Publications

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2010
Barbot, S, Fialko Y.  2010.  Fourier-domain Green's function for an elastic semi-infinite solid under gravity, with applications to earthquake and volcano deformation. Geophysical Journal International. 182:568-582.   10.1111/j.1365-246X.2010.04655.x   AbstractWebsite

We present an analytic solution in the Fourier domain for an elastic deformation in a semi-infinite solid due to an arbitrary surface traction. We generalize the so-called Boussinesq's and Cerruti's problems to include a restoring buoyancy boundary condition at the surface. Buoyancy due to a large density contrast at the Earth's surface is an approximation to the full effect of gravity that neglects the perturbation of the gravitational potential and the change in density in the interior. Using the perturbation method, and assuming that the effect of gravity is small compared to the elastic deformation, we derive an approximation in the space domain to the Boussinesq's problem that accounts for a buoyancy boundary condition at the surface. The Fourier- and space-domain solutions are shown to be in good agreement. Numerous problems of elastostatic or quasi-static time-dependent deformation relevant to faulting in the Earth's interior (including inelastic deformation) can be modelled using equivalent body forces and surface tractions. Solving the governing equations with the elastic Green's function in the space domain can be impractical as the body force can be distributed over a large volume. We present a computationally efficient method to evaluate the elastic deformation in a 3-D half space due to the presence of an arbitrary distribution of internal forces and tractions at the surface of the half space. We first evaluate the elastic deformation in a periodic Cartesian volume in the Fourier domain, then use the analytic solutions to the generalized Boussinesq's and Cerruti's problems to satisfy the prescribed mixed boundary condition at the surface. We show some applications for magmatic intrusions and faulting. This approach can be used to solve elastostatic problems involving spatially heterogeneous elastic properties (by employing a homogenization method) and time-dependent problems such as non-linear viscoelastic relaxation, poroelastic rebound and non-steady fault creep under the assumption of spatially homogeneous elastic properties.

2008
Barbot, S, Fialko Y, Sandwell D.  2008.  Effect of a compliant fault zone on the inferred earthquake slip distribution. Journal of Geophysical Research-Solid Earth. 113   10.1029/2007jb005256   AbstractWebsite

We present a new semi-analytic method to evaluate the deformation due to a screw dislocation in arbitrarily heterogeneous and/or anisotropic elastic half plane. The method employs integral transformations to reduce the governing partial differential equations to the integral Fredholm equation of the second kind. Dislocation sources, as well as spatial perturbations in the elastic properties are modeled using equivalent body forces. The solution to the Fredholm equation is obtained in the Fourier domain using a method of successive over-relaxation, and is mapped into the spatial domain using the inverse Fast Fourier Transform. We apply this method to investigate the effect of a soft damage zone around an earthquake fault on the co-seismic displacement field, and on the earthquake slip distribution inferred from inversions of geodetic data. In the presence of a kilometer-wide damage zone with a reduction of the effective shear modulus of a factor of 2, inversions that assume a laterally homogeneous model tend to underestimate the amount of slip in the middle of the seismogenic layer by as much as 20%. This bias may accentuate the inferred maxima in the seismic moment release at depth between 3-6 km suggested by previous studies of large strike-slip earthquakes.