The parameter reconstruction of strong-scattering media is a challenge for conventional full waveform inversion(FWI).Direct envelope inversion(DEI)is an effective method for large-scale and strongscattering structures...The parameter reconstruction of strong-scattering media is a challenge for conventional full waveform inversion(FWI).Direct envelope inversion(DEI)is an effective method for large-scale and strongscattering structures imaging without the need of low-frequency seismic data.However,the current DEI methods are all based on the acoustic approximation.Whereas,in real cases,seismic records are the combined effects of the subsurface multi-parameters.Therefore,the study of DEI in elastic media is necessary for the accurate inversion of strong-scattering structures,such as salt domes.In this paper,we propose an elastic direct envelope inversion(EDEI)method based on wave mode decomposition.We define the objective function of EDEI using multi-component seismic data and derive its gradient formulation.To reduce the coupling effects of multi-parameters,we introduce the wave mode decomposition method into the gradient calculation of EDEI.The update of Vp is primarily the contributions of decomposed P-waves.Two approaches on Vs gradient calculation are proposed,i.e.using the petrophysical relation and wave mode decomposition method.Finally,we test the proposed method on a layered salt model and the SEG/EAGE salt model.The results show that the proposed EDEI method can reconstruct reliable large-scale Vp and Vs models of strong-scattering salt structures.The successive elastic FWI can obtain high-precision inversion results of the strong-scattering salt model.The proposed method also has a good anti-noise performance in the moderate noise level.展开更多
TheWKBJ solution for the one-waywave equations inmediawith smoothly varying velocity variation with depth,c(z),is reformulated from the principle of energy flux conservation for acoustic media.The formulation is then ...TheWKBJ solution for the one-waywave equations inmediawith smoothly varying velocity variation with depth,c(z),is reformulated from the principle of energy flux conservation for acoustic media.The formulation is then extended to general heterogeneous media with local angle domain methods by introducing the concepts of Transparent Boundary Condition(TBC)and Transparent Propagator(TP).The influence of the WKBJ correction on image amplitudes in seismic imaging,such as depth migration in exploration seismology,is investigated in both smoothly varying c(z)and general heterogeneous media.We also compare the effect of the propagator amplitude compensation with the effect of the acquisition aperture correction on the image amplitude.Numerical results in a smoothly varying c(z)medium demonstrate that theWKBJ correction significantly improves the one-way wave propagator amplitudes,which,after compensation,agree very well with those from the full wave equation method.Images for a point scatterer in a smoothly varying c(z)medium show that the WKBJ correction has some improvement on the image amplitude,though it is not very significant.The results in a general heterogeneous medium(2D SEG/EAGE salt model)show similar phenomena.When the acquisition aperture correction is applied,the image improves significantly in both the smoothly varying c(z)medium and the 2D SEG/EAGE saltmodel.The comparisons indicate that although theWKBJ compensation for propagator amplitude may be important for forward modeling(especially for wide-angle waves),its effect on the image amplitude in seismic imaging is much less noticeable compared with the acquisition aperture correction for migration with limited acquisition aperture in general heterogeneous media.展开更多
In the field of geophysics,although the first-order Rytov approximation is widely used,the higher-order approximation is seldom discussed.From both theo-retical analysis and numerical tests,the accumulated phase error...In the field of geophysics,although the first-order Rytov approximation is widely used,the higher-order approximation is seldom discussed.From both theo-retical analysis and numerical tests,the accumulated phase error introduced in the first-order Rytov approximation cannot be neglected in the presence of strong velocity perturbation.In this paper,we are focused on improving the phase accuracy of forward scattered wavefield,especially for the large-scale and strong velocity pertur-bation case.We develop an equivalent source method which can update the imaginary part of the complex phase iteratively,and the higher-order scattered wavefield can be approximated by multiplying the incident wavefield by the exponent of the imaginary part of the complex phase.Although the convergence of the proposed method has not been proved mathematically,numerical examples demonstrate that our method can produce an improved accuracy for traveltime(phase)prediction,even for strong perturbation media.However,due to the neglect of the real part of the complex phase,the amplitude change of the scattered wavefield cannot be recovered.Furthermore,in the presence of multi-arrivals phenomenon,the equivalent scattering source should be handled carefully due to the multi-directions of the wavefield.Further investigations should be done to improve the applicability of the proposed method.展开更多
