Overview of a range of solution methods for elastic dislocation problems in geophysics

Abstract

[1] Tectonic faults are commonly modeled as Volterra or Somigliana dislocations in an elastic medium. Over the years, many practical solution methods have been developed for problems of this type. This work presents a concise overview in consistent mathematical notation of the most prominent of these methods, emphasizing what the various methods have in common and in what aspects they are different. No models other than that of elastic dislocations are considered. Special attention is given to underlying assumptions and range of applicability.Citation: van Zwieten, G. J., R. F. Hanssen, and M. A. Gutie´rrez, (2013), Overview of a range of solution methods for elastic dislocation problems in geophysics,

Discontinuities without discontinuity: The Weakly-enforced Slip Method

“…The second term in the final expression in (21) then vanishes if Γ ε collapses on Γ. Therefore, formally passing to the limit in (21), we obtain…”

“…The model embeds a displacement discontinuity of given location and magnitude in an elastic medium, causing the entire medium to deform under the locked-in stress. Many different solution methods have been developed for this particular problem, based on analytical solutions or numerical approximations; see for instance [21] for an overview of the most prominent methods. However, methods founded on analytical solutions generally dictate severe model simplifications, such as elastic homogeneity or generic geometries, which restricts their validity.…”

A Monte Carlo adapted finite element method for dislocation simulation of faults with uncertain geometry

“…It is supposed that the considered system experiences a new minimum energy state of self-stressed equilibrium. The magnitude and direction of the displacement jump (or slip) is a vector field over the dislocation plane, where a slip vector has normal components, the material opens, and is added to fill the void, just as it happens when a dyke intrudes a fault (van Zwieten et al 2013). The displacements are discontinuous at the dislocation plane and continuous elsewhere.…”

“…There are several approaches to model elastic dislocation of an active fault (van Zwieten et al 2013). Analytical methods are rapid and accurate, but are often restricted to simple problems without complexity.…”

“…This method may be implemented in finite element method (FEM) to consider the discontinuity effects of fault without direct modeling of the discontinuity. Even though the SNT was proposed in 1981, this idea is still a robust tool as it can handle anisotropy, heterogeneity, topography, distributed slip and curved fault effects (Melosh and Raefsky 1983;Melosh and Williams 1989;Andrews 1999;Day 2006, 2007;van Zwieten et al 2013). Recently, van Zwieten et al (2014) developed the weaklyenforced slip method to model tectonic faults without explicitly simulating discontinuities.…”