2-D Frequency Acoustic Wave Equation Modeling And Fullwave Inversion

Frequency-domain wave equation modeling is the foundation of FWI(full waveform inversion) and it’s very important in the numerical simulation of seismic wave. The advantage of frequency-domain modeling over time-domain modeling is that multi-experiment seismic data can be simulated economically and it has no numerical dispersion, modeling the effects of attenuation is more flexible in the frequency domain. Time-domain modeling can be implemented and has higher precision, but this method exists truncation errors which grows while the increased amount of computation constantly accumulate. Compared to time-domain modeling, frequency-domain modeling solving the wave equation on all grid points integrally, every point has its calculation errors. Frequency-domain wave equation modeling can be accelerated by CPU parallel technology because triangular factors of the impedance matrix of the same frequency in different multi-experiment seismic data is same, which Improves computational efficiency highly. Efficiency of Frequency-domain modeling depends largely on the speed of decomposition of the coefficient matrix,The efficiency of decomposition of the coefficient matrix depends on bandwidth of matrix. Minimize the bandwidth has very important sense in the frequency domain while numerical solution is effective.The effectiveness and practicality of frequency FDTD(finite-difference frequencydomain) method can be verified by conducting two-dimensional acoustic wave equation of frequency space FDTD simulation studies, and the studies is preparation for FWI. Firstly, the author briefly describes the development and the research status of frequency-domain wave equation numerical modeling. Secondly, discusses the principles of finite difference method, derives the optimal 9-point differential acoustic wave frequency-domain two-dimensional finite difference scheme, solves the implicit expressions of meshed equation and investigates process of coefficient matrix by using the steepest method. Thirdly, three acoustic(homogenous acoustic medium, twolayered medium model and Marmousi model) wave field tentative calculation are performed using the Matlab programming language. Finally, achieve the optimal 9-point frequency-domain full waveform inversion in two-layered medium model and Marmousi model.In view of computational efficiency in the actual work, this paper uses a compressed sparse column storage method to story the sparse matrix and CPU parallel processing technology to improve the computational efficiency. On this basis, we achieve frequency-domain wave equation modeling and FWI algorithm and validate it.