Assessing the uncertainties on seismic source parameters: Towards realistic error estimates for centroid-moment-tensor determinations

Abstract

The centroid-moment-tensor (CMT) algorithm provides a straightforward, rapid method for the determination of seismic source parameters from waveform data. As such, it has found widespread application, and catalogues of CMT solutions – particularly the catalogue maintained by the Global CMT Project – are routinely used by geoscientists. However, there have been few attempts to quantify the uncertainties associated with any given CMT determination: whilst catalogues typically quote a ‘standard error’ for each source parameter, these are generally accepted to significantly underestimate the true scale of uncertainty, as all systematic effects are ignored. This prevents users of source parameters from properly assessing possible impacts of this uncertainty upon their own analysis. The CMT algorithm determines the best-fitting source parameters within a particular modelling framework, but any deficiencies in this framework may lead to systematic errors. As a result, the minimummisfit source may not be equivalent to the ‘true’ source. We suggest a pragmatic solution to uncertainty assessment, based on accepting that any ‘low-misfit’ source may be a plausible model for a given event. The definition of ‘low-misfit’ should be based upon an assessment of the scale of potential systematic effects. We set out how this can be used to estimate the range of values that each parameter might take, by considering the curvature of the misfit function as minimised by the CMT algorithm. This approach is computationally efficient, with cost similar to that of performing an additional iteration during CMT inversion for each source parameter to be considered. The source inversion process is sensitive to the various choices that must be made regarding dataset, earth model and inversion strategy, and for best results, uncertainty assessment should be performed using the same choices. Unfortunately, this information is rarely available when sources are obtained from catalogues. As already indicated by Valentine and Woodhouse (2010), researchers conducting comparisons between data and synthetic waveforms must ensure that their approach to forward-modelling is consistent with the source parameters used; in practice, this suggests that they should consider performing their own source inversions. However, it is possible to obtain rough estimates of uncertainty using only forward-modelling.