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Abstract

The two-dimensional model chosen for the derivation of GRM parameters consists of multiple plane-dipping layers with constant seismic velocities. This model does not represent the limitation of the method but has been selected for mathematical convenience.

There are several methods of specifying depths and raypath parameters. For example, Dooley (1952) and Adachi (1954) used vertical depths. However, a more convenient approach was used by Ewing et al (1939) and Mota (1954), who specified thicknesses normal to the refractor surface. The surface of the refractor is taken as the envelope of arcs of appropriate radii; hence loci, rather than actual depth points, are determined. The dip information, which is not always readily determined for undulating refractors, is recovered with the construction of the envelope. Therefore, the common assumption of the seismic profile being normal to the strike of the refractor is not necessary. This also permits convenient extension to three-dimensional (3-D) analysis.

Another advantage of the specification of Ewing et al (1939) is the symmetry of the resulting mathematical expressions. This symmetry, in turn, results in a depth conversion factor which is insensitive to dip angles up to about 20 degrees. Therefore, depth calculations are extremely convenient, both when the refractor is undulating and when there are complex velocity distributions above the refractor. These advantages are not readily achieved with the expressions of Mota (1954), who also used perpendicular thicknesses.

Accordingly, layer thicknesses and angles of incidence used in the following analysis are similar to those used by Ewing et al (1939). However, dip angles

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