rayl</span></span></span></span></span>，则：</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><msubsup><mi>p</mi><mn>0</mn><mn>2</mn></msubsup><mrow><mi>ρ</mi><mtext> </mtext><mi>c</mi><mtext> </mtext><msub><mi>I</mi><mn>0</mn></msub></mrow></mfrac><mo>≈</mo><mn>1</mn><mspace width="1em"></mspace><mo>⇒</mo><mspace width="1em"></mspace><mn>10</mn><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mn>10</mn></msub><mo stretchy="false">(</mo><mo>⋅</mo><mo stretchy="false">)</mo><mo>≈</mo><mn>0</mn><mtext>&nbsp;</mtext><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">B</mi></mrow></mrow><annotation encoding="application/x-tex">\frac{p_0^2}{\rho\,c\,I_0}\approx 1 \quad\Rightarrow\quad 10\log_{10}(\cdot)\approx 0\ \mathrm{dB}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.3715em;vertical-align:-0.8804em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.4911em"><span style="top:-2.314em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord mathnormal">ρ</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal">c</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em">I</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:-0.0785em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.677em"><span class="pstrut" style="height:3em"></span><span class="mord"><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-2.4519em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2481em"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">1</span><span class="mspace" style="margin-right:1em"></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">⇒</span><span class="mspace" style="margin-right:1em"></span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.207em"><span style="top:-2.4559em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord">⋅</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6944em"></span><span class="mord">0</span><span class="mspace">&nbsp;</span><span class="mord"><span class="mord mathrm">dB</span></span></span></span></span></span>
<p>因此：</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>L</mi><mi>I</mi></msub><mo>≈</mo><msub><mi>L</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">L_I \approx L_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span></span></span></span></span>
<hr>
<h2 id="6-结论">6. 结论</h2>
<p>在靠近大型、均匀辐射的面声源且满足平面波近似的条件下：</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>L</mi><mi>W</mi></msub><mtext>&nbsp;</mtext><mo stretchy="false">(</mo><mtext>单位面积</mtext><mo stretchy="false">)</mo><mo>=</mo><msub><mi>L</mi><mi>I</mi></msub><mo>≈</mo><msub><mi>L</mi><mi>p</mi></msub><mspace width="1em"></mspace><mo stretchy="false">(</mo><mtext>单位：dB</mtext><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">L_W\ (\text{单位面积}) = L_I \approx L_p \quad (\text{\text{单位}\text{：}dB})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em">W</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace">&nbsp;</span><span class="mopen">(</span><span class="mord text"><span class="mord cjk_fallback">单位面积</span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">≈</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:1em"></span><span class="mopen">(</span><span class="mord text"><span class="mord text"><span class="mord cjk_fallback">单位</span></span><span class="mord text"><span class="mord cjk_fallback">：</span></span><span class="mord">dB</span></span><span class="mclose">)</span></span></span></span></span>
<hr>
<h2 id="重要说明">重要说明</h2>
<ol>
<li><strong>平面波近似条件</strong>：等号成立依赖于测点足够靠近面源，使声场近似平面波。若离得较远形成发散（球面波），一般有 <span class="katex-error" title="ParseError: KaTeX parse error: Expected 'EOF', got '&amp;' at position 5: L_I &amp;̲lt; L_p" style="color:#cc0000">L_I &amp;lt; L_p</span>。</li>
<li><strong>辐射均匀性</strong>：假设面源各处辐射均匀；若不均匀，局部 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">L_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span></span></span></span> 与 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mi>I</mi></msub></mrow><annotation encoding="application/x-tex">L_I</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span> 会随位置变化。</li>
