Fast Computation of Synthetic Seismograms in a Piecewise Continuously Layered Fluid

摘要

An efficient scheme is presented for generating synthetic seismograms in configurations that are typical for marine seismics. Essential to the technique is that the medium parameters are inhomogeneous in a single direction, the vertical direction, say, and that one can use the linearized acoustic differential equations. In the study one also assumes the media to be isotropic, instantaneously reacting and lossless. The inhomogeneity is assumed to be piecewise continuous and is restricted to a bounded region, outside of which the configuration is homogeneous. In one of the homogeneous halfspaces a point source of the injection type or the vertical-force type is located. The acoustic equations describing wave propagation in such a configuration are subjected to a Fourier transformation with respect to time and a Hankel transformation with respect to the radical coordinate in the horizontal plane. This reduces the problem to a one-dimensional integral equation of the contrast type over a finite domain, which must be solved repeatedly for a large number of values of the transform parameters. A recursive solution procedure is derived that is indpendent of the transform parameters. Numerical results are presented for several canonical problems.