Simulation of seismic wave propagation in poroelastic media using vectorized Biot’s equations: an application to a CO$$_{2}$$ sequestration monitoring case

Abstract

Wave propagation through porous media allows us to understand the response and interaction that occur between the elastic rock matrix and the fluid. This interaction has been described by Biot in his theory of poroelasticity. Seismic wave simulation using Biot’s formulations is computationally expensive when compared with the acoustic and elastic cases. This computational burden can be reduced by reformulating the numerical derivative operators to improve the efficiency. To achieve this, we used a staggered-grid finite difference operator to discretize 2D velocity stress equations as given by Biot’s theory. A vectorized derivative is applied on the staggered grid by shifting the coordinates. The reformulated equations were applied to compute the seismic response of a reservoir, where $$\hbox {CO}_2$$ is being injected and the effect of injected $$\hbox {CO}_2$$ in the formation is clearly seen in the synthetic data generated. The algorithm was coded in Python and to test its efficiency, the simulation run-time was compared for both serial and vectorized equations, and the speed-up ratio was calculated. Our results show a decrease in the simulation run-time for the vectorized execution with over a factor of a hundred percent (100%). We further observed that the amplitudes of the events increase with an increase in $$\hbox {CO}_2$$ saturation in the formation. This matches well with the real data.