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.

A method is described which uses the relative amplitudes of related seismic phases to impose constraints on the form of the P and $ wave radiation patterns, from which a moment tensor determination is obtained complete with a well-founded measure of its precision. Two types of teleseismic relative amplitude measurements may be employed: those relating P, pP, and sP and those relating the three components of the direct $ wave. Examples are given which apply the method to (1) smaller shallow earthquakes (mr, <•-5.5) recorded at short period, (2) larger intermediate-depth and deep earthquakes (mr, >•-5.8) using long-period seismograms, and (3) large mr, shallow earthquakes, which require both P and S wave data at long period. The relative amplitude moment tensor program (RAMP) is an advance on the relative amplitude method of Pearce [1977, 1980] in that the a priori double couple assumption is now relaxed. Results are compared with those of other moment tensor methods where available. RAMP is found to be a sensitive indicator of volumetric source component even for small data sets, for which it is less good at discriminating between different constant-volume source types, notably the double couple and the compensated linear vector dipole. Since current inverse methods presume a constant-volume source, our method alone is a reliable indicator of volumetric component, which is important for the analysis of source processes and in earthquake-explosion discrimination. 47, 150-158, 1987. Stimpson, I. G., and R. G. Pearce, Moment tensors and source processes of three deep Sea of Okhotsk earthquakes, Phys. Earth Planet. Inter.,

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The method of specifying the amplitudes of teleseismic phases (P, pP, and sP, or three‐component direct S) used in the relative amplitude moment tensor method (Pearce and Rogers, 1989) is modified to provide for a most likely, or “best fit,” moment tensor. Instead of imposing uniform probability on all amplitudes lying between upper and lower bounds which are specified for each phase, a Gaussian probability function related to these bounds is assumed. This modification acknowledges that an amplitude value nearer to the midpoint of the range is more likely to represent the true value, and results in a probability density function in moment tensor space which is itself peaked, yielding a single most likely solution. By contrast, a uniform likelihood within specified amplitude bounds can yield only a range of solutions acceptable with uniform likelihood. This Gaussian relative amplitude method (GRAM) is applied to several earthquakes previously studied using the original procedure (relative amplitude moment tensor program, RAMP). GRAM yields results which agree closely with those of RAMP, but in which the source type is more tightly defined, particularly in its deviatoric component. Previously, any single solution had to be chosen arbitrarily from near the centroid of the compatible range, but it is shown that, as expected, the most likely solution may lie anywhere within this range.

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