Hypocentral cross-sections and arc-trench curvature

Abstract

A method is shown for obtaining the center of curvature, or pole, as well as the points of inflection of arcuate features such as trenches, on a spherical Earth. This information is needed, among other things, for projecting hypocenters along the are or perpendicular to it, which is better for depicting the geometry of Wadati-Benioff zones than the traditional straight-line approach. As a reference, the basic expressions for arcuate hypocentral projections are also given. As an example, the poles and points of inflection for the Middle America Trench are obtained. Using these parameters, hypocentral cross-sections projected along the are and perpendicular to it for this region are shown. The advantage of such sections as compared to straight-line sections from thc litcrature is dcmonstrated.