基于归一化能量谱目标函数的全波形反演方法
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摘要
基于L2范数的常规全波形反演目标函数是一个强非线性泛函,在反演过程中容易陷入局部极小值.本文提出归一化能量谱目标函数来缓解全波形反演过程中的强非线性问题,同时能够有效地缓解噪声和震源子波不准等因素的影响.能量谱目标函数是通过匹配观测数据与模拟数据随频率分布的能量信息来实现最小二乘反演的,其忽略了地震数据波形与相位变化的细节特征,这在反演的过程中能够有效缓解波形匹配错位等问题.数值测试结果表明,基于归一化能量谱目标函数在构建初始速度模型、抗噪性和缓解震源子波依赖等方面都优于归一化全波形反演目标函数.金属矿模型测试结果表明,即使地震数据缺失低频分量,基于归一化能量谱目标函数的全波形反演方法在像金属矿这样的强散射介质反演问题上同样具有一定的优势.
The L2 norm-based conventional Full Waveform Inversion(FWI)method is a strong nonlinear functional,it is easy to fall into a local minimum during the inversion process.In this paper,the Normalized Energy Spectrum based Full Waveform Inversion(NESFWI)is proposed to alleviate the strong nonlinear problem and reduce the dependence of high Signal to Noise Ratio(SNR)seismic data and source wavelet.The objective function of NESFWI is to match the energy spectrum of the observed and synthetic data in the frequency domain,which ignores the waveform and phase oscillation characteristics of the seismic data.It can effectively mitigate the waveform mismatching problem during the inversion process,while reducing dependence of seismic source wavelet and high SNR seismic data.Numerical examples show that NESFWI results are better than the Normalized Full Waveform Inversion(NFWI)in building an initial velocity model,noise immunity and source wavelet dependence.Tests on a metallic deposit model show that even if the seismic data lack low frequency components,it still can get better inversion results than the conventional FWI method.
The L2 norm-based conventional Full Waveform Inversion(FWI)method is a strong nonlinear functional,it is easy to fall into a local minimum during the inversion process.In this paper,the Normalized Energy Spectrum based Full Waveform Inversion(NESFWI)is proposed to alleviate the strong nonlinear problem and reduce the dependence of high Signal to Noise Ratio(SNR)seismic data and source wavelet.The objective function of NESFWI is to match the energy spectrum of the observed and synthetic data in the frequency domain,which ignores the waveform and phase oscillation characteristics of the seismic data.It can effectively mitigate the waveform mismatching problem during the inversion process,while reducing dependence of seismic source wavelet and high SNR seismic data.Numerical examples show that NESFWI results are better than the Normalized Full Waveform Inversion(NFWI)in building an initial velocity model,noise immunity and source wavelet dependence.Tests on a metallic deposit model show that even if the seismic data lack low frequency components,it still can get better inversion results than the conventional FWI method.
引文
Ao R D,Dong L G,Chi B X.2015.Source-independent envelopebased FWI to build an initial model.Chinese Journal of Geophysics(in Chinese),58(6):1998-2010,doi:10.6038/cjg20150615.
Bharadwaj P,Mulder W,Drijkoningen G.2016.Full waveform inversion with an auxiliary bump functional.Geophysical Journal International,206(2):1076-1092.
Biondi B,Almomin A.2013.Tomographic full-waveform inversion(TFWI)by combining FWI and wave-equation migration velocity analysis.The Leading Edge,32(9):1074-1080.
Bozdag E,Trampert J,Tromp J.2011.Misfit functions for full waveform inversion based on instantaneous phase and envelope measurements.Geophysical Journal International,185(2):845-870.
Bunks C,Saleck F M,Zaleski S,et al.1995.Multiscale seismic waveform inversion.Geophysics,60(5):1457-1473.
Chen G X,Wu R S,Chen S C.2018.Reflection multi-scale envelope inversion.Geophysical Prospecting,66(7):1258-1271.
Chi B X,Dong L G,Liu Y Z.2014.Full waveform inversion method using envelope objective function without low frequency data.Journal of Applied Geophysics,109:36-46.
Choi Y,Alkhalifah T.2011.Source-independent time-domain waveform inversion using convolved wavefields:Application to the encoded multisource waveform inversion.Geophysics,76(5):R125-R134.
