1993-2011 Time dependent deformation of Eyjafjallajokull volcano, Iceland

We analyze synthetic aperture radar data acquired by ERS-1, ERS-2, Envisat, TerraSAR-X and ALOS satellites between 1993 and 2011 to characterize the deformation associated with activity at Eyjafjallajokull. The volcano had shown intermittent unrest for 18 years before erupting in 2010. An effusive lava eruption occurred from 20th March to 12th April and was followed by an explosive summit eruption from 14th April to 22nd May, disrupting air traffic. Satellite radar interferometry (InSAR) captured intrusive events in 1994 and 1999 when several decimeters of deformation occurred on the volcanic edifice. By inverting the geodetic data, Pedersen et al. [2004; 2006] inferred that sills between depths of 5-7 km had increased in volume by approximately 10-17 and 21-31 million cubic meters during each of two intrusive events in 1994 and 1999, respectively. In this study, we extend the time series analysis to the pre-eruptive, co-eruptive, and post-eruptive deformation associated with the 2010 eruptions. To describe the pre-eruptive deformation over several months, Sigmundsson et al. [2010] estimate the total volume increase in two sills and a dike to be 49-71 million cubic meters. During the effusive eruption, no significant deformation was observed in the interferograms. During the explosive eruption, deflation was observed, that continued at a low rate after the eruption ceased. To estimate source parameters, we use the General Inversion of Phase Technique [GIPhT; Feigl and Thurber, 2009] that analyzes the gradient of phase without the need for unwrapping. To quantify the misfit between the observed and modeled values of the phase gradient, the objective function calculates the cost as the absolute value of their difference, averaged over all sampled pixels. To minimize the objective function we use a simulated annealing algorithm. For computational efficiency, we approximate the fitting function using Taylor series. Calculation of derivatives requires evaluating the exact version of the fitting function, which for our particular problem involves solving the elasticity equations using the finite element method. The minimization procedure is performed several times before reaching convergence, typically in 5 to 15 iterations. GIPhT is suitable for monitoring volcanoes because it can be run quickly and automatically, as soon as the interferograms are formed. Preliminary results suggest several sources located between 3 and 8 km depth, consistent with seismic observations. The best-fitting models for the inflationary episodes of 1994, 1999 and 2010 are horizontal sills that increase in volume. The deflationary episode is best described by another horizontal sill that decreased in volume after 14th April 2010. The different location of the sources suggests significant movement of magma. Fitting a piece-wise linear polynomial to the time series of source strength estimated from the InSAR data, we find general agreement with independent data sets, including GPS measurements and earthquake locations.