Modeling seismic wave propagation in a coal-bearing porous medium by a staggered-grid finite difference method

A staggered-grid finite difference method is used to model seismic wave records in a coal bearing, porous medium. The variables analyzed include the order of the difference calculations, the use of a perfect match layer to provide absorbing boundary conditions, the source location, the stability conditions, and dispersion in the medium. The results show that the location of the first derivative of the dynamic variable with respect to space is coincident with the location of the first derivative of the kinematic variable with respect to time. Outgoing waves are effectively absorbed and reflection at the boundary is very weak when more than 20 perfect match layer cells are used. Biot theory considers the liquid phase to be homogeneous so the ratio of liquid to solid exposure of the seismic source depends upon the medium porosity. Numerical dispersion and generation of false frequencies is reduced by increasing the accuracy of the difference calculations and by reducing the grid size and time step. Temporal second order accuracy, a tenth order spatial accuracy, and a wavelength over more than ten grid points gave acceptable numerical results. Larger grid step sizes in the lateral direction and smaller grid sizes in the vertical direction allow control of dispersion when the medium is a low speed body. This provides a useful way to simulate seismic waves in a porous coal bearing medium.