Project Abstract
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We worked on two inter-related approaches for detection of transient deformation. The fundamental assumption in both is that transient tectonic deformations are spatially coherent and can thus be separated from localized errors. If not required by the data, fault slip-rate or strain-rate is assumed to be steady in time.
The first approach is an extension of the Network Inversion Filter (NIF) known as a Monte Carlo mixture Kalman Filter (MCMKF). The NIF estimates spatially and temporally variable fault slip-rates in the presence of various noise sources. Elastic Green's functions impose spatial coherence on the deformation. The NIF included a constant temporal smoothing parameter ($\alpha^2$). The MCMKF, however, propagates a discrete probability density of $\alpha^2$ that changes with time. When the data reflect steady-state deformation $\alpha^2$ is small (strong smoothing); however during transient slip larger values of $\alpha^2$ are favored. The integrated probability of $\alpha^2$ over a specified threshold is thus a measure of the probability that a transient has occurred.
We also developed a Network Strain Filter (NSF) that seeks coherent transients in the surface strain-rate field. This approach is not dependent on a particular fault model. The two approaches, NIF and NSF, are complementary, in that the NSF may first detect transients, which could be further analyzed with a NIF. In both cases spatial coherence is enforced on the transient signal at the outset. This contrasts with other approaches that analyze station time individually, and then look to see if the deviations from steady-state are spatially coherent. |
