A simulation method for the computation of the effective P-wave velocity in heterogeneous rocks

We propose a set of numerical methods for the computation of the frequency-dependent effective primary wave velocity of heterogeneous rocks. We assume the rocks’ internal microstructure is given by micro-computed tomography images. In the low/medium frequency regime, we propose to solve the acoustic equation in the frequency domain by a finite element method (FEM). We employ a perfectly matched layer to truncate the computational domain and we show the need to repeat the domain a sufficient number of times to obtain accurate results. To make this problem computationally tractable, we equip the FEM with non-fitting meshes and we precompute multiple blocks of the stiffness matrix. In the high-frequency range, we solve the eikonal equation with a fast marching method. Numerical results confirm the validity of the proposed methods and illustrate the effect of density, porosity, and the size and distribution of the pores on the effective compressional wave velocity.