A rotated staggered grid finite-difference with the absorbing boundary condition of a perfectly matched layer

A rotated staggered grid finite-difference (FD) method with a perfectly matched layer (PML) method is proposed for numerically solving elastic wave equations in inhomogeneous elastic and poroelastic media. Compared with a standard staggered-grid FD, the former has the advantage over the latter in that its physical variables need only to be defined at two locations. In the rotated staggered grid, stress and strain components (or particle velocity and displacement components) are defined at elementary cell centers, and the velocity or displacement components (or the stress and strain components) are defined at vertexes. In this way, no elastic moduli need to be interpolated or averaged. Numerical results from the proposed method have been compared with the standard staggered FD method. The results are in good agreement with each other. Our numerical results show that the proposed algorithm can handle much stronger impedance contrast. This is especially true when simulating fractured medium filled with fluids such as water or gas without giving special treatment. On the other hand, the implemented PML absorbing boundary condition works well in efficiently reducing reflected waves from the artificial interfaces. It generates almost no reflection at artificial interfaces with a boundary of PML thickness of half a wavelength. Our theoretical analysis and numerical tests proved that the PML absorbing algorithm in the rotated staggered grid is almost identical to those in the standard staggered grid. In this paper, we also presented all of the formulations of the PML implementation and modeling examples in elastic, poroelastic, and anisotropic media.