deletions | additions       diff --git a/chapter_Methodology_section_Objective_1__.tex b/chapter_Methodology_section_Objective_1__.tex  index daf517e..6f91b3e 100644  --- a/chapter_Methodology_section_Objective_1__.tex  +++ b/chapter_Methodology_section_Objective_1__.tex 
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For this work we relied heavily on the seismic processing Python package Obspy \cite{Krischer_2015}. Matched filter detection was done using an open-source Python package called EQcorrscan \cite{Chamberlain_2014}, which allowed for a scalable, multi-parallel approach to the matched filtering routine. The package's so-called "embarassingly parallel" approach allowed us to make use of the PAN computing cluster at the University of Auckland through the New Zealand eScience Infrastructure (NeSI), which cut the processing time from months to a matter of a few days.  \section{Objective 2}  \subsection{Magnitudes}  In order to compute the magnitudes of the events detected using the matched filter method outlined above, we will turn to the SVD method detailed by Rubinstein and Ellsworth \cite{Rubinstein_2010}. This method makes use of the waveform similarity inherent between events in repeating sequences, such as the sequences defined by matched filter detections for a single template event, to calculate the relative moment of all events in the sequence. To implement this, we will separate the matched filter detections out into sequences based first on detecting template, and then on waveform similarity and hypocentral location to ensure a sufficient level of waveform similarity. As each template event was detected and processed automatically, a magnitude has already been assigned to each event. We can use these pre-assigned magnitudes to calibrate the relative moment calculations from the SVD method, provided each sequence contains only one template event (hence creating sequences based first on the detecting template for each event). In this way we will be left with accurate local magnitude calculations based on relative moment calculations via the SVD method.  \subsection{Focal Mechanisms}  \cite{Rubinstein_2010}  \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{Harris_2006}, \cite{Harris_2006a}, \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.