Elastic wave modelling by an integrated finite difference method

We have developed a finite difference method for modelling the elastic wave equation in the time domain, based on integrating the elastic parameters. In this method, we adopt the strategy of integrating the elastic parameters over a limited space; so, it is suitable for wave propagation modelling in fractured media, for which we use an equivalent media with the elastic coefficients averaged over a fractured space. This elastic parameters integration allows us to reduce the five simultaneous equations usually used to describe the velocity and stress propagation to just two, in terms of velocity alone, providing a significant saving in computational memory. In this paper, we discuss the derivation and computational implementation of the method for 2-D media, including the seismic source and both reflecting and absorbing boundary conditions, and illustrate it with some synthetic models of heterogeneous, anisotropic and fractured media.