1 Center for Computational and Exploration Geophysics, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China 2 State Key Laboratory of Geodesy and Earth’s Dynamics, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China
Seismic inversion with generalized Radon transform based on local second-order approximation of scattered field in acoustic media
1 Center for Computational and Exploration Geophysics, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China 2 State Key Laboratory of Geodesy and Earth’s Dynamics, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China
摘要Sound velocity inversion problem based on scattering theory is formulated in terms of a nonlinear integral equation associated with scattered field. Because of its nonlinearity, in practice, linearization algorisms (Born/single scattering approximation) are widely used to obtain an approximate inversion solution. However, the linearized strategy is not congruent with seismic wave propagation mechanics in strong perturbation (heterogeneous) medium. In order to partially dispense with the weak perturbation assumption of the Born approximation, we present a new approach from the following two steps: firstly, to handle the forward scattering by taking into account the secondorder Born approximation, which is related to generalized Radon transform (GRT) about quadratic scattering potential; then to derive a nonlinear quadratic inversion formula by resorting to inverse GRT. In our formulation, there is a significant quadratic term regarding scattering potential, and it can provide an amplitude correction for inversion results beyond standard linear inversion. The numerical experiments demonstrate that the linear single scattering inversion is only good in amplitude for relative velocity perturbation (δc/c0) of background media up to 10 %, and its inversion errors are unacceptable for the perturbation beyond 10 %. In contrast, the quadratic inversion can give more accurate amplitude-preserved recovery for the perturbation up to 40 %. Our inversion scheme is able to manage double scattering effects by estimating a transmission factor from an integral over a small area, and therefore, only a small portion of computational time is added to the original linear migration/inversion process.
Abstract：Sound velocity inversion problem based on scattering theory is formulated in terms of a nonlinear integral equation associated with scattered field. Because of its nonlinearity, in practice, linearization algorisms (Born/single scattering approximation) are widely used to obtain an approximate inversion solution. However, the linearized strategy is not congruent with seismic wave propagation mechanics in strong perturbation (heterogeneous) medium. In order to partially dispense with the weak perturbation assumption of the Born approximation, we present a new approach from the following two steps: firstly, to handle the forward scattering by taking into account the secondorder Born approximation, which is related to generalized Radon transform (GRT) about quadratic scattering potential; then to derive a nonlinear quadratic inversion formula by resorting to inverse GRT. In our formulation, there is a significant quadratic term regarding scattering potential, and it can provide an amplitude correction for inversion results beyond standard linear inversion. The numerical experiments demonstrate that the linear single scattering inversion is only good in amplitude for relative velocity perturbation (δc/c0) of background media up to 10 %, and its inversion errors are unacceptable for the perturbation beyond 10 %. In contrast, the quadratic inversion can give more accurate amplitude-preserved recovery for the perturbation up to 40 %. Our inversion scheme is able to manage double scattering effects by estimating a transmission factor from an integral over a small area, and therefore, only a small portion of computational time is added to the original linear migration/inversion process.
基金资助:Innovation Project of Chinese Academy of Sciences and State Key Laboratory of Marine Geology, Tongji University (No. MGK1408).
通讯作者:
Weijian Mao
E-mail: wjmao@whigg.ac.cn
引用本文:
Wei Ouyang, Weijian Mao, Xuelei Li, Wuqun Li. Seismic inversion with generalized Radon transform based on local second-order approximation of scattered field in acoustic media[J]. 《地震学报》英文版, 2014, 27(4): 433-439.
Wei Ouyang, Weijian Mao, Xuelei Li, Wuqun Li. Seismic inversion with generalized Radon transform based on local second-order approximation of scattered field in acoustic media. Earthquake Science, 2014, 27(4): 433-439.
