二维地震波形小波多尺度反演
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摘要
多尺度反演具有对初始模型依赖性低、收敛速度快、反演结果稳定等优点 ,是一种很有希望的反演方法。基于小波变换讨论二维地震波形多尺度反演问题 ,将地震参数反演转化为小波域重要系数的优化问题 ,有效改善了局部极值等。并引入了EZW思想 ,用小波系数的零树来预测待优化参数的位置 ,加速优化参数的搜索 ,使反演更有目的性
Multiscale inversion is a promising method because of its low dependence of the initial model, convergence efficiency and robustness. A wavelet multiscale inversion (WMI) method using the orthogonal wavelet transform is applied to inverse two dimension seismic waveform. The inversion result can be re-directed for the optimization of the wavelet significant coefficients (WSC) rather than the traditional seismic parameters in physical space. Also, the computational urden and local minimum are significantly less due to the sparseness and spatial relativity of the WSC. As an aid in prediction of significant coefficient, the idea of embedded zerotree wavelet (EZW) is imtroduced for the first time. Sequentially, the optimized parameter can be predicted using the zerotree and the process of inversion becomes better purpose.
Multiscale inversion is a promising method because of its low dependence of the initial model, convergence efficiency and robustness. A wavelet multiscale inversion (WMI) method using the orthogonal wavelet transform is applied to inverse two dimension seismic waveform. The inversion result can be re-directed for the optimization of the wavelet significant coefficients (WSC) rather than the traditional seismic parameters in physical space. Also, the computational urden and local minimum are significantly less due to the sparseness and spatial relativity of the WSC. As an aid in prediction of significant coefficient, the idea of embedded zerotree wavelet (EZW) is imtroduced for the first time. Sequentially, the optimized parameter can be predicted using the zerotree and the process of inversion becomes better purpose.
引文
[1] BunksC ,SaleckFM ,ZaleskiS .Multiscaleseismicwaveforminversion[J].Geophysics,1995;60(5):1457-1473
[2] 杨丽华,孟昭波.一维波动方程小波逐版本反演[J].地球物理学报,1995;38(6):815-821
[3] 孟鸿鹰,刘贵忠.小波变换多尺度地震波形反演[J].地球物理学报,1999;42(2):241-248
[4] 马坚伟,朱亚平,杨慧珠.地震波形多尺度反演的一点讨论[J].地球物理学进展,2000;15(4):55-61
[5] MaJW ,ZhuYP ,YangHZ .Multiscale combinedseismicwaveforminversionusingorthogonalwavelettransform[J].ElectronLett,2001;37:261-262
[6] ShapiroJM .Embeddedimagecodingusingzerotreesofwaveletcoefficients[J].IEEETransSignalProcessing,1993;41(12):3445-3462
[7] CreusereCD .Anewmethodofrobustimagecompressionbasedontheembeddedzerotreewaveletalgorithm[J].IEEETransImageProcessing,1997;(10)6:1436-1446
[8] DaubechiesI.Orthonormalbasesofcompactlysupportedwavelets[J].CommunPureandAppliedMath,1988;41:901-996
[9] 朱亚平.基于小波变换的地震勘探数据多尺度反演研究[D].博士学位论文,北京:清华大学,2000
[10] 马坚伟,杨慧珠,朱亚平.多尺度有限差分法模拟复杂介质波传问题[J].物理学报,2001;8:10-16
[2] 杨丽华,孟昭波.一维波动方程小波逐版本反演[J].地球物理学报,1995;38(6):815-821
[3] 孟鸿鹰,刘贵忠.小波变换多尺度地震波形反演[J].地球物理学报,1999;42(2):241-248
[4] 马坚伟,朱亚平,杨慧珠.地震波形多尺度反演的一点讨论[J].地球物理学进展,2000;15(4):55-61
[5] MaJW ,ZhuYP ,YangHZ .Multiscale combinedseismicwaveforminversionusingorthogonalwavelettransform[J].ElectronLett,2001;37:261-262
[6] ShapiroJM .Embeddedimagecodingusingzerotreesofwaveletcoefficients[J].IEEETransSignalProcessing,1993;41(12):3445-3462
[7] CreusereCD .Anewmethodofrobustimagecompressionbasedontheembeddedzerotreewaveletalgorithm[J].IEEETransImageProcessing,1997;(10)6:1436-1446
[8] DaubechiesI.Orthonormalbasesofcompactlysupportedwavelets[J].CommunPureandAppliedMath,1988;41:901-996
[9] 朱亚平.基于小波变换的地震勘探数据多尺度反演研究[D].博士学位论文,北京:清华大学,2000
[10] 马坚伟,杨慧珠,朱亚平.多尺度有限差分法模拟复杂介质波传问题[J].物理学报,2001;8:10-16
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