A mathematical method is developed for approximating the elastostatic surface deformation fields (strains and displacements) produced by a buried strike-slip fault or long shear crack in a mildly uneven, homogeneous elastic half-space. The approximation scheme assumes that the wavelengths of surface topography are much longer than their respective amplitudes. The final solution is the method of images solution for a screw dislocation in a flat half-space plus a residual linear term from the uneveness of the half-space
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