A finite-difference model to study the elastic-wave interactions with buried land mines

A two-dimensional (2-D) finite-difference model for elastic waves in the ground has been developed. The model uses the equation of motion and the stress-strain relation, from which a first-order stress-velocity formulation is obtained. The resulting system of equations is discretized using centered finite-differences. A perfectly matched layer surrounds the discretized solution space and absorbs the outward traveling waves. The numerical model is validated by comparison to an analytical solution. The numerical model is used to study the interaction of elastic waves with a buried land mine. It is seen that the presence of an air-chamber within the mine gives rise to resonant oscillations that are clearly visible on the surface above the mine. The resonance is shown to be due to flexural waves being trapped within the thin layer between the surface of the ground and the air chamber of the mine. The numerical results are in good qualitative agreement with experimental observations.