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\section{Objective 2}
\subsection{Magnitudes}
In order to To compute the magnitudes of the events detected using the matched
filter method outlined above, we will
turn to use 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. location. As each template
event
was detected and processed automatically, a generally represents the largest magnitude
has already been assigned to event in each
event. of these sequences,
they are likely the best candidate for waveform-based moment tensor inversion.
We
can propose calculating seismic moment of these template events following the technique
outlined by both Jiao et al. \cite{Jiao_2014} and Guilhem et al. \cite{Guilhem_2014}
and to use these
pre-assigned magnitudes moment tensors to calibrate the relative moment calculations from the
SVD
method, provided each sequence contains method. This will work only
for sequences which contain at least one template event
(hence creating sequences based first on the detecting template for
each event). In this way which we
can calculate a reliable moment tensor solution but will
be left with provide accurate
local moment magnitude
calculations based on relative values within these sequences down to potentially very small values.
Using the method of Guilhem and others \cite{Guilhem_2014} to calculate the focal
mechanisms for the templates will allow us to investigate the non-double-couple
components of these events which can account for large percentages of seismic moment
calculations via in a geothermal environment \cite{Guilhem_2014}. Furthermore, non-double-couple components of the
SVD method. moment tensor offer extremely valuable information about the cause of seismicity.
For instance, we might expect to see an increase in the
non-double-couple component of the moment tensor near injection wells, transitioning
to largely double-couple events away from the well or after well shut-in reflecting
a mechanism which contains parts shear failure and tensile opening in areas where
fluid movement is occurring \cite{Guilhem_2014}.
\subsection{Focal Mechanisms}
Calculation of the focal mechanisms for the matched filter-detected events in this study will be done using the approach outlined in \cite{Pugh_2016} which expresses the first motion of a given phase arrival as the probability of both negative and positive polarities instead of the standard, binary "up or down" approach. This approach can also be fully automated which is useful when dealing with datasets of the size of matched filter detection catalogs.