Regularized Full Waveform Inversion Of Acoustic Wave Equation In Frequency Domai

Full waveform inversion(FWI)fully utilizes the amplitude,phase,and other information of seismic waves,and it can thus provide high accuracy of subsurface structure.However,FWI is a nonlinear and ill-posed inverse problem,which leads to the nonuniqueness of its reconstruction results.This means that the same seismic record can correspond to different physical parameter models.To obtain a unique and stable solution,regularization methods are necessary.In this thesis,studies are conducted to address the issues of ill-posedness and low reconstruction accuracy for frequency domain acoustic wave equation FWI problems.The total variation(TV)regularization method has the property of maintaining the discontinuity of the solution.However,it often results in stair-casing artifacts in slanted regions,such as those with segmented linearity.To address this problem,a new method called rotation TV regularization has been proposed to reduce the stair-casing phenomenon in TV regularization reconstruction results.In order to take into account the discontinuities in different directions,a hybrid regularization method is proposed to take advantage of both rotational TV and TV regularization methods.Numerical experiments based on the Sigsbee and Marmousi2 models demonstrate the effectiveness of the proposed method.The second-order TV(TV2)regularization method can attenuate the stair-casing artifacts while retaining the edge information.However,compared with the traditional TV regularization method,the TV2 regularization method is inferior to the TV regularization method in terms of computational effort and reconstruction efficiency.In this thesis,we propose a hybrid first-order and second-order TV regularization methods by combining TV regularization and TV2 regularization methods.Numerical experiments based on the Marmousi2 and Sigsbee models are conducted to verify the effectiveness of this hybrid regularization method in dealing with the FWI problem where the model parameters have skewed angles.The truncated Newton method based on the linear conjugate gradient method is particularly suitable for dealing with multiple scattering wavefields and high velocity ratio FWI problems.However,when the initial value is far from the minimum point or the medium model is complex,the ill-posedness of the objective function can cause the corresponding Hessian matrix to be non-positive definite.As a result,it becomes challenging to leverage the negative eigenvalue information of the Hessian matrix,leading to the algorithm getting stuck in a local extreme value neighborhood.In this thesis,we introduce the TV regularization for ill-posed FWI problems,and the truncated Newton algorithm based on MINRES-QLP to address non-positive definite Hessian matrices of the objective function.Furthermore,we propose a technique to enable rapid computation of the second-order gradient and vector for the first-and second-order gradients of the TV regularization term.This approach is based on storing and processing the sparse matrix utilizing the Csparse library,taking into account that the majority of its components correspond to zero elements.We verify the efficiency of the second-order optimization method through numerical experiments.