Choi Y,Alkhalifah T.2012.Application of multi-source waveform inversion to marine streamer data using the global correlation norm.Geophysical Prospecting,60(4):748-758.
Choi Y,Alkhalifah T.2013.Frequency-domain waveform inversion using the phase derivative.Geophysical Journal International,195(3):1904-1916.
Dong L G,Huang C,Chi B X,et al.2015.Strategy and application of waveform inversion based on seismic data subset.Chinese Journal of Geophysics(in Chinese),58(10):3735-3745,doi:10.6038/cjg20151024.
Engquist B,Hamfeldt B F.2013.Application of the Wasserstein metric to seismic signals.Communications in Mathematical Sciences,12(5):979-988.
Fichtner A,Kennett B L N,Igel H,et al.2008.Theoretical background for continental-and global-scale full-waveform inversion in the time-frequency domain.Geophysical Journal International,175(2):665-685.
Ha J,Kim S,Koo N,et al.2018.Full waveform inversion using a decomposed single frequency component from a spectrogram.Journal of Applied Geophysics,153:154-167.
Hu Y,Han L G,Xu Z,et al.2017.Adaptive multi-step full waveform inversion based on waveform mode decomposition.Journal of Applied Geophysics,139:195-210.
Hu Y,Han L G,Xu Z,et al.2017.Demodulation envelope multiscale full waveform inversion based on precise seismic source function.Chinese Journal of Geophysics(in Chinese),60(3):1088-1105,doi:10.6038/cjg20170321.
Hu Y,Han L G,Yu J L,et al.2018.Time-frequency domain multi-scale full waveform inversion based on adaptive nonstationary phase correction.Chinese Journal of Geophysics(in Chinese),61(7):2969-2988,doi:10.6038/cjg2018L0421.
Hu Y,Wu R S,Han L G,et al.2018.Multi-Scale energy weighted envelope-phase inversion using direct envelope Fréchet derivative in local time-frequency.∥88th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts.
Hu Y,Wu R S,Han L G,et al.2019.Joint multiscale direct envelope inversion of phase and amplitude in the time-frequency domain.IEEE Transactions on Geoscience and Remote Sensing,in Press.
Lailly P.1983.The seismic inverse problem as a sequence of before stack migrations.∥Conference on Inverse Scattering:Theory and Application.Philadelphia,PA:Society for Industrial and Applied Mathematics,206-220.
Lian Y G,LüQ T,Han L G,et al.2011.Research of seismic modeling of complex metal ore body-examples of the Luzong Luohe,Nihe and Dabaozhuang deposits.Acta Geologica Sinica(in Chinese),85(5):887-899.
Liu Y S,Teng J W,Xu T,et al.2016.Robust time-domain full waveform inversion with normalized zero-lag cross-correlation objective function.Geophysical Journal International,209(1):106-122.
Luo J R,Wu R S.2015.Seismic envelope inversion:reduction of local minima and noise resistance.Geophysical Prospecting,63(3):597-614.
Luo J R,Wu R S,Gao F C.2016.Time-domain full-waveform inversion using instantaneous phase with damping.∥86th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1472-1476.
Luo J R,Wu R S,Gao J H.2016.Local minima reduction of seismic envelope inversion.Chinese Journal of Geophysics(in Chinese),59(7):2510-2518,doi:10.6038/cjg20160716.
Luo Y,Schuster G T.1991.Wave-equation traveltime inversion.Geophysics,56(5):645-653.
LüQ T,Dong S W,Shi D N,et al.2014.Lithosphere architecture and geodynamic model of Middle and Lower Reaches of Yangtze Metallogenic Belt:A review from SinoProbe.Acta Petrologica Sinica(in Chinese),30(4):889-906.
LüQ T,Han L G,Yan J Y,et al.2010.Seismic imaging of volcanic hydrothermal iron-sulfur deposits and its hosting structure in Luzong ore district.Acta Petrologica Sinica(in Chinese),26(9):2598-2612.
Métivier L,Brossier R,Mérigot Q,et al.2016.Measuring the misfit between seismograms using an optimal transport distance:application to full waveform inversion.Geophysical Journal International,205(1):345-377.
Pratt R G,Shin C,Hick G J.1998.Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion.Geophysical Journal International,133(2):341-362.
Rickett J.2013.The variable projection method for waveform inversion with an unknown source function.Geophysical Prospecting,61(4):874-881.