Seismic events have limited time duration,vary with space/traveltime and interact with the local subsurface medium during propagation.Partitioning is a valu-able strategy for nonstationary seismic data analysis,proces...Seismic events have limited time duration,vary with space/traveltime and interact with the local subsurface medium during propagation.Partitioning is a valu-able strategy for nonstationary seismic data analysis,processing and wave propagation.It has the potential for sparse data representation,flexible data operation and highly accurate local wave propagation.Various local transforms are powerful tools for seismic data segmentation and representation.In this paper,a detailed description of a multi-dimensional local harmonic transformed domain wave propagation and imaging method is given.Using a tensor product of a Local Exponential Frame(LEF)vector as the time-frequency atom(a drumbeat)and a Local Cosine Basis(LCB)function as the space-wavenumber atom(a beamlet),we construct a time-frequency-space-wavenumber local atom-dreamlet,which is a combination of drumbeat and beamlet.The dreamlet atoms have limited spatial extension and temporal duration and constitute a complete set of frames,termed as dreamlet frames,to decompose and represent the wavefield.The dreamlet transform first partitions the wavefields using time-space supporting functions and then the data in each time-space blocks is repre-sented by local harmonic bases.The transformed wavefield is downward-continued by the dreamlet propagator,which is the dreamlet atom evolution weightings deduced from the phase-shift one-way propagator.The dreamlet imaging method is formulated with a local background propagator for large-scale medium propagation and com-bined with a local phase-screen correction for small-scale perturbations.The features of dreamlet migration and imaging include sparse seismic data representation,accurate wave propagation and the flexibility of localized time operations during migration.Numerical tests using Sigsbee 2A synthetic data set and real marine seismic data demonstrate the validity and accuracy of this method.With time-domain localization being involved,the dreamlet method can also be applied effectively to target-oriented migration and imaging.展开更多
In the contrast source inversion(CSI)method,the contrast sources(equiva-lent scattering sources)and the contrast(parameter perturbation)are iteratively recon-structed by an alternating optimization scheme.Traditionall...In the contrast source inversion(CSI)method,the contrast sources(equiva-lent scattering sources)and the contrast(parameter perturbation)are iteratively recon-structed by an alternating optimization scheme.Traditionally integral equation CSI method is formulated for transmission tomography using analytic Green’s function in homogeneous background.To extend the method to the case of reflection seismology,in this paper,we use WKBJ method to compute the Green’s function of depth dependent background media and the solving method of equations to initialize the contrast source of different frequencies,resulting in an efficient method to invert multi-frequency reflection seismic data–multi-frequency contrast source inversion method(MFCSI).Numerical results for the Marmousi model show that MFCSI method can obtain good results even when low frequency data are missing,in which case the conventional FWI fails.展开更多
Strong-scattering inversion or the inverse problem for strong scattering has different physical-mathematical foundations from the weak-scattering case.Seismic inversion based on wave equation for strong scattering can...Strong-scattering inversion or the inverse problem for strong scattering has different physical-mathematical foundations from the weak-scattering case.Seismic inversion based on wave equation for strong scattering cannot be directly solved by Newton’s local optimization method which is based on weak-nonlinear assumption.Here I try to illustrate the connection between the Schr̈odinger inverse scattering(inverse problem for Schr̈odinger equation)by GLM(Gel’fand-Levitan-Marchenko)the-ory and the direct envelope inversion(DEI)using reflection data.The difference between wave equation and Schr̈odinger equation is that the latter has a potential independent of frequency while the former has a frequency-square dependency in the potential.I also point out that the traditional GLM equation for potential inversion can only recover the high-wavenumber components of impedance profile.I propose to use the Schr̈odinger impedance equation for direct impedance inversion and introduce a singular impedance function which also corresponds to a singular potential for the reconstruction of impedance profile,including discontinuities and long-wavelength velocity structure.I will review the GLM theory and its application to impedance inversion including some numerical examples.Then I analyze the recently developed multi-scale direct envelope inversion(MS-DEI)and its connection to the inverse Schr̈odinger scattering.It is conceivable that the combination of strong-scattering inversion(inverse Schr̈odinger scattering)and weak-scattering inversion(local optimization based inversion)may create some inversion methods working for a whole range of inversion problems in geophysical exploration.展开更多
