Seismic imaging of fractured elastic media on the basis of the grid-characteristic method

Wave processes occurring in a fractured rock material in seismic exploration are numerically simulated and studied. The grid-characteristic method on hexahedral grids is extended to construct a seismic image of a fractured elastic medium (i.e., the positions of the reflecting layers under the daytime surface). The underlying idea is that the method is applied to both direct and adjoint problems (in the latter problem, seismometer data recorded on the daytime surface are transformed into corresponding seismic sources). In this case, a seismic image is obtained as the convolution of the direct and adjoint fields. Numerical computations are used to produce synthetic seismograms (time dependences of point oscillations on the daytime surface) for rock materials with gas-saturated and liquid-saturated cracks. The inhomogeneities are explicitly described (at the stage of hexahedral grid generation) and the stressed state on their boundaries is updated at every time step (by solving a contact discontinuity problem). The algorithm is used to construct seismic images for media. An analysis of the results yields information not only on the locations of the cracks, but also on their spatial orientations.