Shin C,Ha W.2017.Accumulated energy norm for full waveform inversion of marine data.Journal of Applied Geophysics,147:91-101.
Sun H Y,Han L G,Han M,et al.2015.Elastic full waveform inversion based on visibility analysis and energy compensation for metallic deposit exploration.Chinese Journal of Geophysics(in Chinese),58(12):4605-4616,doi:10.6038/cjg20151222.
Symes W W.2008.Migration velocity analysis and waveform inversion.Geophysical Prospecting,56(6):765-790.
Tao K,Grand S P,Niu F L.2018.Full-waveform inversion of triplicated data using a normalized-correlation-coefficient-based misfit function.Geophysical Journal International,210(3):1517-1524.
Tarantola A.1984.Inversion of seismic reflection data in the acoustic approximation.Geophysics,49(8):1259-1266.
Virieux J,Operto S.2009.An overview of full-waveform inversion in exploration geophysics.Geophysics,74(6):WCC1-WCC26.
Wu R S,Chen G X.2017.New frechet derivative for envelope data and multi-scale envelope inversion.∥87th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts.
Wu R S,Chen G X.2018.Multi-scale seismic envelope inversion using a direct envelope Frechet derivative for strong-nonlinear full waveform inversion.arXiv preprint arXiv:1808.05275.
Wu R S,Luo J R,Wu B Y.2014.Seismic envelope inversion and modulation signal model.Geophysics,79(3):WA13-WA24.
Yang Y N,Engquist B.2017.Analysis of optimal transport and related misfit functions in full-waveform inversion.∥87th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1291-1296.
Zhang P,Han L G,Xu Z,et al.2017.Sparse blind deconvolution based low-frequency seismic data reconstruction for multiscale full waveform inversion.Journal of Applied Geophysics,139:91-108.
Zhang P,Wu R S,Han L G.2018.Source-independent seismic envelope inversion based on the direct envelope Fréchet derivative.Geophysics,83(6):R581-R595.
敖瑞德,董良国,迟本鑫.2015.不依赖子波、基于包络的FWI初始模型建立方法研究.地球物理学报,58(6):1998-2010,doi:10.6038/cjg20150615.
董良国,黄超,迟本鑫等.2015.基于地震数据子集的波形反演思路、方法与应用.地球物理学报,58(10):3735-3745,doi:10.6038/cjg20151024.
胡勇,韩立国,许卓等.2017.基于精确震源函数的解调包络多尺度全波形反演.地球物理学报,60(3):1088-1105,doi:10.6038/cjg20170321.
胡勇,韩立国,于江龙等.2018.基于自适应非稳态相位校正的时频域多尺度全波形反演.地球物理学报,61(7):2969-2988,doi:10.6038/cjg2018L0421.
廉玉广,吕庆田,韩立国等.2011.复杂金属矿体地震波正演模拟研究-以庐枞盆地罗河、泥河和大包庄矿床为例.地质学报,85(5):887-899.
罗静蕊,吴如山,高静怀.2016.地震包络反演对局部极小值的抑制特性.地球物理学报,59(7):2510-2518,doi:10.6038/cjg20160716.
吕庆田,董树文,史大年等.2014.长江中下游成矿带岩石圈结构与成矿动力学模型-深部探测(SinoProbe)综述.岩石学报,30(4):889-906.
吕庆田,韩立国,严加永等.2010.庐枞矿集区火山气液型铁、硫矿床及控矿构造的反射地震成像.岩石学报,26(9):2598-2612.
孙宏宇,韩立国,韩淼等.2015.基于可视性分析与能量补偿的金属矿弹性波全波形反演.地球物理学报,58(12):4605-4616,doi:10.6038/cjg20151222.
Bharadwaj P,Mulder W,Drijkoningen G.2016.Full waveform inversion with an auxiliary bump functional.Geophysical Journal International,206(2):1076-1092.
Biondi B,Almomin A.2013.Tomographic full-waveform inversion(TFWI)by combining FWI and wave-equation migration velocity analysis.The Leading Edge,32(9):1074-1080.
Bozdag E,Trampert J,Tromp J.2011.Misfit functions for full waveform inversion based on instantaneous phase and envelope measurements.Geophysical Journal International,185(2):845-870.
Bunks C,Saleck F M,Zaleski S,et al.1995.Multiscale seismic waveform inversion.Geophysics,60(5):1457-1473.
