f Source signatures in finite difference schemes

For a marine seismic air gun array each gun location does not necessarily coincide with the nodes in a finite difference grid. Especially for coarse grid finite difference modeling this problem must be handled with care since there might be up to three or four air guns between two grid points. Most examples of coarse grid finite differente modeling of seismic data have up to now used single point sources. A conventional marine source array consists of a number (from 10 to 70) of individual air guns, typically separated by about 2 - 4 meters. For coarse grid finite difference schemes, however, the distante between each grid point is typically 10m or more. This means that effective point sources (i.e. notional sources) estimated from measurements can not directly be implemented in a coarse grid finite difference scheme. We will circumvent this problem by introducing several different source functions at the same node in the finite difference grid. The set of grid source functions at each node is a multipole expansion, and we will estimate how many terms in the multipole expansion, that are sufficient in order to achieve a reasonable representation of the directive source wavefield.