Methodologies Of Sparse Regularized Seismic Inversion

Seismic inversion method is the predominant method for us to estimate the elastic parameters of sublayer from seismic data.In general,seismic inversion problem is typically illposed in the sense that slight noise contained in the observed data will lead to enormous changes in the estimated parameters.Another problem of seismic inversion says that there are numerous models fitting the data adequately because the seismic data are band limited.It is common to add additional information to stabilize the inversion process and to reduce the number of feasible solutions.This is generally referred to as regularization in which Tikhonov regularization is the most popular regularization method.However,we may often achieve the smoothed solutions by using Tikhonov regularization,while the interfaces of sublayers are sparse.This dissertation concentrates on the sparsity and the sparse representation of elastic parameters of sublayers which can be utilized as the regularization function.Different types of sparse regularized seismic inversion methods are proposed for particular geology and geophysics problems,which aims at improving the resolution,stability and lateral continuity of inversion incorporating the sparsity of reflectivities itself,sparsity in wedge dictionary,structure sparsity and sparsity in transform domain.The sparseness the reflection coefficients train can be achieved by fixing the number of reflectors and using global optimization algorithms to estimate their amplitudes.This dissertation utilizes L0 norm to regularize the seismic inverse problem.Orthogonal matching pursuit algorithm(OMP)algorithm is utilized to seek the reflectivity locations first and then to re-estiamte the amplitudes.The inversion results of post-stack and pre-stack inversion using the proposed OMP-based seismic inversion method have an obvious characteristics of the layer boundary and better resolution with respect to conventional seismic inversion.The top and bottom reflection coefficient of a reflector can be sparse represented by dipole decomposition,which was applied into seismic inversion called basis pursuit inversion(BPI).However,there is no low frequency information contained in the results of BPI,which often results in discontinuity in lateral.In order to supplement the low frequency,improve the lateral continuity and the stability of basis pursuit(BPI),the low frequency model(LFM)regularized BPI method is proposed to estimate the sublayers' elastic parameters,such as P/S-wave velocity,Young's modulus,Poisson ratio and so on.The LFM regularized BPI is being taken to estimate the elastic impedance for deep reservoir because of its' stability.This dissertation derived a novel two-parameter seismic reflection coefficient and elastic impedance function in terms of fluid/pore term and shear modulus and developed the method of the deep reservoir fluids identification based on LFM regularized BPI for elastic impedance.The two methods proposed above only take the sparsity of the reflectivities vector into consideration not the sparsity of structural features of the reflectivities.We group the reflectivity and utilize the group sparsity to constraint the inverse problem.For horizontally layered media,the laterally position of the reflection should be the same;the post-stack inverse problem is regularized by the mixed norm,L2,1 norm.Different elastic parameters have the exact same sparsity in terms of reflections.Therefore,this dissertation suggests using the modified Cauchy distribution to characterize the group sparsity,and obtain the MAP solution under Bayesian inference.The group sparsity regularized post-stack multi-trace seismic inversion improves the lateral continuity and resolution of the estimation.The group sparsity regularized pre-strack AVO inversion ensures that different elastic parameters estimates have the same consistent stratigraphic structural features.The reflectivity-based inversion method involves estimating a set of sparse reflection coefficients from the seismic data,constraining these reflection coefficients with the model and then inverting the coefficients produce the elastic parameters which produces superior results on a sparse model but produces less detailed results than model-based inversion.Total variation(TV)regularization is used to ensure the parameters are blocky,and the boundary constraint is taken into consideration to make sure the inversion is effective and stable.A hybrid split Bregman iteration bounded variables least squares(SBI-BVLS)algorithm is intended to solve this blocky inverse problem.However,lateral coherency of the parameter's profile may be deteriorated since the inversion method is solved on a trace-by-trace basis.To gain desired results with good lateral continuity,sparsity of multi-scale and multi-dirction sparse transformation is used for multi-traces inversion.The sparse transformation and TV norm joint sparsity regularized seismic inversion is therefore proposed to preserve the edge of the layer and enhance the lateral coherency.All these methods proposed in this dissertation are tested by designed model.Furthermore,this dissertation explores the application of these methods in field data.