Finite-difference modeling of seismic wave propagation in fractured media

We investigate the application of the method of finite-differences to the modeling of seismic wave propagation in media in non-welded contact. Traditionally, two alternate approaches to finite-differencing have been used: the homogeneous and the heterogeneous. In earlier work, non-welded contact has been modeled using only the heterogeneous approach. In the present study we investigate the application of the homogeneous approach to this problem.; Using a generalized version of the homogeneous approach, we first develop a finite-difference scheme for modeling SH wave propagation in two-dimensional media in non-welded contact, and analyze its numerical properties. We then develop an alternate SH wave scheme using the heterogeneous approach. The homogeneous and heterogeneous schemes are shown to have the same structure, differing only in the expressions used for effective elastic moduli. Neither scheme appears in the existing literature.; Next we use the generalized homogeneous approach to develop a finite-difference scheme for modeling P-SV wave propagation. The P-SV case presents a number of features absent from the SH case, and the homogeneous approach must be modified in important ways to allow its application to the P-SV problem. In previous work, the homogeneous approach had been used only to model P-SV wave propagation across isolated interfaces in welded contact. We derive a scheme capable of modeling P-SV wave propagation in arbitrarily inhomogeneous two-dimensional media. In the P-SV case, the difference between the homogeneous and heterogeneous schemes is no longer simply characterized by the expressions used for effective elastic moduli. Finally we use the generalized homogeneous approach to develop a finite-difference scheme for modeling P-SV wave propagation in two-dimensional media in non-welded contact, and analyze its stability properties.; We present numerical examples for both the SH and P-SV cases. We use the simpler SH case to investigate properties of the finite-difference schemes through numerical experiments. The synthetic seismograms also serve to illustrate physical effects associated with non-welded contact.