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scripts/window_weights/README.md

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### Introduction
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## Introduction
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This directory contains example files for two different weighting strategies,
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both of which are already implemented in pypaw.
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##### Weighting Strategy Version I
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---
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#### Weighting Strategy Version I
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The weightings is determined in order of category, receiver and finally, source.
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1. determine the category weightings ratio based on number of window counts in each category.
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Attention here that we determined is the ratio between each category but not the absolute
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values. The absolut values will be determined on each event level(to satisfy the
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normalization equation).
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2. determine the receiver weightings based on station geographic distribution(ratios) and window
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counts(normalization) of each receiver given one event.
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Also, determine the absolute values of category weightings for each source.
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Once you reach this step, you can use the weights
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(category and receiver combined) to sum the adjoint source from each category for each event.
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And once you get summed adjoint source for each event, you can then launch the adjoint simulation
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to calculate the kernel for each source.
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3. determine the source weightings based on source geographic distribution(ratio) and
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number of windows(normalization) of each source. The source weightings are applied on kernels
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number of windows(normalization) of each source.
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The source weightings are applied on kernels
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when summing all the kernels together.
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The benefit of version I is that you can freely combine kernels from different number of sources.
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The draw back of that is it doesn't gurantee the weightins for different categories are
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evenly balanced(but will not be too deviated, based on my experiment).
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---
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###### Weighting Strategy Version II
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#### Weighting Strategy Version II
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The weightings are determined in order of receiver, source and finally category.
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1. determine the receiver weightings based on window counts and station distribution.
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(same as version I)
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2. determine the source weightings based on source geographic distribution(ratio) and
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number of sources(the sum of source weights eqaul to number of sources)
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3. determine the category weightings based on source weights(ws) number of windows in
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each category(Nsc) and number of categories(C).
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wc = 1 / (C * \sum_{s} ws * Nsc)
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```
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W_{} = 1 / (C * \sum_{s} ws * N_{sc})
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```
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4. Finally, you combine the receiver, source and category weightings
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The benefit of this weighting is you can guarantee that the sum of weightings from each

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