Study On Methodology Of Pre-stack Seismic Inversion Based On Scattering Matrix Decomposition

Pre-stack seismic inversion is the core technology of reservoir prediction and fluid identification.With the development of oil and gas exploration,the inversion accuracy of medium and long offset seismic data needs to be improved,and the complex interface with strong medium parameter variations also increases the difficulty of inversion.In this paper,the propagation characteristic of far-field plane wave is studied,and the reflection coefficient approximation with strong adaptability and high accuracy is further constructed.The response of seismic wave to parameters variation can be described more accurately.Pre-stack seismic inversion method based on the approximation is further studied,which can improve the utilization of seismic data and inversion accuracy.It has theoretical significance and practical value for the exploration of complex oil and gas reservoirs in middle and deep strata.The propagation characteristic of far-field plane wave at the elastic medium interface are the theoretical basis of pre-stack seismic forward and inversion.The Zoeppritz equation,which represents the propagation characteristics of far-field plane P-wave,can be obtained based on the conditions of continuous stress and displacement at the interface only considering the case of P-wave source.It is difficult to characterize the reflection and transmission characteristics of real multi-interfaces because of the complex form and the unclear physical meaning of the equation.In order to improve the stability and efficiency of forward and inversion calculation,the first-order linear approximation of reflection and transmission coefficient can be derived based on the medium decomposition theory and seismic scattering principle,under the assumption of small angle incidence and weak medium variations.And the approximation for different elastic parameters,which suitable for different exploration requirements can be further obtained.The pre-stack seismic inversion method based on linear approximation equation is more suitable for the conventional reservoirs because only the influence of linear parameters perturbation is considered.Characterizing the influence of parameters higher order perturbations on seismic wave propagation is an effective way to improve the accuracy of approximate equation of reflection coefficient.In this paper,the scattering matrix is derived based on the P-SV plane wave incidence and scattering complete system.The scattering matrix can be decomposed by the perturbation theory,and the perturbations of medium parameters are expressed as matrices.A simplified theoretical method for deriving higher order approximation of reflection and transmission coefficients is given by making full use of the relationship between parameter matrices.A more accurate and complete second-order approximation of P-wave reflection coefficient is further derived here.Compared with the linear approximation and the second-order approximation obtained by predecessors,the second-order terms of elastic parameter perturbations become more complete and the S-wave factor are added.The situations of medium and high angle incidence and strong medium variations are considered,limitation of linear approximation can be overcome,and the accuracy get improved.And it's more sensitive to the parameters variations.This approximation of reflection coefficients lays a foundation for the accurate exploration of complex reservoirs in middle and deep strata.Building forward operator based on the second order approximation equation and establishing non-linear pre-stack seismic inversion method are important means to improve the prediction accuracy of complex reservoirs in the deep strata.Based on the generalized linear idea,a linear forward operator of the second order approximation equation is constructed in this paper.Combining with Bayesian inversion theory,parameter prior distribution and noise likelihood function are introduced,and parameter inversion is carried out by solving maximum posterior probability distribution,which reduces the uncertainty of inversion problem.The model test shows that the inversion method based on second order approximation is stable,and has anti-noise ability and higher accuracy.The inversion results of actual data also improve the reliability of the inversion method used in the prediction and fluid identification of complex reservoirs in middle and deep strata,and the accuracy of describing complex sedimentary structures,which verifies the value in practical application.