Abstract
We introduce in this study an algorithm for the imaging of faults and of slip fields on those faults. The physics of this problem are modeled using the equations of linear elasticity. We define a regularized functional to be minimized for building the image. We first prove that the minimum of that functional converges to the unique solution of the related fault inverse problem. Due to inherent uncertainties in measurements, rather than seeking a deterministic solution to the fault inverse problem, we then consider a Bayesian approach. The randomness involved in the unknown slip is teased out by assuming independence of the priors, and we show how the regularized error functional introduced earlier can be used to recover the probability density of the geometry parameter. The advantage of this Bayesian approach is that we obtain a way of quantifying uncertainties as part of our final answer. On the downside, this approach leads to a very large computation which we implemented on a parallel platform. After showing how this algorithm performs on simulated data, we apply it to measured data. The data was recorded during a slow slip event in Guerrero, Mexico.
Highlights
Subduction zones around the world are periodically prone to devastating earthquakes
We introduce and analyze error functionals for the reconstruction of fault geometries based on surface measurements of displacement fields, and we derive a stochastic inversion procedure which relies on these functionals
The physics of our problem are modeled using the equations of linear elasticity and the data for the fault inverse problem consists of measurements of surface displacements
Summary
Subduction zones around the world are periodically prone to devastating earthquakes. The 2011 Tohoku Oki earthquake in Japan was a stark reminder of that occurrence. As customary in Bayesian modeling of inverse problems, the difference between measured data and predicted surface displacements for a given geometry of the fault and a given slip is assumed to be a Gaussian random variable with mean zero. Our last numerical computation involves real world measurements and results in the reconstruction of the part of the subduction interface beneath the Guerrero region which was active during the 2007 SSE. In this last simulation the only benchmarks for our calculation are geometries estimated by other authors (in most cases, based on other physical processes). We observe that many of the profiles found by other authors fall in the plus or minus one standard deviation envelope of the profile derived in this present study
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