Faraday resonance in thin sedimentary layers

Abstract

SUMMARY It is well established that earthquake waves passing through soft alluvial valleys and sedimentary basins will generally amplify, so that signals are stronger, longer and more complex on such sites than on adjacent crystalline rocks. One anomalous feature of the amplification there is the rather significant variability in the recorded strong ground motion, especially over relatively short length-scales. This paper explains such short-scale variability in the amplification factor by proposing a novel seismic resonance mechanism in thin flat layers. The variability is attributed to the subharmonic generation of standing elastic waves on the surface of the deposit. Nodal regions of little horizontal shaking, or little destruction, are separated by antinodal regions of strong horizontal shaking, i.e. significant damage. Vertical ground shaking follows a similar pattern. The subharmonic surface waves are forced by the vertical component of an input seismic shaking at the base of the deposit, through a linear instability mechanism in the layer. A perturbation theory is worked out to describe the conditions for resonance, and a small shaking-tank experiment is conducted to confirm some of the theoretical findings.