基金financial support jointly provided by the National Key R&D Program of China under contract number 2019YFC0605503Cthe Major Projects during the 14th Five-year Plan period under contract number 2021QNLM020001+2 种基金the National Outstanding Youth Science Foundation under contract number 41922028the Funds for Creative Research Groups of China under contract number 41821002the Major Projects of CNPC under contract number ZD2019-183-003。
文摘The parameter reconstruction of strong-scattering media is a challenge for conventional full waveform inversion(FWI).Direct envelope inversion(DEI)is an effective method for large-scale and strongscattering structures imaging without the need of low-frequency seismic data.However,the current DEI methods are all based on the acoustic approximation.Whereas,in real cases,seismic records are the combined effects of the subsurface multi-parameters.Therefore,the study of DEI in elastic media is necessary for the accurate inversion of strong-scattering structures,such as salt domes.In this paper,we propose an elastic direct envelope inversion(EDEI)method based on wave mode decomposition.We define the objective function of EDEI using multi-component seismic data and derive its gradient formulation.To reduce the coupling effects of multi-parameters,we introduce the wave mode decomposition method into the gradient calculation of EDEI.The update of Vp is primarily the contributions of decomposed P-waves.Two approaches on Vs gradient calculation are proposed,i.e.using the petrophysical relation and wave mode decomposition method.Finally,we test the proposed method on a layered salt model and the SEG/EAGE salt model.The results show that the proposed EDEI method can reconstruct reliable large-scale Vp and Vs models of strong-scattering salt structures.The successive elastic FWI can obtain high-precision inversion results of the strong-scattering salt model.The proposed method also has a good anti-noise performance in the moderate noise level.
文摘TheWKBJ solution for the one-waywave equations inmediawith smoothly varying velocity variation with depth,c(z),is reformulated from the principle of energy flux conservation for acoustic media.The formulation is then extended to general heterogeneous media with local angle domain methods by introducing the concepts of Transparent Boundary Condition(TBC)and Transparent Propagator(TP).The influence of the WKBJ correction on image amplitudes in seismic imaging,such as depth migration in exploration seismology,is investigated in both smoothly varying c(z)and general heterogeneous media.We also compare the effect of the propagator amplitude compensation with the effect of the acquisition aperture correction on the image amplitude.Numerical results in a smoothly varying c(z)medium demonstrate that theWKBJ correction significantly improves the one-way wave propagator amplitudes,which,after compensation,agree very well with those from the full wave equation method.Images for a point scatterer in a smoothly varying c(z)medium show that the WKBJ correction has some improvement on the image amplitude,though it is not very significant.The results in a general heterogeneous medium(2D SEG/EAGE salt model)show similar phenomena.When the acquisition aperture correction is applied,the image improves significantly in both the smoothly varying c(z)medium and the 2D SEG/EAGE saltmodel.The comparisons indicate that although theWKBJ compensation for propagator amplitude may be important for forward modeling(especially for wide-angle waves),its effect on the image amplitude in seismic imaging is much less noticeable compared with the acquisition aperture correction for migration with limited acquisition aperture in general heterogeneous media.
基金supported by National Natural Science Foundation of China(41604091,41704111,41774126)the great and special project(2016ZX05024-001,2016ZX05006-002).
文摘In the field of geophysics,although the first-order Rytov approximation is widely used,the higher-order approximation is seldom discussed.From both theo-retical analysis and numerical tests,the accumulated phase error introduced in the first-order Rytov approximation cannot be neglected in the presence of strong velocity perturbation.In this paper,we are focused on improving the phase accuracy of forward scattered wavefield,especially for the large-scale and strong velocity pertur-bation case.We develop an equivalent source method which can update the imaginary part of the complex phase iteratively,and the higher-order scattered wavefield can be approximated by multiplying the incident wavefield by the exponent of the imaginary part of the complex phase.Although the convergence of the proposed method has not been proved mathematically,numerical examples demonstrate that our method can produce an improved accuracy for traveltime(phase)prediction,even for strong perturbation media.However,due to the neglect of the real part of the complex phase,the amplitude change of the scattered wavefield cannot be recovered.Furthermore,in the presence of multi-arrivals phenomenon,the equivalent scattering source should be handled carefully due to the multi-directions of the wavefield.Further investigations should be done to improve the applicability of the proposed method.
