Modelling the effects of diffusive-viscous waves in a 3-D fluid-saturated media using two numerical approaches

Abstract

Summary The accurate numerical modelling of 3-D seismic wave propagation is essential in understanding details to seismic wavefields which are, observed on regional and global scales on the Earth’s surface. The diffusive-viscous wave (DVW) equation was proposed to study the connection between fluid saturation and frequency dependence of reflections and to characterise the attenuation property of the seismic wave in a fluid-saturated medium. The attenuation of DVW is primarily described by the Active Attenuation Parameters (AAP) in the equation. It is, therefore, imperative to acquire these parameters and to additionally specify the characteristics of the DVW. In this paper, Quality Factor, Q is used to obtain the AAP, and they are compared to those of the visco-acoustic wave. We further derive the 3-D numerical schemes based on a second order accurate finite volume scheme with a second order Runger-Kutta approximation for the time discretisation and a fourth order accurate finite difference scheme with a fourth order Runger-Kutta approximation for the time discretisation. We then simulate the propagation of seismic waves in a 3-D fluid-saturated medium based on the derived schemes. The numerical results indicate stronger attenuation when compared to the visco-acoustic case.