Schoenberg's Model-Based Simulation of Wave Propagation in Fractured Geological Media

Schoenberg's mathematical model of fractured geological media has been widely used in studies related to seismic exploration of oil fields. This paper proposes to use this model for computing wave processes in geological media by the grid-characteristic method. In that case, the sought-for functions are components of the velocity vector and stress tensor in the vicinity of the fracture, the values of which are determined at grid points. We simulated seismic pulse propagation through a homogeneous elastic medium with a fracture in the case that the wave front is totally reflected from the fracture edge. We used the grid-characteristic method in simulating wave fields with Schoenberg's and two-edge fracture models. It is found that the models produce broadly similar results.