Yet another moment-tensor parameterization: Moment tensors

The source mechanism of a microseismic event, or any smallearthquake, can be described by its moment tensor. The source type is described by a 3-vector formed from the ordered,principal (eigen) values of the moment tensor and the source orientation fromthe normalizedeigenvectors. The direction and magnitude of the principal-value vector describe the sourcetype and scalar moment,respectively. The source type can be described by the position of the principal-valuevector on the permittedlune of a unitsphere. As with any projection or cartography mapping, manyparameterizations have been suggested to describe this position. Two dominate in the literature - the Riedesel-Jordan andHudson-Pearce-Rogers parameters. All have advantages anddisadvantages. In this paper, we review the most popular parameterizations,illustrating their similarities and the distortion they cause in themapping between a uniform distributionof source types in the permitted lune and the parameter space. A new parameterization is suggested based on the solid angles formed bythe principal-value vector. This has the advantage of being simple to define geometrically in the principal-value space (although the formulaeare complicated), being naturally normalized and having a more uniformmapping than other parameterizations. However, we do not claim that this isthe best or ideal parameterization, just a reasonablechoice.