An accurate and efficient method for including the effects of topography in three-dimensional elastic models of ground deformation with applications to radar interferometry

Topography has a large effect on the results predicted by elastic surface deformation models in regions of significant relief. In some cases, topography may have more influence on the predicted deformation field than do model source parameters. We have developed an approximate analytical technique for including topographic effects that retains most of the computational simplicity of elastic half-space models while providing an accurate representation of topographic effects. We use a series expansion of the elastic half-space solution with a small slope approximation, yielding a set of higher-order corrections. The integrated effect of these corrections is evaluated using Fourier methods. We investigate the effectiveness of our method by comparing predicted results for a tilted triaxial ellipsoid with those predicted by finite element models. The resulting displacements and displacement gradients are in good agreement with finite element results both for relatively smooth topography (synthetically generated) and for the greater relief in the vicinity of Mount Etna volcano. We then compare the results of our method with those predicted by traditional elastic half-space models using different reference elevations, and with a previously proposed method of estimating topographic effects. Our new method provides a significantly better fit to the finite element results than do the other methods. Our method is able to accurately portray both the number and the horizontal pattern of fringes in a synthetic interferogram when compared with finite element results. In particular, the method accurately represents the broadening of fringes that is observed in regions of high relief, as well as reproducing the location of the fringe center and the topographically induced deviation of the fringes from a regular pattern. Elastic half-space models typically show a fringe center that is displaced with respect to the finite element results, indicating that parameter inversions based on such a model would provide incorrect estimates of the horizontal source position. The lack of topographically generated fringe distortions in elastic half-space results would also likely lead to inaccuracies in the predicted magnitude and orientation of proposed deformation sources. Our new technique overcomes these limitations and should be useful when evaluating either traditional geodetic results or the greater areal coverage provided by interferometric observations.