Source type plot for inversion of the moment tensor

Seismic signals provide information about the underlying moment tensor which, in turn, may be interpreted in terms of source mechanism. This paper is concerned with a two‐dimensional graphical display of all possible relative sizes of the three principal moments; it provides a method of representing the probability density of these relative sizes deduced from a given set of data. Information provided by such a display, together with that relating to the orientation of the principal moments, provides as full a picture of the moment tensor as possible apart from an indication of its absolute magnitude. As with the compatibility plot, which was previously introduced to portray probability measures for different forms of P wave seismogram given a presumed source type, this “source type plot” for display of the principal moments is constructed to be “equal area” in the sense that the a priori probability density of the moment ratios is uniform over the whole plot. This a priori probability is based on the assumption that, with no information whatsoever concerning the source mechanism, each principal moment may independently take any value up to some arbitrary upper limit of magnitude, with equal likelihood. Although we have in mind the study of teleseismic relative amplitude data, the ideas can, in principle, be applied quite generally. The aim is to be able to display the degree of constraint imposed on the moment tensor by any set of observed data; estimates of the sizes of the principal moments together with their errors, when displayed on the source type plot, show directly the range of moment tensors compatible with the data.