Modeling of elastic waves in fractured media using the rotated staggered finite‐difference grid

Abstract

Summary The modeling of elastic waves with an explicit Finite Difference (FD) scheme on a staggered grid causes instability problems when the medium possesses high contrast discontinuities (cracks). We have derived a rotated staggered grid in 2D and 3D where all medium parameters are defined at appropriate positions within an elementary cell for the essential operations. Using this modified grid it is possible to simulate the propagation of elastic waves in a medium containing cracks, pores or free surfaces without applying boundary conditions. In this paper we show the von Neumann stability criterion and the dispersion error for the rotated staggered grid. Additionally, we show a synthetic example to demonstrate the rotated staggered grid in modeling fractured media.