An image segmentation based algorithm for imaging of slow slip earthquakes

Laboratory experiments next to a variety of observations, especially in subduction zones, have explored the existence of a premonitory stable slow slip growth phase preceding large earthquakes. These phenomena play an important role in the earthquake cycle, including their impacts on stress transfer, and nucleation and triggering processes. They are also considered as potential earthquake precursors; thus precise imaging and monitoring these events using deformation data sets are of great significance. Because our signal of interest, which is related to the slip on the fault, has been contaminated with different types of noise sources, including local benchmark motion, measuring device errors, etc., the imaging problem is not straightforward and is thus challenging. In the literature, Extended Network Inversion Filter (ENIF) has been proposed as a rigorous algorithm capable of isolating different types of signals and consequently provides us with some insight into spatio-temporal evolution of slow slip events. Since Extended Kalman Filter (EKF) forms the core of ENIF and is also a framework for data fusion, we can combine different types of surface deformation data sets via ENIF. As a variant of Sequential Bayesian Filter, EKF further provides an effective tool for stochastic estimation of slip, slip rate and their uncertainties. Despite its considerable advantages, ENIF still suffers from some limitations. ENIF employs Tikhonov method of regularization which itself uses a quadratic form of cost function. While images regarding spatio-temporal slow slip events contain anomalous slip regions, which have clear contrast with the background slip, Tikhonov, with its quadratic form, tends to over smooth (globally smooth) the image. In order to avoid over smoothing phenomenon, we have incorporated into ENIF an image segmentation based regularization scheme which is known as an edge preserving regularizer. As a second limitation, propagating uncertainty through model is not simple with regard to the nonlinearity imposed by some constraints such as non-negativity of slip rate. The EKF performs uncertainty propagation by linearization of nonlinear model using Jacobian and Hessian matrices. As an alternative for EKF, we have also investigated the application of Unscented Kalman Filter (UKF) which uses Unscented Transform (UT) for uncertainty propagation.

Finally, we tested our proposed algorithm using a low signal to noise ratio simulated data set. In case segmentation is applied to EKF filter, the results show a significant decrease by 0.47 and 0.86 for slip and slip rate, respectively, in terms of the summed squared residual between the true slip and slip-rate distributions and the recovered distributions This is while the figures are 0.93 and 1.38 for slip and slip rate, respectively, in case the segmentation is applied to UKF filter.