Analysing seismic‐source mechanisms by linear‐programming methods

Abstract

Summary. Linear‐programming methods are powerful and efficient tools for objectively analysing seismic focal mechanisms and are applicable to a wide range of problems, including tsunami warning and nuclear explosion identification. The source mechanism is represented as a point in the six‐dimensional space of moment‐tensor components. Each observed polarity provides an inequality constraint, linear with respect to the moment tensor components, that restricts the solution to a half‐space bounded by a hyperplane passing through the origin. The intersection of these half‐spaces is the convex set of all acceptable solutions. Using linear programming, a solution consistent with the polarity constraints can be obtained that maximizes or minimizes any desired linear function of the moment tensor components; the dilatation, the thrust‐like nature, and the strike‐slip‐like nature of an event are examples of such functions. The present method can easily be extended to fit observed seismic‐wave amplitudes (either signed or absolute) subject to polarity constraints, and to assess the range of mechanisms consistent with a set of measured amplitudes. Copyright © 1986, Wiley Blackwell. All rights reserved