#### Vol. 7, No. 10, 2012

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The inverse problem of seismic fault determination using part time measurements

### Huy Duong Bui, Andrei Constantinescu and Hubert Maigre

Vol. 7 (2012), No. 10, 997–1007
##### Abstract

This paper shows how a part time measurement $T$ of the acceleration on the ground can be done to avoid the consideration of reflections of seismic waves on the Moho discontinuity. A bounded hemispherical solid is considered with radius greater than ${c}_{p}T$, but smaller than the Moho depth, in order to get the null boundary conditions on the hemispherical surface. The inverse problem to determine the fault plane and the time-dependent fault geometry is well-defined and solved in closed form by the reciprocity gap functional method. Two formulae are established for the components of the fault slip, which involve time and spatial Fourier transforms of some quantities related to the reciprocity gap functional. A forward initial boundary value problem in elastodynamics enables us to get the internal wave field, the shear stress as well as the normal stress on the fault. This full solution would be useful for understanding the friction mechanism on the fault during a real strike, whenever the initial uniform tectonic stresses are known from geophysical considerations.

##### Keywords
earthquake, inverse problem, reciprocity gap, elastic wave, fault history