Transmission of acoustic waves through strongly heterogeneous, two-dimensional velocity models

Abstract

An explicit expression, based on the second-order Neumann expansion, is derived for computing the gradual evolution of the pulse shape of a scalar seismic wave as it propagates through a medium, the slowness of which varies both horizontally and vertically. In particular, the case is considered where these variations take place on a scale, which is small with respect to the pulse width of the wavefield. The apparent absorption, time delay and dispersion caused by small-scale multiple-scattering effects are quantified and illustrated by a number of examples. The results indicate that the effects can be significant and should therefore be taken into account in seismic modeling and inversion. For monochromatic plane waves propagating in a particular direction, a medium containing small-scale inhomogeneities can be replaced by a smoother “apparent” medium. The apparent medium accounts for both first- and second-order scattering effects, is frequency-dependent and also depends on the direction of propagation. With the aid of these smoother apparent media, it can be analyzed how small-scale inhomogeneities tend to decrease the temporal and spatial coherence of the wavefield and how they can be incorporated efficiently into forward and inverse wave-propagation schemes.