Near depth a reference Earth model gives and

PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · The solid Earth: structure, fields and thermal history · Seismology, tectonics and geodynamics

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

Problem

Near 2500 km2500\,\mathrm{km} depth a reference Earth model gives vP≈13.0 km s−1v_P \approx 13.0\,\mathrm{km\,s^{-1}} and vS≈7.05 km s−1v_S \approx 7.05\,\mathrm{km\,s^{-1}}. Take g≈10 m s−2g \approx 10\,\mathrm{m\,s^{-2}} at this depth. ((a)) Estimate the seismic parameter Φ=vP2−43vS2\Phi = v_P^2 - \tfrac43v_S^2 at this depth. ((b)) Use the Adams-Williamson equation to estimate the fractional increase in density, as a percentage, for each 1000 km1000\,\mathrm{km} increase in depth at this level.

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