Numerical modelling of the propagation of diffusive-viscous waves in a fluid-saturated reservoir using finite volume method

Numerical modelling of seismic waves is a method for simulating the propagation of waves in the Earth. The objective is to make a prediction of the seismogram when given an assumed structure of the subsurface. The diffusive-viscous theory can be used to describe the attenuation of seismic waves propagating in fluid-saturated rocks, and to study the relationship between the frequency dependence of reflections and fluid-saturation in a porous medium, since the generally used theories such as acoustic, elastic theory, among others, are unable to effectively characterize the subsurface of the earth. We derive the second-order Runge-Kutta finite-volume scheme for the diffusive-viscous wave equation and based on this scheme, we simulate the propagation of seismic waves in a fluid-saturated medium. The numerical results indicate that the propagating waves in the fluid-saturated media attenuate greatly when compared with those of the acoustic scenario.