ANNALS OF GEOPHYSICS,60, 6, S0664, 2017; doi: 10.4401/ag-7450 Computation of wave attenuation and dispersion, by using quasi-static finite difference modeling method in frequency domain Qazi Adnan Ahmad 1,* , Guochen Wu 2 , Wu Jianlu 3 1 China University of Petroleum (East China), School of Geoscienc, Qingdao, Shandong, China 2 China University of Petroleum (East China), College of Geo Resources and Information, Department of Geophysics Dong Ying, Shan Dong, China 3 China University of Petroleum Huadong, Dongying, Shandong, China Article history Received May 21, 2017; accepted October 9, 2017. Subject classification: Exploration geophysics; Seismic methods; Seismology; Waves and wave analysis; measurements and monitoring; Mathematical Geophysics. S0664 ABSTRACT In seismology, seismic numerical modeling is regarded as a useful tool to interpret seismic responses. The presence of sub- surface heterogeneities at various scales can lead to attenua- tion and dispersion during seismic wave propagation. In ongoing global research, the study of wave attenuation and velocity dispersion due to wave induced fluid flow (WIFF) at mesoscopic scale become the subject of great interest. Al- though, seismic modeling technique is efficient in estimating wave attenuation and velocity dispersion due to wave induced fluid flow (WIFF) at mesoscopic scale. It is possible to further improve the efficiency to accurately predict wave attenuation and velocity dispersion at mesoscopic scale. To achieve this goal, a quasi-static finite difference modeling method in fre- quency domain is implemented to estimate frequency depen- dent P-wave modulus of mesoscopic heterogeneous porous media. The estimated complex and frequency dependent P- wave modulus will assist to estimate frequency dependent wave attenuation and velocity dispersion within a saturated porous media exhibiting mesoscopic heterogeneities. The pro- posed quasi-static finite difference modeling method is further validated with theoretically predicted high and low-frequency limits and also with the analytical solution of White’s 1-D model which is for rock saturated with two immiscible fluids creating heterogeneity at mesoscopic scale. Furthermore, the proposed method is further extended to rock saturated with three phase fluids exhibiting heterogeneity at mesoscopic scale. Subsequently, seismic wave attenuation (inverse quality factor Q-1) and the effects on P-wave velocity in 1-D models with dif- ferent patch size under same gas saturation were also com- puted. Our proposed quasi-static method is simple to be im- plemented by the computing scheme of parallelization and have a potential to extend it for two-dimensional case com- paratively in a flexible way. 1. Introduction The main challenge we are facing in oil and gas ex- ploration is the estimation of effects on wave character- istics due to the presence of multiscale subsurface heterogeneities. During wave propagation, the hetero- geneous nature of earth subsurface results into pressure gradient at different spatial scale. Consequently, the re- sulted pressured gradient will accelerate the fluid to flow (at different scales) from high pressured zone to com- paratively low-pressure zone. The wave induced fluid flow (WIFF) at wavelength scale is named as macro- scopic, whereas, at pore scale, it is termed as micro- scopic, on the other hand, at a scale much smaller than wavelength but larger than the pores scale it is named as mesoscopic fluid flow [Muller et al. 2010]. The influences of fluids on seismic responses re- main a key topic among researchers. Biot’s [M. A. Biot 1956, M. A. Biot 1956] classical theory of poroelasticity led the investigation regarding wave attenuation and ve- locity dispersion in a saturated porous medium. In his theory, macroscopic scale heterogeneities due to pres- ence of single phase fluid were outlined as predicted cause of wave attenuation and velocity dispersion. Wave propagation through such macroscopic heterogeneous media creates pressure gradient at wavelength scale,