Q full-waveform inversion based on the viscoacoustic equation*
Wang En-Jiang, Liu Yang, Ji Yu-Xin, Chen Tian-Sheng, and Liu Tao
1. State Key Laboratory of Shale Oil and Gas Enrichment Mechanisms and Effective Development, Beijing, 100083.
2. School of Earth Science and Engineering, Hohai University, Nanjing, 210098.
3. College of Geophysics and Information Engineering, China University of Petroleum (Beijing), Beijing, 102249.
4. Sinopec Petroleum Exploration and Production Research Institute, Beijing, 100083.
5. Sinopec Key Laboratory of Multiwave Seismic Technology, Beijing, 100083.
Abstract：
Presently, most full-waveform inversion methods are developed for elastic media and ignore the effect of attenuation. The calculation of the quality factor Q is based on velocity parameter inversion under the assumption of a given Q-model that is obtained by tomographic inversion. However, the resolution of the latter is low and cannot reflect the amplitude attenuation and phase distortion during wave propagation in viscoelastic media. Thus, a Q waveform inversion method is proposed. First, we use standard linear body theory to describe attenuation and then we derive the simplified viscoacoustic equation that characterizes amplitude attenuation and phase distortion. In comparison with conventional equations, the simplified equation involves no memory variables and therefore requires less memory during computation. Moreover, the implementations of the attenuation compensation are easier. The adjoint equation and the corresponding gradient equation with respect to either L2-norm or the zero-lag cross-correlation objective function are then derived and the regularization strategy for overcoming the instability during numerical solution of the adjoint equation is proposed. The Q waveform inversion is developed using the limited-memory Broyden–Fletcher– Goldfarb–Shanno (L-BFGS) iteration method for known velocity. To alleviate the dependence of the waveform inversion on the initial model and overcome cycle skipping to some extent, we adopt multiscale analysis. Furthermore, anti-noise property and double-parameter inversion are assessed based on the results of numerical modeling.
2019, Vol. 16 
