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I地震数值模拟研究及应用摘要本论文是对数值模拟中波动方程相移法及相移加插值方法的应用。使用相移法对地下的地层模型进行正演和偏移，但是相移法只针对纵向速度变化的模型。为了得到更好的地质模型的效果，引入了相移加插值的方法对水平变化的复杂模型进行延拓，最终跟相移法进行比对，分析了两种方法的优势与不足。在对相移法的实验过程中，采用了模型简化，以求取平均速度的方式采用深度延拓，然后对点脉冲进行正演以及偏移，印证了实验的正确性后，又采用了这种方法对其他复杂模型进行了实验，另外还在相移的基础上使用了相移加插值的方法，对模型进行了检验和分析。通过一系列的试算后，发现相移加插值的方法比起相移法精度更高，并且在倾角很大的速度模型上，相移加插值的方法更能够识别地层的有效信息，并且在一些复杂的模型上也体现了出来，但是，相移加插值有计算量较大的缺点。关键词：波场偏移脉冲相移插值IITheresearchandapplicationofseismicnumericalsimulationAbstract:Theresearchandapplicationofthephaseshiftandinterpolationofwaveequationinnumericalsimulationisstudiedinthispaper.Theforwardmodelingandmigrationoftheundergroundstrataarecarriedoutbyusingthephaseshiftmethod,butthephaseshiftmethodisonlyusedtomodelthelongitudinalvelocitychange.Inordertogetbettergeologicalmodels,theintroductionofthereferencevelocityinterpolationmethodonchangesinthelevelofcomplexmodelextension,eventuallywithphaseshiftmethodforcomparison,analysesadvantagesanddisadvantagesofthetwomethods.Inthephaseshiftmethodinthecourseoftheexperiment,themodelissimplified,inordertoobtainthemeanvelocitywithdepthextrapolationandtopointpulseforwardmodelingandmigration,confirmsthecorrectnessoftheexperimentandusesthismethodtoothercomplexmodelexperimentswerecarriedout,stillanotherphaseshiftbasedonusingthereferencevelocityofwavefieldinterpolation,themodelweretestandanalysis.Throughaseriesoftrialanderroranalysisfoundhigherthanphaseshiftprecisioninterpolationmethodofphaseshift,andtheinclinationangleisverybigvelocitymodelandinterpolationmethodcaneffectiverecognitionofstratigraphicinformation,andinsomecomplexmodelsisalsoreflectedinit.However,phaseshiftinterpolationcalculationoflargeamountofdefects.Keywords:wavefieldmigrationpulsephaseshiftinterpolation目录摘要................................................................................................................................IABSTRACT..................................................................................................................II第一章：前言................................................................................................................11.1课题研究背景及意义.....................................................................................11.2研究现状.........................................................................................................11.3主要研究内容..................................................................................................3第二章波动方程偏移成像..........................................................................................42.1偏移..................................................................................................................42.1.1偏移的概念..........................................................................................42.1.2偏移脉冲响应......................................................................................72.2波动方程偏移的成象原理.............................................................................72.2.1爆炸反射界面成象原理......................................................................82.3相移波动方程偏移.........................................................................................92.3.1基本概念及公式..................................................................................92.3.2傅里叶变换的微分性质......................................................................92.3.3单程声波方程波场延拓公式............................................................102.3.4相移加插值延拓................................................................................13第三章程序算法流程................................................................................................163.1数字化...........................................................................................................163.1.1频率-波数域离散化..........................................................................163.1.2边界反射问题....................................................................................163.1.3插值计算............................................................................................173.2程序流程.......................................................................................................173.2.1叠后相移正演流程............................................................................173.2.2叠后相移偏移流程............................................................................183.2.3叠后相移插值正演流程.....................................................................183.2.4叠后相移插值偏移流程.....................................................................18第四章叠后深度偏移算例........................................................................................19结论及建议..................................................................................................................25致谢................................................................................................错误!未定义书签。参考文献......................................................................................................................261第一章：前言1.1课题研究背景及意义地震数值模拟在当前地球物理学勘探中有着广泛的应用和相当的份量，当前的勘探技术正在往更加先进，要求更加高的层面上发展，在这种情况下就要求科研人员们对于一些特别的地质模型，复杂的地质要求下利用已经学过的知识采用一