Chen G X,Wu R S,Chen S C.2018.Reflection multi-scale envelope inversion.Geophysical Prospecting,66(7):1258-1271.
Chi B X,Dong L G,Liu Y Z.2014.Full waveform inversion method using envelope objective function without low frequency data.Journal of Applied Geophysics,109:36-46.
Choi Y,Alkhalifah T.2011.Source-independent time-domain waveform inversion using convolved wavefields:Application to the encoded multisource waveform inversion.Geophysics,76(5):R125-R134.
Choi Y,Alkhalifah T.2012.Application of multi-source waveform inversion to marine streamer data using the global correlation norm.Geophysical Prospecting,60(4):748-758.
Choi Y,Alkhalifah T.2013.Frequency-domain waveform inversion using the phase derivative.Geophysical Journal International,195(3):1904-1916.
Dong L G,Huang C,Chi B X,et al.2015.Strategy and application of waveform inversion based on seismic data subset.Chinese Journal of Geophysics(in Chinese),58(10):3735-3745,doi:10.6038/cjg20151024.
Engquist B,Hamfeldt B F.2013.Application of the Wasserstein metric to seismic signals.Communications in Mathematical Sciences,12(5):979-988.
Fichtner A,Kennett B L N,Igel H,et al.2008.Theoretical background for continental-and global-scale full-waveform inversion in the time-frequency domain.Geophysical Journal International,175(2):665-685.
Ha J,Kim S,Koo N,et al.2018.Full waveform inversion using a decomposed single frequency component from a spectrogram.Journal of Applied Geophysics,153:154-167.
Hu Y,Han L G,Xu Z,et al.2017.Adaptive multi-step full waveform inversion based on waveform mode decomposition.Journal of Applied Geophysics,139:195-210.
Hu Y,Han L G,Xu Z,et al.2017.Demodulation envelope multiscale full waveform inversion based on precise seismic source function.Chinese Journal of Geophysics(in Chinese),60(3):1088-1105,doi:10.6038/cjg20170321.
Hu Y,Han L G,Yu J L,et al.2018.Time-frequency domain multi-scale full waveform inversion based on adaptive nonstationary phase correction.Chinese Journal of Geophysics(in Chinese),61(7):2969-2988,doi:10.6038/cjg2018L0421.
Hu Y,Wu R S,Han L G,et al.2018.Multi-Scale energy weighted envelope-phase inversion using direct envelope Fréchet derivative in local time-frequency.∥88th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts.
Hu Y,Wu R S,Han L G,et al.2019.Joint multiscale direct envelope inversion of phase and amplitude in the time-frequency domain.IEEE Transactions on Geoscience and Remote Sensing,in Press.
Lailly P.1983.The seismic inverse problem as a sequence of before stack migrations.∥Conference on Inverse Scattering:Theory and Application.Philadelphia,PA:Society for Industrial and Applied Mathematics,206-220.
Lian Y G,LüQ T,Han L G,et al.2011.Research of seismic modeling of complex metal ore body-examples of the Luzong Luohe,Nihe and Dabaozhuang deposits.Acta Geologica Sinica(in Chinese),85(5):887-899.
Liu Y S,Teng J W,Xu T,et al.2016.Robust time-domain full waveform inversion with normalized zero-lag cross-correlation objective function.Geophysical Journal International,209(1):106-122.
Luo J R,Wu R S.2015.Seismic envelope inversion:reduction of local minima and noise resistance.Geophysical Prospecting,63(3):597-614.
Luo J R,Wu R S,Gao F C.2016.Time-domain full-waveform inversion using instantaneous phase with damping.∥86th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1472-1476.
Luo J R,Wu R S,Gao J H.2016.Local minima reduction of seismic envelope inversion.Chinese Journal of Geophysics(in Chinese),59(7):2510-2518,doi:10.6038/cjg20160716.
Luo Y,Schuster G T.1991.Wave-equation traveltime inversion.Geophysics,56(5):645-653.
LüQ T,Dong S W,Shi D N,et al.2014.Lithosphere architecture and geodynamic model of Middle and Lower Reaches of Yangtze Metallogenic Belt:A review from SinoProbe.Acta Petrologica Sinica(in Chinese),30(4):889-906.
