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Chet Hopp edited chapter_Methodology_section_Objective_1__.tex
almost 8 years ago
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\section{Objective 2}
\section{Objective 3}
Match filter detection techniques are computationally expensive when applied across large datasets. The expense is multiplied as more earthquakes are added to the list of desired template events (referred to by Barrett and Beroza as the design set) \cite{Barrett_2014} and as larger seismograph networks, with more channels of data, are used. At the same time, it is important that a design set effectively represent the variety of sources present in a given study area or risk missing what might be important seismicity. Subspace detection has been used to address these considerations (e.g. \cite{Gibbons_2006}, \cite{Barrett_2014}). Subspace detection tries to represent a design set of template events, which would be used as individual detectors for matched filtering, as a single subspace detector. These detectors are subspaces made up of n eigenvectors representing the design set space, where n is some integer less than the number of templates. Detection is performed within the subspace defined by each detector. Continuous data is projected into this subspace, producing a detection statistic of between 0 and 1.
In order to divide the entire set of 637 templates used above into representative design sets, we will use a hierarchical clustering technique to create groups of similar templates based on both inter-event distance and waveform cross-correlation. These groups will then be represented by a series of subspace detectors and used in much the same way as templates are use in the matched filtering process. The results of the subspace detection will be compared to the results of the above matched filtering in order to assess the appropriateness of subspace detection in the context of a geothermal microseismicity and investigate methods of template clustering for subspace detector creation.
