Abstract. Dike intrusions often cause complex ground displacements that are not sufficiently explained by simple analytical models. We develop a method to find complex and realistic dike geometries and overpressures from interferometric synthetic aperture radar (InSAR) data. This method is based on a combination of a boundary element method with realistic topography and a neighbourhood algorithm inversion. Dike model geometry is roughly a quadrangle with its top reaching the ground. The inversion has two stages: search and appraisal. The appraisal stage involves calculations of model marginal probability density functions using misfit values calculated during the search stage. The misfit function takes into account the variance and correlation of data noise. Synthetic tests show that a model is successfully retrieved within predicted narrow confidence intervals. We apply the method on InSAR data of the February 2000 flank eruption at Piton de la Fournaise and get a trapezoid dike dipping seaward (61.0 • -67.3 • ) with its bottom passing 800-1000 m beneath the summit. A model with a basal slip plane does not better explain observed asymmetric displacements and thus this asymmetry is solely attributed to the dipping dike. The dike lies above a narrow band of pre-eruption seismicity, suggesting that lateral magma propagation occurred. Neglecting topography results in poor modeling at depth and in overestimations of overpressure (or opening), height (both about 30%), and volume (about 20%).Citation: Fukushima, Y., V. Cayol, and P. Durand (2005), Finding realistic dike models from interferometric synthetic aperture radar data:

Stress changes in the Earth's crust are generally estimated from model calculations that use near-surface deformation as an observational constraint. But the widespread correlation of changes of earthquake activity with stress has led to suggestions that stress changes might be calculated from earthquake occurrence rates obtained from seismicity catalogues. Although this possibility has considerable appeal, because seismicity data are routinely collected and have good spatial and temporal resolution, the method has not yet proven successful, owing to the non-linearity of earthquake rate changes with respect to both stress and time. Here, however, we present two methods for inverting earthquake rate data to infer stress changes, using a formulation for the stress- and time-dependence of earthquake rates. Application of these methods at Kilauea volcano, in Hawaii, yields good agreement with independent estimates, indicating that earthquake rates can provide a practical remote-sensing stress meter.

Abstract. We have investigated the effects of topography on the surface-deformation field of volcanoes. Our study provides limits to the use of classical half-space models. Considering axisymmetrical volcanoes, we show that interpreting ground-surface displacements with half-space models can lead to erroneous estimations of the shape of the deformation source. When the average slope of the flanks of a volcano exceeds 20 ø, tilting in the summit area is reversed to that expected for a flat surface. Thus, neglecting topography may lead to misinterpreting an inflation of the source as a deflation. Comparisons of Mogi's model with a three-dimensional model shows that ignoring topography may lead to an overestimate of the source-volume change by as much as 50% for a slope of 30 ø. This comparison also shows that the depths calculated by using Mogi's solution for prominent volcanoes should be considered as depths from the summit of the edifices. Finally, we illustrate these topographic effects by analyzing the deformation field measured by radar interferometry at Mount Etna during its 1991-1993 eruption. A three-dimensional modeling calculation shows that the flattening of the deflation field near the volcano's summit is probably a topographic effect.

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