Hybrid Ray-mode Formulation of Sh Motion in a Two-layer Half-space by A. Kamel and L

A hybrid ray-mode formulation is presented as an attractive alternative to the generalized ray formulation or normal mode formulation for the construction of synthetic seismograms. By the hybrid method, the motion is expressed as a combination of ray fields, modal fields, and a remainder. The number of retained ray fields can be chosen at will, and the required number of modes is thereby determined. Thus, the hybrid method quantifies the truncation effect of a ray series in terms of a certain number of modes, plus a remainder, and vice versa. The remainder field provides the fine tuning that ensures continuity of the total motion; its effect is greatest near the arrival time of the last retained ray and diminishes soon thereafter. The hybrid scheme incorporates within a single concise framework the advantages of a ray description for early observation times and of a modal description for later observation times. Therefore, over a prolonged range of observation times, it is numerically more efficient and physically more appealing than either the pure ray or pure mode formulations. These aspects are demonstrated on the simple example of a two-layer (sediment atop bedrock) half-space excited by a line source of SH waves in the semi* infinite bedrock. Numerical results are presented for parameters employed in a similar calculation by Heaton and Helmberger and by Swanger and Boore.