Analysing seismic-source mechanisms by linear-programming methods

• Published in: Geophysical Journal of the Royal Astronomical Society Vol. 84; no. 2; pp. 431 - 443
• Main Author: Julian, Bruce R.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.02.1986
• Subjects: earthquake mechanism; earthquake monitoring; linear programming; seismic moment tensor
• ISSN: 0956-540X; 0016-8009; 1365-246X
• DOI: 10.1111/j.1365-246X.1986.tb04364.x

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.