Non‐normal Incidence State‐space Model and Line Source Reflection Synthetic Seismogram*

This paper is directed at modeling layered media. We extend the plane‐wave normal‐incidence state‐space model developed by Mendel, Nahi and Chan in 1979, to the non‐normal incidence case. To do this we introduce a shifting principle, a zero‐offset wavefront, and zero‐offset travel times for different layers. We also develop an algorithm for obtaining a synthetic line source reflection seismogram. In this algorithm non‐normal incidence plane‐wave seismograms are summed over a range of incident angles. The algorithm is based on a modified version of Sommerfield's (1896) theorem. Simulations of acoustic and elastic media are included which illustrate the applicability of our plane‐wave and line source seismograms for both elastic and acoustic cases.