Mexico City sits on a former lake bed: soft lacustrine clay of density and shear-wave…
PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics
The Solid Earth, Ch Stress, strain and elastic waves in the Earth
Problem
Mexico City sits on a former lake bed: soft lacustrine clay of density 1200kgm−3 and shear-wave speed 80ms−1 overlies volcanic bedrock of density 2500kgm−3 and shear-wave speed 1500ms−1 (representative values quoted for the basin). Model the base of the clay as a single sharp, welded, horizontal interface, ignore reverberation within the clay (the same one-interface model used for sediment over rock), and consider an SH wave arriving at normal incidence from the bedrock.
((a)) Compute the SH impedance ratio between the bedrock and the clay.
((b)) Find the displacement reflection coefficient R and transmission coefficient T at the interface, and check that energy is conserved.
((c)) State the factor by which shaking amplitude at the ground surface on the clay exceeds that on bare bedrock, on this model, and say briefly why the amplification actually recorded in the 1985 Michoacán earthquake at Mexico City was substantially larger than this one-interface estimate.