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
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.
