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 d eformation models in regions of significant relief. In some cases, topograp hy may have more influence on the predicted deformation field than do model source parameters. We have developed an approximate analytical technique f or including topographic effects that retains most of the computational sim plicity of elastic half-space models while providing an accurate representa tion of topographic effects. We use a series expansion of the elastic half- space solution with a small slope approximation, yielding a set of higher-o rder corrections. The integrated effect of these corrections is evaluated u sing Fourier methods. We investigate the effectiveness of our method by com paring predicted results for a tilted triaxial ellipsoid with those predict ed by finite element models. The resulting displacements and displacement g radients are in good agreement with finite element results both for relativ ely smooth topography (synthetically generated) and for the greater relief in the vicinity of Mount Etna volcano. We then compare the results of our m ethod with those predicted by traditional elastic half-space models using d ifferent reference elevations, and with a previously proposed method of est imating 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 f ringes in a synthetic interferogram when compared with finite element resul ts. In particular, the method accurately represents the broadening of fring es that is observed in regions of high relief, as well as reproducing the l ocation of the fringe center and the topographically induced deviation of t he fringes from a regular pattern. Elastic half-space models typically show a fringe center that is displaced with respect to the finite element resul ts, indicating that parameter inversions based on such a model would provid e incorrect estimates of the horizontal source position. The lack of topogr aphically 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 limitat ions and should be useful when evaluating either traditional geodetic resul ts or the greater areal coverage provided by interferometric observations.