Garvin’s generalized problem revisited

One of the great classical problems in theoretical seismology is Garvin’s problem, which deals with the response of an elastic half-space subjected to a blast line source applied in its interior. However, Garvin (Exact transient solution of the buried line source problem. Proceedings of the Royal Society of London, Series A 1956;528–541[4]) himself provided only the solution for points on the free surface of the half-space. Although a rigorous extension to points in the interior of the half-space was given nearly decade-and-a-half later by Alterman and Loewenthal (Algebraic expressions for the impulsive motion of an elastic half-space. Israel Journal of Technology 1969; 7 (6):495–504[1]), these scientists published their paper in a technical journal of rather restricted circulation, as a result of which their complete solution remained largely unnoticed by the geophysical and soil dynamics communities. This article revisits Garvin’s generalized problem, presents a concise rendition and summary together with a very effective and accurate simplification, and examines the response characteristics for a pair of buried source-receiver location. It also includes a compact and very effective Matlab program for its evaluation. ► Revision of Alterman & Lowental 1969 extension to Garvin's problem. ► Ideal tool to be used as a benchmark for the validation of numerical solutions.► Details of the quartic equation needed for the inversion of the Cagniard-DeHoop path. ► 4.-A Matlab program allows obtaining theoretical seismograms.