A Numerical Study of Diffraction in Reentrant Geologic Structure.
Abstract
Diffraction effects in complicated geologic and topographic structures of interest to the Air Force Geophysics Lab. were investigated. This report examines diffraction by reentrant corners, i.e., corners with included angle greater than 180 degrees, which idealize the abrupt topographic relief commonly found at the base of escarpments and mesas. Reentrant landforms are also common in tectonic regions, and include fault scarps and other block joints. Approximating these regions of high curvature by perfect edges defines so-called generalized models--where curvature is concentrated at singular points (corners) on the free-surface. Diffraction from a single corner is studied in detail. Effects of more realistic distributed curvature in local and regional models will be examined in subsequent reports. The principal tool for the study is finite element modeling, since no mathematical solutions presently exist for P-SV wave edge diffraction in even the simplest geologic diffractors. Diffraction of plane P- and SV-waves and a Rayleigh wave are calculated for various reentrant wedges. This necessary emphasis on numerical simulation is balanced by a mathematical analysis of self-similar vector wave diffraction theory. The analysis yields a formal reduction of the general problem to a system of singular integral equations. The resulting integral expressions provide a new calculational basis for solutions to a variety of diffraction problems in mathematical physics. Keywords: Reentrant geologic corners; Finite element diffraction analysis; Topographic structure; Mathematical diffraction analysis; Mesas and escarpments.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 15, 1985
- Accession Number
- ADA168562
Entities
People
- Gregory L. Wojcik
- Rudolf Mak