Time domain modeling of seismic waves in visco-acoustic media with variable density and topography

Seismic wave propagation modeling, one of the key steps in seismic imaging, plays an important role in oil geomechanics studies based on subsurface non-destructive imaging. Two of the most accurate non-destructive seismic imaging methods are full waveform inversion (FWI), and least squares reverse time migration (LSRTM). Since the general approach of these methods to recover geomechanical properties is based on minimization of data residuals, an accurate forward modeling operator makes the inversion results independent from the modeling errors. Seismic modeling is based on the numerical solution of the partial differential equation of wave propagation using methods such as finite difference or finite element. In the simplest case, this equation is solved under conditions of constant density and for an acoustic medium. Different methods have been conducted to develop modeling methods by considering real conditions. One of these considerations, which has a significant impact in geomechanics onshore studies, is the topography. In this research, we used the immersion boundary method to solve the wave equation in the time domain in environments with complex topography, and we developed this method for wave propagation in a visco-acoustic medium with variable density. In visco-acoustic environments, including the effect of absorption (dispersion and dissipation) in modeling, requires the complex wave equation, which is challenging to solve in the time domain. In this study, a novel method is used to incorporate the effect of absorption in wave propagation in the time domain. Finally, the performance of the proposed method is investigated by modeling the wave propagation in visco-acoustic models with complex topography and variable density.