The inverse problem of seismic fault determination using part time measurements

Huy Duong Bui (1, 2) , Andrei Constantinescu (1) , Hubert Maigre (3)

1 LMS - Laboratoire de mécanique des solides
2 LAMSID - UMR 8193 - Laboratoire de Mécanique des Structures Industrielles Durables
3 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]

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 cpT , 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.

Domaines: Equations aux dérivées partielles [math.AP]; Mécanique [physics.med-ph]

Huy Duong Bui, Andrei Constantinescu, Hubert Maigre. The inverse problem of seismic fault determination using part time measurements. Journal of Mechanics of Materials and Structures, 2012, 7 (10), ⟨10.2140/jomms.2012.7.997⟩. ⟨hal-00913588⟩