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.
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Figure 1. The Guerrero gap region of Mexico. The subduction zone studied in this paper meets the sea floor of the Pacific ocean along a nearly linear course called the Middle American Trench: it appears on this figure as a dashed line. The large triangles mark the locations of GPS stations that were used to record the 2006 Guerrero SSE
Figure 2.
Test case 1. Top left: the fault
Figure 4.
Test case 1. Computed marginal distributions for the geometry parameters
Figure 5.
Test case 1. Solid grid: the points with depth
Figure 6.
Test case 1. Left: Computed local minima of the error functional (3.2) from [27]. These minima were obtained by using a grid of starting points. Right: corresponding values of
Figure 7.
Test case 2. Top left: the fault
Figure 8.
Test case 2: computed marginal distributions for the geometry parameters
Figure 10.
Test case 2. Solid grid: the points with depth
Figure 11.
Test case 2. Left: Computed local minima of the error functional (3.2) from [27]. These minima were obtained by using a grid of starting points. Right: corresponding values of
Figure 12.
Test case 3: the fault
Figure 13.
Test case 3: computed marginal distributions for the geometry parameters
Figure 14.
Solid grid: the points with depth
Figure 15.
Test case 3. Left: Computed local minima of the error functional (3.2) from [27]. These minima were obtained by using a grid of starting points. Right: corresponding values of
Figure 16.
The 2007 Guerrero SSE. Computed marginal distributions for the geometry parameters
Figure 18.
Computed geometry profile and slip 2007 SSE. Dashed grid: the points with depth
Figure 19.
Computed geometry profile and slip 2007 SSE. Left: Computed local minima of the error functional (3.2) from [27]. These minima were obtained by using a grid of starting points. Right: corresponding values of
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