Article

# Synthetic seismograms at nonvertical incidence

College of Engineering and Physical Sciences, University of Tulsa, 600 College Ave., Tulsa, Oklahoma 74104, U.S.A.

Geophysical Prospecting (Impact Factor: 1.47). 04/2006; 27(3):564 - 575. DOI: 10.1111/j.1365-2478.1979.tb00985.x **ABSTRACT**

Synthetic seismograms are usually computed for reflections from vertical incidence of P waves for a horizontally layered medium. In actual practice the angle of incidence departs from the vertical, as receivers are usually located at some distance from the source. At angles other than the vertical, the conversion of P- to S-wave energy and changes in the reflection coefficient affect the shape of the synthetic seismograms. The effect of non-vertical incidence on synthetic seismograms is examined in this paper.

Seismograms at non-vertical incidence have been computed using the plane-wave approach of Haskell (1953) for a layered medium. The use of plane waves is an approximation to the actual case of spherical wavefronts from a surface source.

Using plane-wave theory, the expected wave forms as a function of angle of incidence were computed numerically for several simple models. The results indicate that the synthetic seismograms do not change significantly for angles of incidence between o and 25 degrees. For larger angles the changes in the wave forms may be severe. The effect is more pronounced for high-velocity layers than for low-velocity layers.

Seismograms at non-vertical incidence have been computed using the plane-wave approach of Haskell (1953) for a layered medium. The use of plane waves is an approximation to the actual case of spherical wavefronts from a surface source.

Using plane-wave theory, the expected wave forms as a function of angle of incidence were computed numerically for several simple models. The results indicate that the synthetic seismograms do not change significantly for angles of incidence between o and 25 degrees. For larger angles the changes in the wave forms may be severe. The effect is more pronounced for high-velocity layers than for low-velocity layers.

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**ABSTRACT:**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. - [Show abstract] [Hide abstract]

**ABSTRACT:**The notion of nonvertical incidence plane wave seismograms and nonzero effect point source seismograms are sometimes confused with each other in the literature. This short note attempts to clarify this confusion which is observed in Douze (1979).

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