Approximate Computation of the 3D Seismic Response of Small-size Buried Objects

We present an approximate method to compute the three-dimensional seismic response of small-size solid objects of arbitrary shape buried in the subsurface. The computation method relies on a representation of the objects by a set of closely spaced point scatterers simulating weak material perturbations in terms of density and P- and S-wave velocities. The method is illustrated with a parallelepiped structure embedded in an elastic half space, whose theoretical seismic response is compared to finite difference computations. The results obtained with the two computation techniques show that the proposed approach can accurately reproduce the main features of the seismic response of buried objects, provided that the following conditions are fulfilled: i) 5 to 10 scatterers are required per wavelength, ii) the contrasts in density and P- and S-wave velocities between the buried objects and surrounding medium must be moderate, and iii) the size of the objects considered must be small enough to ensure that the propagation time through the objects remains accurate.