Elastic finite-difference modeling in TTI media with fracture zones

Abstract

To simulate wave propagation in a tilted transversely isotropic (TTI) medium with a tilting symmetry axis of anisotropy, we develop 2D and 3D elastic forward modeling algorithms. In these algorithms, we use the staggered-grid finite-difference method which has fourth-order accuracy in space and second-order accuracy in time domain. Through comparisons of displacements obtained from our algorithms not only with analytical solutions but also with finite element solutions, we are able to validate that the free surface conditions operate appropriately and elastic waves propagate correctly. In order to handle the artificial boundary reflections efficiently, we also implement convolutional perfectly matched layer (CPML) absorbing boundaries in our algorithms. The CPML sufficiently attenuates energy at the grazing incidence by modifying the damping profile of the PML boundary. At the free surface, the numerical results show good agreement with analytical solutions not only for body waves but also for the Rayleigh wave which has strong amplitude along the surface both 2D and 3D cases. Moreover, we demonstrate the elastic wave propagation and efficiency of CPML for a homogeneous TI medium. Only using few grid points to the CPML regions, the artificial reflections are successfully suppressed and the energy of the boundary reflection back into the effective modeling area is significantly decayed. In addition, through parallelization of the model space in z-direction with message passing interface (MPI), we can dramatically reduce the computation time and required memory in 3D case. Using developed 2D and 3D algorithms, we can exactly simulate the elastic wave propagation in the model with complex anisotropic parameters of fracture zones.