Finite‐difference modeling of faults and fractures

Abstract

For the purposes of seismic propagation, a slip fault may be regarded as a surface across which the displacement caused by a seismic wave is discontinuous while the stress traction remains continuous. The simplest assumption is that this slip and the stress traction are linearly related. Such a linear slip interface condition is easily modeled when the fault is parallel to the finite‐difference grid, but is more difficult to do for arbitrary nonplanar fault surfaces. To handle such situations we introduce equivalent medium theory to model material behavior in the cells of the finite‐ difference grid intersected by the fault. Virtually identical results were obtained from modeling the fault by (1) an explicit slip interface condition (fault parallel to the grid) and (2) using the equivalent medium theory when the finite‐difference grid was rotated relative to the fault and receiver array. No additional computation time is needed except for the preprocessing required to find the relevant cells and their associated moduli. The formulation is sufficiently general to include faults in and between arbitrary anisotropic materials with slip properties that vary as a function of position.