1-4244-2547-1/08/$20.00 ©2008 IEEE Automated procedure for InSAR data inversion using Finite Element Method Gilda Currenti, Ciro Del Negro, Danila Scandura Istituto Nazionale di Geofisica e Vulcanologia Sezione di Catania Catania, Italy currenti@ct.ingv.it Charles A. Williams GNS Science Avalon, New Zealand Abstract— Source inversions performed using different kind of static deformation data, such as GPS displacements, DInSAR imagery, levelling and EDM measurements, suggest that slip on fault is usually not uniform and is better modeled as a distribution of dislocation sources. To this aim, we developed an automated procedure for geodetic data inversion to estimate slip distribution along the fault interfaces. Finite Element Models are used to compute synthetic Green’s functions for static displacement. FEM-generated synthetic Green’s functions are combined with inverse methods to estimate slip distributions that explain the observed ground deformation. Keywords-InSar Data; geodetic inversion; numerical modeling I. INTRODUCTION The continuous increase of spatial and temporal coverage of geodetic data provided by Interferometric Synthetic Aperture Radar (InSAR) opens new perspectives in the study of deformation sources. The large amount of available observations has definitely highlighted that slip along faults is not uniform and can be better described as a distribution of dislocation sources. We propose an automated procedure for InSAR data inversion to estimate slip distribution along the fault interfaces. Geodetic data inversions are usually based on a homogeneous elastic half-space model, although medium heterogeneity and topography are likely to affect the magnitude and pattern of the deformation field [2]. To account for topographic effects as well as a complicated distribution of material properties, we use the finite-element method (FEM) for computing synthetic Green's functions and estimating the static displacement. The procedure is parallelized to run on cluster for speeding up the computation time. In order to recover the slip distribution, we invert the InSar data using a Quadratic Programming (QP) algorithm with bound constraints on slip values. A number of tests were carried out both on synthetically generated data and on DInSAR observations expected at Mt Etna volcano to assess the performance and the implication of the inversion procedure. II. NUMERICAL PROCEDURE The relationship between slip along a fault and surface displacements can generally be described by a linear relationship: Gs d i = . (1) where G is the elastic response of the Earth (Green’s functions), s is the fault slip and d i are displacements observed on ground surface. Although uniform slip models can provide a fair fit to geodetic data, heterogeneous slip along the fault plane is expected. Discretizing the fault planes into M sub-faults (patches hereafter) leads to the displacement: j j ij i s G d ∑ = . (2) where the G ij coefficients are the contributions to the displacement at the i-th observation point due to a unitary dislocation of the j-th patch. Therefore, the inverse problem can be formulated as the solution of a system of N linear equations as: Gs d = (3) where s is the M vector of unknown slip values of the patches, d is the N vector of observed ground displacements, and G is a matrix with elements G ij . Summing up, the procedure can be subdivided into three main points (Fig. 1): • Subdividing the faults in a finite number of patches; • Computing the Green's Function for all the patches and the measurement points; • Solving a linear inversion problem to determine the slip distribution. The last two points are described below in more detail.