Deriving source-time functions using principal component analysis

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Abstract
Factors such as source complexity, microseismic noise, and lateral heterogeneity all introduce nonuniqueness into the source-time function. The technique of principal component analysis is used to factor the moment tensor into a set of orthogonal source-time functions. This is accomplished through the singular value decomposition of the time-varying moment tensor. The adequacy of assuming a single source-time function may then be examined through the singular values of the decomposition. The F test can also be used to assess the significance of the various principal component basis functions. The set of significant basis functions can be used to test models of the source-time functions, including multiple sources. Application of this technique to the Harzer nuclear explosion indicated that a single source-time function was found to adequately explain the moment tensor. It consists of a single pulse appearing on the diagonal elements of the moment-rate tensor. The decomposition of the moment tensor for a deep teleseism in the Bonin Islands revealed three basis functions associated with relatively large singular values. The F test indicated that only two of the principal components were significant. The principal component associated with the largest singular value consists of a large pulse followed 16-sec later by a diminished pulse. The second principal component, a long-period oscillation, appears to be a manifestation of the poor resolution of the moment-rate tensor at low frequencies.