<li><strong>自由场假设</strong>：推导默认自由场；近反射面需考虑镜像源影响。</li>
<li><strong>半空间辐射</strong>：墙面设备常向半空间（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mi>π</mi></mrow><annotation encoding="application/x-tex">2\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">2</span><span class="mord mathnormal" style="margin-right:0.03588em">π</span></span></span></span> 立体角）辐射。局部仍有 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi><mo>=</mo><msup><mi>p</mi><mn>2</mn></msup><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><mi>ρ</mi><mi>c</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">I = p^2/(\rho c)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.07847em">I</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord">/</span><span class="mopen">(</span><span class="mord mathnormal">ρ</span><span class="mord mathnormal">c</span><span class="mclose">)</span></span></span></span> 成立；<strong>总声功率级</strong>需对整个辐射面积分，远大于任一点的单位面积值。</li>
</ol>
<hr>
<p><strong>总结：</strong></p>
<p>对于“靠近面源处某一点”，该点的声压级 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">L_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span></span></span></span> 在满足平面波条件时，就近似等于通过该点单位面积的声功率级 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mi>W</mi></msub></mrow><annotation encoding="application/x-tex">L_W</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em">W</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span>（即声强级 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>L</mi><mi>I</mi></msub></mrow><annotation encoding="application/x-tex">L_I</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">L</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07847em">I</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span>）。<br>
两者数值上相等（单位都是 dB）。<br>
理解这个关系对于通过测量靠近噪声源表面的声压来估算其表面辐射声强（功率密度）非常有用。</p>]]></content>
        <author>
            <name>杨工</name>
            <email>sjzhakj@163.com</email>
        </author>
        <category label="aerscreen" term="aerscreen"/>
    </entry>
    <entry>
        <title type="html"><![CDATA[AERSCREEN输入文件编写规则]]></title>
        <id>https://guide.ihamodel.com/blog/aerscreen-input-file-preparation-rules</id>
        <link href="https://guide.ihamodel.com/blog/aerscreen-input-file-preparation-rules"/>
        <updated>2025-11-03T00:00:00.000Z</updated>
        <summary type="html"><![CDATA[AERSCREEN输入文件编写规则。]]></summary>
        <content type="html"><![CDATA[<p>AERSCREEN输入文件分了十个数据块，分别是：<br>第一个数据块为污染源信息，<br>第二个数据块为建筑物下洗参数设置，<br>第三个数据块为MAKEMET数据设置，包括气候设置和地表参数设置。<br>第四个数据块为地表摩擦速度调整。<br>第五个数据块为地形数据，<br>第六个数据块为离散点设置，<br>第七个数据块为单位和城乡选择，<br>第八个数据块为熏烟选项，<br>第九个数据块为调试选项，<br>第十个数据块为输出文件设置。</p>
<p>每个数据块的格式类似，都以**开头，完整的输入文件如下：</p>
<blockquote>
<p>** STACK DATA Rate Height Temp. Velocity Diam. Flow
** 0.4631E+01 120.0000 323.1500 12.3000 3.0000 184224.</p>
<p>** BUILDING DATA BPIP Height Max dim. Min dim. Orient. Direct. Offset
** N 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000</p>
<p>** MAKEMET DATA MinT MaxT Speed AnemHt Surf Clim Albedo Bowen Length SC FILE
** 261.15 314.15 0.5 10.000 5 1 0.6000 1.5000 0.0100 "NA"</p>
<p>** ADJUST U* N</p>
<p>** TERRAIN DATA Terrain UTM East UTM North Zone Nada Probe PROFBASE Use AERMAP elev
** Y 680588.3 4227706.0 49 4 25000.0 1186.72 N</p>
<p>** DISCRETE RECEPTORS Discflag Receptor file
** N "NA"</p>
<p>** UNITS/POPULATION Units R/U Population Amb. dist. Flagpole Flagpole height
** M R 0. 1.000 N 0.00</p>
<p>** FUMIGATION Inversion Break-up Shoreline Distance Direct Run AERSCREEN
** N N -999.00 -9.0 Y</p>
<p>** DEBUG OPTION Debug
** N</p>
<p>** OUTPUT FILE "AERSCREEN.OUT"</p>
</blockquote>
<p>第一行为参数标识，第二行为具体的参数值。</p>]]></content>
        <author>
            <name>杨工</name>
            <email>sjzhakj@163.com</email>
        </author>
        <category label="aerscreen" term="aerscreen"/>
    </entry>
    <entry>
        <title type="html"><![CDATA[大气预测评价中气象数据处理流程]]></title>
        <id>https://guide.ihamodel.com/blog/meteorological-data-processing-service-workflow</id>
        <link href="https://guide.ihamodel.com/blog/meteorological-data-processing-service-workflow"/>
