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Surface waves in structures with locally irregular boundaries

LABORATOIRE D'ETUDE GÉOPHYSIQUE DE STRUCTURES PROFONDES ASSOCIÉ AU C.N.R.S. N^O 195 UNIVERSITÉ PIERRE ET MARIE CURIE INSTITUT DE PHYSIQUE DU GLOBE, TOUR 14, 4 PLACE JUSSIEU, 75230 PARIS CEDEX 05 France

Abstract

The transmitted field due to surface waves incident on a local irregularity of a plane-layered medium has been studied. A perturbation method to the first order and the Born approximation can be used if the variations in the thickness of the layers are sufficiently smooth and the wavelengths are long when compared to the size of the irregularities. The spectrum of the perturbed part of the displacement field at the surface is a sum over the surface-wave modes for the regular medium, with an additional term involving the scattered body waves. Numerical computations have been performed for structures composed of a layer overlying a half-space. The contribution of the various modes to the transmitted Love or Rayleigh fields has been studied for several structures. A general method has been obtained to analyze the effect of a complex structure as the superposition of the fields due to simpler ones. When the layer thickness is kept unchanged, the incident mode is not perturbed to the first order. Synthetic seismograms, computed at stations sufficiently close to the irregular region, show how the perturbation of the signal depends on distance. A comparison has been made for Love waves with a finite element method. Both methods give very similar results when the stations are not too close to the irregularities so that the body-wave contribution is negligible. The local phase velocity shows departures from the curves for a regular model.