Approximation of Velocity Distributions for Calculation of P-Wave Times and Amplitudes
An algorithm for calculating travel-time and amplitude curves of P waves by the ray theory is described in . 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.
KeywordsVelocity Distribution Velocity Gradient Seismic Wave Epicentral Distance Seismic Wave Prop
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