A method for modelling radar interferograms without phase unwrapping: application to the M 5 Fawnskin, California earthquake of 1992 December 4

Abstract

SUMMARY Interferometric analysis of synthetic aperture radar images (InSAR) measures the phase shifts between two images acquired at two distinct times. These ambiguous ‘wrapped’ phase values range from −½ to +½ cycles. The standard approach interprets the phase values in terms of the change in distance between the ground and the radar instrument by resolving the integer ambiguities in a process known as ‘unwrapping’. To avoid unwrapping, we have developed, validated and applied a new method for modelling the wrapped phase data directly. The method defines a cost function in terms of wrapped phase to measure the misfit between the observed and modelled values of phase. By minimizing the cost function with a simulated annealing algorithm, the method estimates parameters in a non-linear model. Since the wrapped phase residuals are compatible with a von Mises distribution, several parametric statistical tests can be used to evaluate the fit of the model to the data. The method, named General Inversion for Phase Technique (GIPhT), can handle noisy, wrapped phase data. Applying GIPhT to two interferograms in the area of Fawnskin, California, we estimate a set of model parameters describing a magnitude 5 aftershock of the 1992 Landers earthquake. The resulting simulation fits the data well. The phase final residuals have a circular mean deviation less than 0.15 cycles per datum. Sampling the final residuals, we find the circular standard deviation of a phase measurement to be approximately 0.2 cycle, corresponding to 6 mm in range.