Amplification and differential motion due to an antiplane 2D resonance in the sediment valleys embedded in a layer over the half-space

Abstract

Abstract We investigate an antiplane 2D resonance in a certain class of the sedimentary structures using the finite-difference modeling. Our models are derived from the realistic local geologic conditions beneath the colosseum in Rome and are significantly different from those investigated in the previous theoretical articles on a 2D resonance. They include a trough at the bottom of the horizontal surface layer as well as relatively deep sediment valleys embedded in a single layer over the halfspace. We present the finite-difference algorithm for SH waves on a combined (h × h and 2h × 2h) rectangular grid. Although being simple, the algorithm allowed us to save up to 75% of the grid points compared with the regular grid h × h that would cover the same computational region. A 2D resonance may develop in the valleys that do not satisfy Bard and Bouchon's existence condition. A simple trough at the bottom of the horizontal surface layer can give rise to the fundamental mode of a 2D resonance whose frequency, spectral amplification, and the maximum time-domain differential motion are very close to those in the closed sediment valley. Our results confirm that the resonance phenomenon is quite robust and that it is to be expected in many configurations of sediment valleys or basins.