基金supported by the National Natural Science Foundation of China(41604106,41674123,11871392)the Fundamental Research Funds for the Center Universities(xjj2018260)+1 种基金the China Postdoctoral Foundation(2016M600780)WTOPI(Wavelet Transform On Propagation and Imaging for seismic exploration)Project at University of California,Santa Cruz.
文摘Seismic events have limited time duration,vary with space/traveltime and interact with the local subsurface medium during propagation.Partitioning is a valu-able strategy for nonstationary seismic data analysis,processing and wave propagation.It has the potential for sparse data representation,flexible data operation and highly accurate local wave propagation.Various local transforms are powerful tools for seismic data segmentation and representation.In this paper,a detailed description of a multi-dimensional local harmonic transformed domain wave propagation and imaging method is given.Using a tensor product of a Local Exponential Frame(LEF)vector as the time-frequency atom(a drumbeat)and a Local Cosine Basis(LCB)function as the space-wavenumber atom(a beamlet),we construct a time-frequency-space-wavenumber local atom-dreamlet,which is a combination of drumbeat and beamlet.The dreamlet atoms have limited spatial extension and temporal duration and constitute a complete set of frames,termed as dreamlet frames,to decompose and represent the wavefield.The dreamlet transform first partitions the wavefields using time-space supporting functions and then the data in each time-space blocks is repre-sented by local harmonic bases.The transformed wavefield is downward-continued by the dreamlet propagator,which is the dreamlet atom evolution weightings deduced from the phase-shift one-way propagator.The dreamlet imaging method is formulated with a local background propagator for large-scale medium propagation and com-bined with a local phase-screen correction for small-scale perturbations.The features of dreamlet migration and imaging include sparse seismic data representation,accurate wave propagation and the flexibility of localized time operations during migration.Numerical tests using Sigsbee 2A synthetic data set and real marine seismic data demonstrate the validity and accuracy of this method.With time-domain localization being involved,the dreamlet method can also be applied effectively to target-oriented migration and imaging.
基金supported by the National Science and Technology of Major Projects of China(grant no.2016ZX05024-001-004)the WTOPI Research Consortium of Modeling and Imaging Laboratory,University of California Santa Cruz,US。
文摘In the contrast source inversion(CSI)method,the contrast sources(equiva-lent scattering sources)and the contrast(parameter perturbation)are iteratively recon-structed by an alternating optimization scheme.Traditionally integral equation CSI method is formulated for transmission tomography using analytic Green’s function in homogeneous background.To extend the method to the case of reflection seismology,in this paper,we use WKBJ method to compute the Green’s function of depth dependent background media and the solving method of equations to initialize the contrast source of different frequencies,resulting in an efficient method to invert multi-frequency reflection seismic data–multi-frequency contrast source inversion method(MFCSI).Numerical results for the Marmousi model show that MFCSI method can obtain good results even when low frequency data are missing,in which case the conventional FWI fails.
文摘Strong-scattering inversion or the inverse problem for strong scattering has different physical-mathematical foundations from the weak-scattering case.Seismic inversion based on wave equation for strong scattering cannot be directly solved by Newton’s local optimization method which is based on weak-nonlinear assumption.Here I try to illustrate the connection between the Schr̈odinger inverse scattering(inverse problem for Schr̈odinger equation)by GLM(Gel’fand-Levitan-Marchenko)the-ory and the direct envelope inversion(DEI)using reflection data.The difference between wave equation and Schr̈odinger equation is that the latter has a potential independent of frequency while the former has a frequency-square dependency in the potential.I also point out that the traditional GLM equation for potential inversion can only recover the high-wavenumber components of impedance profile.I propose to use the Schr̈odinger impedance equation for direct impedance inversion and introduce a singular impedance function which also corresponds to a singular potential for the reconstruction of impedance profile,including discontinuities and long-wavelength velocity structure.I will review the GLM theory and its application to impedance inversion including some numerical examples.Then I analyze the recently developed multi-scale direct envelope inversion(MS-DEI)and its connection to the inverse Schr̈odinger scattering.It is conceivable that the combination of strong-scattering inversion(inverse Schr̈odinger scattering)and weak-scattering inversion(local optimization based inversion)may create some inversion methods working for a whole range of inversion problems in geophysical exploration.
