Generalized impedance blocky inversion based on analytic solution to wave equation

LI Yuanqiang1,2,3 HUO Zhizhou4 LI Jingye1,2,3 CHEN Xiaohong1,2,3 ZHANG Jian1,2,3 GENG Weiheng1,2,3

(1.College of Geophysics, China University of Petroleum (Beijing), Beijing 102249)
(2.State Key Laboratory of Petroleum Resources and Prospecting, Beijing 102249)
(3.National Engineering Laboratory for Offshore Oil Exploration, Beijing 102249)
(4.Sinopec Petroleum Exploration and Production Research Institute, Beijing 100083)
【Knowledge Link】Snell's law

【Abstract】Since the pre-processing of pre-stack gathers is based on the assumption of acoustic media in many cases, the gathers tend to be with more acoustic amplitude variation with offset (AVO) features. In addition, density inversion is unstable. This paper proposes a generalized impedance blocky inversion based on analytic solution to acoustic wave equation. The generalized acoustic impedance is inverted by a partially stacked profile, which varies with the angle of incidence; on this basis, more accurate velocity and stable density are extracted. In the conventional impedance inversion method, transmission loss and interlayer multiples are neglected. On the basis of the recursive formula of derivation, the one-dimensional acoustic wave equation is solved analytically to obtain the full-wavefield responses at different incident angles, and the Fréchet derivatives are analytically derived for gradient-descent inversion algorithm. Most of the inversion methods are based on smoothing constraints, which fundamentally lead to unfocused boundaries for inversion results. For the higher resolution of inversion results, blocky constraints can be introduced based on the Bayesian inference framework for stable high-resolution inversion results. According to the above theory, we first use model data to analyze the influence of the incompleteness of the forward method on seismic responses to verify the validity of the inversion method and extract the accurate velocity and density. Then the ability to characterize the boundary for blocky constraints is tested by adding noises. Both model and actual data prove that the inversion results from the new method have higher resolution. The boundary is clearer, and the extracted velocity and density profiles are stable and accurate.

【Keywords】 analytical solution; nonlinear; generalized impedance; blocky constraint; wave equation inversion;


【Funds】 National Science and Technology Major Project (2017ZX05049-002-004) National Natural Science Foundation of China (41772419) National Natural Science Foundation of China (41774131) Project of China University of Petroleum (2462018qzdx01)

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This Article


CN: 13-1095/TE

Vol 55, No. 05, Pages 1073-1083+934-935

October 2020


Article Outline



  • 0 Introduction
  • 1 Methodology
  • 2 Numerical simulation
  • 3 Actual data test
  • 4 Conclusion and discussion
  • References