LüQ T,Han L G,Yan J Y,et al.2010.Seismic imaging of volcanic hydrothermal iron-sulfur deposits and its hosting structure in Luzong ore district.Acta Petrologica Sinica(in Chinese),26(9):2598-2612.
Métivier L,Brossier R,Mérigot Q,et al.2016.Measuring the misfit between seismograms using an optimal transport distance:application to full waveform inversion.Geophysical Journal International,205(1):345-377.
Pratt R G,Shin C,Hick G J.1998.Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion.Geophysical Journal International,133(2):341-362.
Rickett J.2013.The variable projection method for waveform inversion with an unknown source function.Geophysical Prospecting,61(4):874-881.
Shin C,Ha W.2017.Accumulated energy norm for full waveform inversion of marine data.Journal of Applied Geophysics,147:91-101.
Sun H Y,Han L G,Han M,et al.2015.Elastic full waveform inversion based on visibility analysis and energy compensation for metallic deposit exploration.Chinese Journal of Geophysics(in Chinese),58(12):4605-4616,doi:10.6038/cjg20151222.
Symes W W.2008.Migration velocity analysis and waveform inversion.Geophysical Prospecting,56(6):765-790.
Tao K,Grand S P,Niu F L.2018.Full-waveform inversion of triplicated data using a normalized-correlation-coefficient-based misfit function.Geophysical Journal International,210(3):1517-1524.
Tarantola A.1984.Inversion of seismic reflection data in the acoustic approximation.Geophysics,49(8):1259-1266.
Virieux J,Operto S.2009.An overview of full-waveform inversion in exploration geophysics.Geophysics,74(6):WCC1-WCC26.
Wu R S,Chen G X.2017.New frechet derivative for envelope data and multi-scale envelope inversion.∥87th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts.
Wu R S,Chen G X.2018.Multi-scale seismic envelope inversion using a direct envelope Frechet derivative for strong-nonlinear full waveform inversion.arXiv preprint arXiv:1808.05275.
Wu R S,Luo J R,Wu B Y.2014.Seismic envelope inversion and modulation signal model.Geophysics,79(3):WA13-WA24.
Yang Y N,Engquist B.2017.Analysis of optimal transport and related misfit functions in full-waveform inversion.∥87th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1291-1296.
Zhang P,Han L G,Xu Z,et al.2017.Sparse blind deconvolution based low-frequency seismic data reconstruction for multiscale full waveform inversion.Journal of Applied Geophysics,139:91-108.
Zhang P,Wu R S,Han L G.2018.Source-independent seismic envelope inversion based on the direct envelope Fréchet derivative.Geophysics,83(6):R581-R595.
敖瑞德,董良国,迟本鑫.2015.不依赖子波、基于包络的FWI初始模型建立方法研究.地球物理学报,58(6):1998-2010,doi:10.6038/cjg20150615.
董良国,黄超,迟本鑫等.2015.基于地震数据子集的波形反演思路、方法与应用.地球物理学报,58(10):3735-3745,doi:10.6038/cjg20151024.
胡勇,韩立国,许卓等.2017.基于精确震源函数的解调包络多尺度全波形反演.地球物理学报,60(3):1088-1105,doi:10.6038/cjg20170321.
胡勇,韩立国,于江龙等.2018.基于自适应非稳态相位校正的时频域多尺度全波形反演.地球物理学报,61(7):2969-2988,doi:10.6038/cjg2018L0421.
廉玉广,吕庆田,韩立国等.2011.复杂金属矿体地震波正演模拟研究-以庐枞盆地罗河、泥河和大包庄矿床为例.地质学报,85(5):887-899.
罗静蕊,吴如山,高静怀.2016.地震包络反演对局部极小值的抑制特性.地球物理学报,59(7):2510-2518,doi:10.6038/cjg20160716.
吕庆田,董树文,史大年等.2014.长江中下游成矿带岩石圈结构与成矿动力学模型-深部探测(SinoProbe)综述.岩石学报,30(4):889-906.
吕庆田,韩立国,严加永等.2010.庐枞矿集区火山气液型铁、硫矿床及控矿构造的反射地震成像.岩石学报,26(9):2598-2612.
孙宏宇,韩立国,韩淼等.2015.基于可视性分析与能量补偿的金属矿弹性波全波形反演.地球物理学报,58(12):4605-4616,doi:10.6038/cjg20151222.