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Bulletin of the Seismological Society of America; May 2009; v. 99; no. 2B; p. 1147-1161; DOI: 10.1785/0120080096
© 2009 Seismological Society of America
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Numerical Simulation of Ground Rotations along 2D Topographical Profiles under the Incidence of Elastic Plane Waves

L. Godinho, P. Amado Mendes, and A. Tadeu

Centro de Investigação em Ciências da Construção, Department of Civil Engineering, University of Coimbra, Rua Luis Reis Santos Pólo 2-FCTUC, 3030-788 Coimbra, Portugal lgodinho{at}dec.uc.pt pamendes{at}dec.uc.pt tadeu{at}dec.uc.pt

A. Cadena-Isaza

Instituto de Ingeniería, Universidad Nacional Autónoma de México, Ciudad Universitaria, Coyoacán 04510, Mexico, D.F., Mexico acadenai{at}ii.unam.mx

C. Smerzini

ROSE School, c/o EUCENTRE, via Ferrata 1, Pavia 27100, Italy csmerzini{at}roseschool.it

F. J. Sánchez-Sesma

Instituto de Ingeniería, Universidad Nacional Autónoma de México, Ciudad Universitaria, Coyoacán 04510, Mexico, D.F., Mexico sesma{at}servidor.unam.mx

R. Madec and D. Komatitsch

Laboratoire de Modélisation et d’Imagerie en Géosciences de Pau (CNRS) UMR 5212, Université de Pau et des Pays de l’Adour and INRIA MAGIQUE-3D, Bâtiment IPRA, Avenue de l’Université, BP 1155, 64013 Pau Cedex, France ronan.madec{at}gmail.com dimitri.komatitsch{at}univ-pau.fr

Online Material: Analysis of the dependence of rotational motion on incident plane-wave frequency.

The surface displacement field along a topographical profile of an elastic half-space subjected to the incidence of elastic waves can be computed using different numerical methods. The method of fundamental solutions (MFS) is one of such techniques in which the diffracted field is constructed by means of a representation in terms of the Green’s functions for discrete forces located outside the domain of interest. From the enforcement of boundary conditions, such forces can be computed; thus, the ground motion can be calculated. One important advantage of MFS over boundary integral techniques is that singularities are avoided. The computation of ground-motion rotations implies the application of the rotational operator to the displacement field. This can be done using either numerical derivatives or analytical expressions to compute the rotational Green’s tensor. We validate the method using exact analytical solutions in terms of both displacement and rotation, which are known for simple geometries. To demonstrate the accuracy for generic geometries, we compare results against those obtained using the spectral-element method. We compute surface rotations for incoming plane waves (P, SV, and Rayleigh) near a topographical profile. We point out the effects of topography on rotational ground motion in both frequency and time domains.




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W. H. K Lee, M. Celebi, M. I. Todorovska, and H. Igel
Introduction to the Special Issue on Rotational Seismology and Engineering Applications
Bulletin of the Seismological Society of America, May 1, 2009; 99(2B): 945 - 957.
[Abstract] [Full Text] [PDF]


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