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 (i0) and epicentral distances, Δ(i0)) is calculated by numerical integration, while the amplitudes are found by numerical differentiation of the travel-time curve.
Translated from Vychislitel’naya Seismologiya, No. 2, Moscow, Nauka (1966), pp. 56–70.
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Literature Cited
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.
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.
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Azhel’, I.Y., Yanovskaya, T.B. (1972). Approximation of Velocity Distributions for Calculation of P-Wave Times and Amplitudes. In: Keilis-Borok, V.I., Flinn, E.A. (eds) Computational Seismology. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-8815-9_8
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DOI: https://doi.org/10.1007/978-1-4684-8815-9_8
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