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.

我们提出了一套数值方法，用于计算非均质岩石的频率相关有效一次波速。我们假设岩石的内部微观结构是由显微计算机断层扫描图像给出的。在中低频率范围内，我们建议通过有限元方法（FEM）求解频域中的声学方程。我们使用一个完美匹配的层来截断计算域，并且表明需要重复该域足够的次数才能获得准确的结果。为了使该问题在计算上易于处理，我们为FEM配备了非拟合网格，并预先计算了刚度矩阵的多个块。在高频范围内，我们使用快速行进法求解本征方程。