Abstract
We develop, validate, and apply a new strategy for estimating parameters in a geophysical model from interferometric synthetic aperture radar (InSAR) measurements. The observable quantity is a particular component of the deformation gradient tensor, defined as the derivative of the change in range with respect to the easting coordinate. This range change gradient is derived from wrapped phase data by a quadtree resampling procedure. Since the range change gradient is a continuous function of position, the strategy avoids the pitfalls associated with phase unwrapping techniques. To quantify the misfit between the observed and modeled values of the range gradient, the objective function calculates the cost as the absolute value of their difference, averaged over all samples. To minimize the objective function, we use a simulated annealing algorithm. This algorithm requires several thousand evaluations of the fitting function to find the optimum solution: the estimate of the model parameters that produces the lowest value of cost. For computational efficiency, we approximate the fitting function using a Taylor series. The simulated annealing algorithm then evaluates the approximate and fast version of the fitting function. After performing these two steps several times, the scheme converges, typically in a few iterations. We apply the strategy to Krafla central volcano in Iceland. Using a data set composed of eight interferometric pairs acquired by the ERS-1 and ERS-2 satellites over a 6-year interval between 1993 and 1999, we estimate the four parameters in a Mogi model. Results suggest a source at 4.98 +/- 0.21 km depth and a deflation rate that decays exponentially over the interval, in agreement with previous studies.