错格实数傅里叶变换微分算子及其在非均匀介质波动传播研究中的应用
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摘要
提出一种新的数值微分运算方法 ,即错格实数傅里叶变换微分法 .该方法的运算速度比错格复数傅里叶变换数值微分解法快 0 .33倍 ;因为该微分算法在整个微分运算过程中保留了奈奎斯特分量 ,使得它比普通分格的实数傅里叶变换数值微分算法的精度高 ,稳定性好 .将该方法和Cagniard DeHoop解析法在求解半无限空间地震波动的问题中进行比较 ,结果表明 ,新微分法的精度和解析方法的精度相同 .在非均匀介质中的地震波传播数值模拟的结果表明 ,该方法是一种研究非均匀介质中地震波传播问题的有效的数值微分方法 .
A new fast differentiation operator,“staggered grid real value FFT differentiation operator”,is proposed in this paper. The method is one third faster on average than the traditional differentiation method by using the complex FFT differentiation,and is very efficient in economy. Furthermore,the new method has higher accuracy and higher stability than the traditional grid real FFT method because the Nyquist component is remained throughout calculation procedure. The validity of staggered grid real value FFT differentiation operator is confirmed by comparing with the analytic Cagniard-De Hoop method in the half space SH problem. The new operation is applied to simulate seismic wave propagation in inhomogeneous medium,and the results show that the staggered grid real value FFT differentiation operator for the pseudospectral method is valid for the seismic wave simulation in the heterogeneous medium.
A new fast differentiation operator,“staggered grid real value FFT differentiation operator”,is proposed in this paper. The method is one third faster on average than the traditional differentiation method by using the complex FFT differentiation,and is very efficient in economy. Furthermore,the new method has higher accuracy and higher stability than the traditional grid real FFT method because the Nyquist component is remained throughout calculation procedure. The validity of staggered grid real value FFT differentiation operator is confirmed by comparing with the analytic Cagniard-De Hoop method in the half space SH problem. The new operation is applied to simulate seismic wave propagation in inhomogeneous medium,and the results show that the staggered grid real value FFT differentiation operator for the pseudospectral method is valid for the seismic wave simulation in the heterogeneous medium.
引文
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[2] ZhouB .OntheuseoftheHartleytransformingeophysicalapplications.Geophysics,1992,57:196～197
[3] OrszagSA .Comparisonofpseudospectralandspectralapproximation.Stud.Appl.Math.,1972,51:253～259
[4] OzdenvarT.GAMcMechan.Causesandreductionofnumericalarte factsinpseudo spectralwavefieldextrapolation.Geophys.J.Int.,1996,126:819～828
[5] KosloffR ,EBaysal.ForwardmodelingbyaFouriermethod.Geophysics,1982,42:1402～1412
[6] FornbergB .Thepseudospectralmethod:Comparisonswithfinitedifferencefortheelasticwaveequation.Geophysics,1987,52:483～501
[7] 赵志新,久保田隆二.やや深い地下构造の变化による强震动分布———兵库县南部地震による被害分布との比较.物理探查学会第97回学术讲演论文集.日本物理探查学会出版,1997.71～74ZHAOZhixin,RKubota.Thedistributionofstronggroundmotionfromuppermostcrustalstructure comparisonwithdisasterfromtheHyogo kennanbuearthquake.Proceedingofthe97thSEGJConference.In:TheSocietyofExplorationGeophysicistsofJapan.1997.71～74
[8] ReshefM ,DKosloff,MEdwards,etal.Three dimensionalelasticmodelingbytheFouriermethod.Geophysics:1988,53:1184～1193
[9] 古村孝志,竹中.端に不连续を持つデ-タのためのFourier微分法———对称法.物理探查,1992,45:303～309FurumuraT,HTakenaka.Astablemethodfornumericaldifferentiationofdatawithdiscontinuitiesatend pointsbymeansofFouriertransform symmetricdifferentiation.Geophys.Expl.,1992,45:303～309
[10] ZhaoZX ,RKubota.TheempiricalGreen’sfunctionmethodbyusingsimulatedwaveforms.In:KIrikura,KKudo,HOkada,etal.eds.TheEffectofSurfaceGgeologyonSeismicMotionRecentProgressandNewHorizononESGStudy,Volume3.Netherlands:AABalkemaRotterdamPress,1999.1435～1442
[11] FurumuraT.BLN .KennettH .Takenaka.Parallel3Dpseudospectralsimulationofseismicwavepropagation.Geophysics,1998,63:279～288
[12] ChenH .W .Staggeredgridpseudospectralsimulationinviscoacousticwavefieldsimulation.J.Acoust.Soc.Am.,1996,100:120～131
[13] WitteDC .Thepseudospectralmethodforsimulatingwavepropagation[DoctorThesis].ColumbiaUniversity,1989
[14] AkiKP .G .Richards.QuantitativeSeismologyTheoryandMethods.SanFrancisco:W .H .FreemanandCompany,1980.224～243
[15] CerjanC .D .KosloffR .kosloffM .Reshef.Anonreflectingboundaryconditionfordiscreteacousticandelasticwaveequation.Geophysics,1985,50:705～708
[16] HerrmannR ,B .SH wavegenerationbydislocationsourcesAnumericalstudy.BSSA,1979,69:1～15
[17] IrikuraK ,KKudoHOkada,etal.TheEffectofSurfaceGeologyonSeismicMotionRecentProgressandNewHorizononESGStudy,Volume3.Netherlands:AABalkemaRotterdamPress,1999
[18] PitarkaAK ,IrikuraT,IwataH .Sekikuchi.Three dimensionalsimulationofthenear faultgroundmotionforthe1995Hyogo kenNanbu(Kobe),Japan,earthquake.BSSA ,1998,88:428～440
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