1
- ### Introduction
1
+ ## Introduction
2
2
3
3
This directory contains example files for two different weighting strategies,
4
4
both of which are already implemented in pypaw.
5
5
6
- ##### Weighting Strategy Version I
6
+ ---
7
+ #### Weighting Strategy Version I
7
8
8
9
The weightings is determined in order of category, receiver and finally, source.
9
10
1 . determine the category weightings ratio based on number of window counts in each category.
11
+
10
12
Attention here that we determined is the ratio between each category but not the absolute
11
13
values. The absolut values will be determined on each event level(to satisfy the
12
14
normalization equation).
15
+
13
16
2 . determine the receiver weightings based on station geographic distribution(ratios) and window
14
17
counts(normalization) of each receiver given one event.
18
+
15
19
Also, determine the absolute values of category weightings for each source.
16
20
Once you reach this step, you can use the weights
17
21
(category and receiver combined) to sum the adjoint source from each category for each event.
18
22
And once you get summed adjoint source for each event, you can then launch the adjoint simulation
19
23
to calculate the kernel for each source.
24
+
20
25
3 . determine the source weightings based on source geographic distribution(ratio) and
21
- number of windows(normalization) of each source. The source weightings are applied on kernels
26
+ number of windows(normalization) of each source.
27
+
28
+ The source weightings are applied on kernels
22
29
when summing all the kernels together.
23
30
24
31
The benefit of version I is that you can freely combine kernels from different number of sources.
@@ -34,16 +41,22 @@ this weighting gives you more freedom when combining kernels.
34
41
The draw back of that is it doesn't gurantee the weightins for different categories are
35
42
evenly balanced(but will not be too deviated, based on my experiment).
36
43
44
+ ---
37
45
38
- ###### Weighting Strategy Version II
46
+ #### Weighting Strategy Version II
39
47
The weightings are determined in order of receiver, source and finally category.
40
48
1 . determine the receiver weightings based on window counts and station distribution.
41
49
(same as version I)
50
+
42
51
2 . determine the source weightings based on source geographic distribution(ratio) and
43
52
number of sources(the sum of source weights eqaul to number of sources)
53
+
44
54
3 . determine the category weightings based on source weights(ws) number of windows in
45
55
each category(Nsc) and number of categories(C).
46
- wc = 1 / (C * \sum_ {s} ws * Nsc)
56
+
57
+ ```
58
+ W_{} = 1 / (C * \sum_{s} ws * N_{sc})
59
+ ```
47
60
4. Finally, you combine the receiver, source and category weightings
48
61
49
62
The benefit of this weighting is you can guarantee that the sum of weightings from each
0 commit comments