An Iterative Linear Method with Variable Shear Stress Magnitudes for
Estimating the Stress Tensor from Earthquake Focal Mechanism Data:
Method and Examples
Abstract
Earthquake focal mechanism data provide information about the stress
state at the origin of these earthquakes. The inversion methods that are
commonly used to infer the stress tensor from focal mechanisms have
varying complexity but always rely on a number of assumptions. We
present an iterative method built upon a classic linear stress tensor
inversion that allows to relax the assumption on shear stress magnitudes
while preserving the computational simplicity of the linear problem.
Every iteration of our method computes the least-squares solution of the
problem, which makes the method fast enough to estimate the inverted
parameter errors with non-parametric resampling methods such as
bootstrapping. Following previous studies, this method removes the fault
plane ambiguity in focal mechanism data by selecting the nodal plane
that best satisfies the Mohr-Coulomb failure criterion. We first test
the performance and the robustness to noise of the proposed method on
synthetic data sets, and then apply it to data from Southern California
and from the Geysers geothermal field. We focus the study on
investigating the consequences of relaxing the assumption of constant
shear stress magnitudes. Our variable shear method successfully
generalizes its constant shear counterpart: it is able to perform
similarly when the constant shear assumption is a good approximation and
provides more accurate results when it is not. We provide the Python
package ILSI to implement the proposed method.