A P travel-time curve has slope at epicentral distance

PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics · Seismology, tectonics and geodynamics

The Solid Earth, Ch Rays and travel times: from arrivals to a layered planet

Problem

A P travel-time curve has slope dT/dΔ=7.60 s deg−1\mathrm{d}T/\mathrm{d}\Delta = 7.60\,\mathrm{s\,deg^{-1}} at epicentral distance Δ=50∘\Delta = 50^\circ. At the turning point of the corresponding ray, the P speed is vt=11.9 km s−1v_t = 11.9\,\mathrm{km\,s^{-1}}. Take the Earth's radius as a=6371 kma = 6371\,\mathrm{km} and use 1 s deg−1=57.30 s rad−11\,\mathrm{s\,deg^{-1}} = 57.30\,\mathrm{s\,rad^{-1}}. ((a)) Convert the slope to the ray parameter in s rad−1\mathrm{s\,rad^{-1}}. ((b)) Find the turning radius rtr_t and the turning depth.

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