Postseismic viscoelastic-gravitational half space computations: Problems and solutions

We consider the problem of surface deformation arising from a fault in a semi‐infinite, elastic‐gravitational, and/or viscoelastic‐gravitational, plane‐layered medium, subject to an externally imposed gravitational acceleration g. Rundle [1981, 1982] presented a calculation in which self‐gravitation, represented by terms proportional to G are neglected, and the externally imposed acceleration due to gravity, g, is considered constant in the medium. Because of the recent strong interest in computations of this type, we examine the assumptions involved in these computations. We show that these assumptions are not likely to have serious consequences in the relatively near‐field viscoelastic displacements, where the earth's curvature is neglected. We also show that the approximation described by Rundle [1981, 1982], which was technically not regular as z → ∞, can easily be regularized using a new approach without appreciable change in the resulting displacement field.