        <updated>2025-11-03T00:00:00.000Z</updated>
        <summary type="html"><![CDATA[气象数据类型分为气候数据、逐时地面气象数据、探空气象数据、云量数据。**气候数据**主要是多年气象资料统计分析，主要包括累年月均值的风速风频气温等、逐年风速风频气温等、累年极值风速气温降水量等。]]></summary>
        <content type="html"><![CDATA[<p><strong>温馨提示：</strong></p>
<p><strong>逐时地面气象数据和气候数据处理需要一定时间，数据成品会有1~2个工作日的延迟发送，请合理安排时间</strong></p>
<p>石家庄环安科技有限公司<br>
网站：<a href="http://www.ihamodel.com/">www.ihamodel.com</a><br>
客服电话：4006768186</p>
<h2 id="1--气象数据服务类型">1.  气象数据服务类型</h2>
<p>气象数据类型分为气候数据、逐时地面气象数据、探空气象数据、云量数据。<strong>气候数据</strong>主要是多年气象资料统计分析，主要包括累年月均值的风速风频气温等、逐年风速风频气温等、累年极值风速气温降水量等；<strong>逐时地面气象数据</strong>用于导则推荐的进一步预测模型，包含风向、风速、云量数据、干球温度、相对湿度、站点气压等气象要素；<strong>探空气象数据</strong>用于导则推荐的进一步预测模型，包含一天早晚两次不同等压面上的气压、离地高度、干球温度、风向及风速，其中离地高度3000m以内的有效数据层数不小于10层；<strong>云量数据</strong>也为逐时数据，利用中尺度气象模型WRF模拟的数据，默认作为总云量。</p>
<p>平台提供了近20年的气候数据，近3年的逐时地面气象数据、探空气象数据和云量数据，用户可以根据评价年，来选择相应的数据年份。<strong>其中逐时地面气象数据可以包含了云量数据，勿重复购买。</strong></p>
<p>逐时地面气象数据和气候数据处理需要一定时间，数据成品会有1~2个工作日的延迟发送，请合理安排时间。探空气象数据和云量数据为已处理好的成品数据，购买后可以立即获取。</p>
<p>气候数据和云量数据文件储存格式为**.xlsx**，逐时地面气象数据和探空气象数据文件储存格式为**.OQA**。</p>
<h2 id="2--环境质量现状数据">2.  环境质量现状数据</h2>
<p>平台可以提供项目所在位置周边的常规监测站点的环境质量现状数据，包括区域环境质量现状评价、基本污染物<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><msub><mi>O</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">SO_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord mathnormal" style="margin-right:0.05764em">S</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span>、<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>N</mi><msub><mi>O</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">NO_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord mathnormal" style="margin-right:0.10903em">N</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span>、<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><msub><mi>M</mi><mn>10</mn></msub></mrow><annotation encoding="application/x-tex">PM_{10}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord mathnormal" style="margin-right:0.13889em">P</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">10</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span>、<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><msub><mi>M</mi><mn>2.5</mn></msub></mrow><annotation encoding="application/x-tex">PM_{2.5}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord mathnormal" style="margin-right:0.13889em">P</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em">M</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:-0.109em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2.5</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span>、CO逐日数据和<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>O</mi><mn>3</mn></msub></mrow><annotation encoding="application/x-tex">O_3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span>的8小时滑动平均值。环境质量现状数据为已处理好的成品数据，购买后可以立即获取。区域环境质量现状评价储存格式为**.docx**，基本污染物的监测数据储存格式为**.txt**。</p>
<h2 id="3--数据服务费用">3.  数据服务费用</h2>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/1-1024x491.png" alt="img"></p>
<h2 id="4数据服务购买">4.数据服务购买</h2>
<p>平台提供**“微信”<strong>、</strong>“支付宝”<strong>两种支付方式，用户自行选择支付方式，然后点击</strong>“我已阅读并同意**”，点击界面下方的**“支付”**按钮，进入扫码支付界面，扫码支付即可。支付完成以后，请耐心等待1~2个工作日。</p>
<h2 id="5数据下载">5.数据下载</h2>
<p>在用户中心点击“资源中心”，然后点击**“气象数据购买列表”<strong>，在</strong>“数据状态**”选择**“购买成功数据”<strong>，最后，勾选自己自己购买的数据，点击界面右上角</strong>“下载选中数据”**，下载数据。</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/01.png" alt="01"></p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/02.png" alt="02"></p>
<h2 id="6发票申请">6.发票申请</h2>
<p>在用户中心点击**“充值”<strong>，然后点击</strong>“发票”<strong>，点击</strong>“未开具过发票的订单”<strong>，选择相应的订单，点击界面右上角</strong>“申请发票”**，按照相应要求填写发票信息及收件地址（开具纸板发票）。</p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/03.png" alt="03"></p>
<p><img src="https://ihamodel.oss-cn-beijing.aliyuncs.com/img/04.png" alt="04"></p>]]></content>
        <author>
            <name>赵工</name>
            <email>sjzhakj@163.com</email>
        </author>
        <category label="aermod" term="aermod"/>
    </entry>
</feed>