Computational Seismology pp 62-69 | Cite as

# Approximation of Velocity Distributions for Calculation of P-Wave Times and Amplitudes

## Abstract

An algorithm for calculating travel-time and amplitude curves of P waves by the ray theory is described in [1]. The earth model was a layered sphere. The dependence of velocity v upon depth r in each layer was represented by a cubical parabola. This approximation makes v(r) smooth enough to justify use of the ray theory (with the exception of regions where the ray theory is entirely inapplicable: caustics and shadow zones). The disadvantage of this approximation is that the travel-time curve (travel times τ (i_{0}) and epicentral distances, Δ(i_{0})) is calculated by numerical integration, while the amplitudes are found by numerical differentiation of the travel-time curve.

## Keywords

Velocity Distribution Velocity Gradient Seismic Wave Epicentral Distance Seismic Wave Prop## Preview

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## Literature Cited

- 1.Yanovskaya, T. B., and G. V. Golikova (1964), “Method and program for calculating P wave dynamics in the earth’s mantle,” in; Problems of the Dynamic Theory of Seismic Wave Propagation, No. 7, pp. 123–129.Google Scholar
- 2.Yanovskaya, T. B., G. V. Golikova, and Yu. A. Surkhov (1964), “Amplitude curves of P waves,” in; Problems of Dynamic Theory of Seismic Wave Propagation, No. 7, pp. 104–114.Google Scholar