Inversion of SAR data in active volcanic areas by optimization techniques

Abstract

Abstract. The inversion problem concerns the identification of parameters of a volcanic source causing observable changes in ground deformation data recorded in volcanic areas. In particular, this paper deals with the inversion of ground deformation measured by using SAR (Synthetic Aperture Radar) interferometry and an inversion approach formulated in terms of an optimization problem is proposed. Based on this inversion scheme, it is shown that the problem of inverting ground deformation data in terms of a single source, of Mogi or Okada type, is numerically well conditioned. In the paper, two case studies of inverting actual SAR data recorded on Mt. Etna during eruptions occurring in 1998 and 2001 are investigated, showing the suitability of the proposed technique.

Composite ground deformation pattern forerunning the 2004–2005 Mount Etna eruption

“…where N represents the number of measured points, O i and P i represent the observed and predicted values, respectively, and O and P represent their mean values [Nunnari et al, 2005].…”

“…[24] To invert the data set, we applied the Genetic Algorithm (GA) by using an optimization algorithm implemented by Nunnari et al [2005]. GA is generally better suited than typical gradient-based techniques to find global minimums for nonlinear optimization problems with many variables.…”

FEM and ANN combined approach for predicting pressure source parameters at Etna volcano

“…Inverse problems are usually formulated and solved as optimization problems based on iterative procedures, minimizing an objective function that quantifies the misfit between the observed data and the estimated solutions from forward models. Analytical solutions are often used to represent the forward model because of computational convenience and fast computer implementation (e.g., Currenti et al, 2005;Nunnari et al, 2005). The intrinsic limitation of inverse methods based on analytical solutions is that irregular Correspondence to: G. Currenti (currenti@ct.ingv.it) geometries, complicated distribution of medium properties, and topography effects cannot be accounted for.…”

“…The main advantage of inverting with ANNs consists in the availability of an approximation of the inverse model, avoiding a search for the minimum and speeding up the computation of the optimal solution that fits the observed data. ANNs have been widely used to invert geophysical models based on straightforward analytical solutions (Langer et al, 1996;Maugeri et al, 1996Maugeri et al, , 1997Nunnari et al, 2001) because of low computational effort. On the contrary, FEM-based numerical solutions are not often combined to ANN inversion scheme because they are time-consuming both in length of time required to design a mesh and in actual computation time.…”

“…The ANNs are trained with numerical patterns, obtained computing geophysical changes caused by pressure sources through FEM analysis. We propose an integrated approach in which geophysical data of different nature, that can be ascribed to the same volcanic source, are jointly modeled in order to identify the source parameters with a greater degree of confidence than when only one kind of data is used (Nunnari et al, 2001).…”