S43C-02: Incorporating the Uncertainties of Nodal-Plane Orientation in the Seismo-Lineament Analysis Method (SLAM)

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Authors: V. Cronin1, K. A. Sverdrup2

Author Institutions: 1. Geology, Baylor University, Waco, TX, United States. 2. Geosciences, University of Wisconsin-Milwaukee, Milwaukee, WI, United States.

The process of delineating a seismo-lineament has evolved since the first description of the Seismo-Lineament Analysis Method (SLAM) by Cronin et al. (2008, Env & Eng Geol 14(3) 199-219). SLAM is a reconnaissance tool to find the trace of the fault that produced an shallow-focus earthquake by projecting the corresponding nodal planes (NP) upward to their intersections with the ground surface, as represented by a DEM or topographic map. A seismo-lineament is formed by the intersection of the uncertainty volume associated with a given NP and the ground surface. The ground-surface trace of the fault that produced the earthquake is likely to be within one of the two seismo-lineaments associated with the two NPs derived from the earthquake’s focal mechanism solution. When no uncertainty estimate has been reported for the NP orientation, the uncertainty volume associated with a given NP is bounded by parallel planes that are [1] tangent to the ellipsoidal uncertainty volume around the focus and [2] parallel to the NP. If the ground surface is planar, the resulting seismo-lineament is bounded by parallel lines. When an uncertainty is reported for the NP orientation, the seismo-lineament resembles a bow tie, with the epicenter located adjacent to or within the ‘knot.’ Some published lists of focal mechanisms include only one NP with associated uncertainties. The NP orientation uncertainties in strike azimuth (+/– gamma), dip angle (+/– epsilon) and rake that are output from an FPFIT analysis (Reasenberg and Oppenheimer, 1985, USGS OFR 85-739) are taken to be the same for both NPs (Oppenheimer, 2013, pers com). The boundaries of the NP uncertainty volume are each comprised by planes that are tangent to the focal uncertainty ellipsoid. One boundary, whose nearest horizontal distance from the epicenter is greater than or equal to that of the other boundary, is formed by the set of all planes with strike azimuths equal to the reported NP strike azimuth +/– gamma, and dip angle equal to the reported NP dip angle – epsilon. For all elevations above the mean focus, this boundary is a simple shape effectively formed by the intersection of two planes whose strike azimuths are the mean strike + gamma and the mean strike – gamma, respectively. The other boundary is formed by the set of all planes with strike azimuths equal to the reported NP strike azimuth +/– gamma, and dip angle equal to the reported NP dip angle + epsilon. For all elevations above the mean focus, this boundary simplifies to the intersection of two planes in some cases, but involves two planes plus a segment of a cone in others. Description of the relevant details would exhaust the limits of this abstract; the essential geometry of this boundary is simple for all elevations above the mean focus. Code written in Mathematica delineates the trace of seismo-lineament boundaries on a DEM-derived ground-surface map. A manual procedure to define these boundaries has also been developed that requires a simple calculator with trig functions, ruler, pencil and topographic map of the epicentral area. http://bearspace.baylor.edu/Vince_Cronin/www/SLAM/

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