Getting Started
Python Packages
This module requires the python packages: multiprocessing, matplotlib, numpy, math and numba which can be installed using pip from a terminal using
pip install multiprocessing matplotlib numpy math numba
Importing Codes
These codes can be run using the ALI_FMM class. The other module functions are used in this class and do not need calling directly. The class can be input using the command
from Anis_TTF_rays import ALI_FMM
with Anis_TTF_rays.py in the same directory.
Note
The folder __pycache__ stores some compiled functions. Functions requiring compiling will be slow to run initially if not already compiled.
Creating an instance of the ALI_FMM class
An instance of the class can be created using
Forward_Model = ALI_FMM(veln, velpn, vel_map, scx, scz)
The name of this instance can be whatever you want. See __init__() command for additional arguments.
Class functions can then be called using the instance variable. For example
Forward_Model.plot_phase(1)
This will plot the phase velocity of material with index 1 which is stored within Forward_Model. All functions must be called from an instance of the class except for generate_group_vel() and generate_phase_vel() which can also be called using
ALI_FMM.generate_group_vel(None, c_22, c_23, c_33, c_44, density)
ALI_FMM.generate_phase_vel(None, c_22, c_23, c_33, c_44, density)
Defining Materials
There are two ways in which materials can be defined for these codes. The first way is by using a table of velocity curves which can be input when the class instance is initialised. These variables can be accessed using Forward_Model.group_vel and Forward_Model.phase_vel. The group and phase velocities must both be input as a table with the first column being the angle from 0 to 360 in 1 deg increments, and other columns being the velocities for each material. If no argument is given, an isotropic material with a velocity of 1m/s is used. This can be used for all isotropic materials as the variable vel_map can be used to scale all velocities.
Example velocity table
Velocity table with a single material
0.0 |
5085.0026 |
1.0 |
5088.2812 |
2.0 |
5097.9530 |
3.0 |
5113.5586 |
4.0 |
5134.4274 |
5.0 |
5159.7804 |
6.0 |
5188.8210 |
7.0 |
5220.7981 |
8.0 |
5255.0399 |
9.0 |
5290.9659 |
10.0 |
5328.0849 |
11.0 |
5365.9866 |
12.0 |
5404.3296 |
13.0 |
5442.8306 |
14.0 |
5481.2538 |
15.0 |
5519.4023 |
16.0 |
5557.1106 |
17.0 |
5594.2389 |
18.0 |
5630.6681 |
19.0 |
5666.2964 |
20.0 |
5701.0359 |
21.0 |
5734.8104 |
22.0 |
5767.5531 |
23.0 |
5799.2058 |
24.0 |
5829.7167 |
25.0 |
5859.0401 |
26.0 |
5887.1352 |
27.0 |
5913.9657 |
28.0 |
5939.4989 |
29.0 |
5963.7055 |
30.0 |
5986.5592 |
31.0 |
6008.0363 |
32.0 |
6028.1154 |
33.0 |
6046.7773 |
34.0 |
6064.0048 |
35.0 |
6079.7826 |
36.0 |
6094.0969 |
37.0 |
6106.9356 |
38.0 |
6118.2881 |
39.0 |
6128.1450 |
40.0 |
6136.4986 |
41.0 |
6143.3422 |
42.0 |
6148.6704 |
43.0 |
6152.4793 |
44.0 |
6154.7657 |
45.0 |
6155.5281 |
46.0 |
6154.7657 |
47.0 |
6152.4793 |
48.0 |
6148.6704 |
49.0 |
6143.3422 |
50.0 |
6136.4986 |
51.0 |
6128.1450 |
52.0 |
6118.2881 |
53.0 |
6106.9356 |
54.0 |
6094.0969 |
55.0 |
6079.7826 |
56.0 |
6064.0048 |
57.0 |
6046.7773 |
58.0 |
6028.1154 |
59.0 |
6008.0363 |
60.0 |
5986.5592 |
61.0 |
5963.7055 |
62.0 |
5939.4989 |
63.0 |
5913.9657 |
64.0 |
5887.1352 |
65.0 |
5859.0401 |
66.0 |
5829.7167 |
67.0 |
5799.2058 |
68.0 |
5767.5531 |
69.0 |
5734.8104 |
70.0 |
5701.0359 |
71.0 |
5666.2964 |
72.0 |
5630.6681 |
73.0 |
5594.2389 |
74.0 |
5557.1106 |
75.0 |
5519.4023 |
76.0 |
5481.2538 |
77.0 |
5442.8306 |
78.0 |
5404.3296 |
79.0 |
5365.9866 |
80.0 |
5328.0849 |
81.0 |
5290.9659 |
82.0 |
5255.0399 |
83.0 |
5220.7981 |
84.0 |
5188.8210 |
85.0 |
5159.7804 |
86.0 |
5134.4274 |
87.0 |
5113.5586 |
88.0 |
5097.9530 |
89.0 |
5088.2812 |
90.0 |
5085.0026 |
91.0 |
5088.2812 |
92.0 |
5097.9530 |
93.0 |
5113.5586 |
94.0 |
5134.4274 |
95.0 |
5159.7804 |
96.0 |
5188.8210 |
97.0 |
5220.7981 |
98.0 |
5255.0399 |
99.0 |
5290.9659 |
100.0 |
5328.0849 |
101.0 |
5365.9866 |
102.0 |
5404.3296 |
103.0 |
5442.8306 |
104.0 |
5481.2538 |
105.0 |
5519.4023 |
106.0 |
5557.1106 |
107.0 |
5594.2389 |
108.0 |
5630.6681 |
109.0 |
5666.2964 |
110.0 |
5701.0359 |
111.0 |
5734.8104 |
112.0 |
5767.5531 |
113.0 |
5799.2058 |
114.0 |
5829.7167 |
115.0 |
5859.0401 |
116.0 |
5887.1352 |
117.0 |
5913.9657 |
118.0 |
5939.4989 |
119.0 |
5963.7055 |
120.0 |
5986.5592 |
121.0 |
6008.0363 |
122.0 |
6028.1154 |
123.0 |
6046.7773 |
124.0 |
6064.0048 |
125.0 |
6079.7826 |
126.0 |
6094.0969 |
127.0 |
6106.9356 |
128.0 |
6118.2881 |
129.0 |
6128.1450 |
130.0 |
6136.4986 |
131.0 |
6143.3422 |
132.0 |
6148.6704 |
133.0 |
6152.4793 |
134.0 |
6154.7657 |
135.0 |
6155.5281 |
136.0 |
6154.7657 |
137.0 |
6152.4793 |
138.0 |
6148.6704 |
139.0 |
6143.3422 |
140.0 |
6136.4986 |
141.0 |
6128.1450 |
142.0 |
6118.2881 |
143.0 |
6106.9356 |
144.0 |
6094.0969 |
145.0 |
6079.7826 |
146.0 |
6064.0048 |
147.0 |
6046.7773 |
148.0 |
6028.1154 |
149.0 |
6008.0363 |
150.0 |
5986.5592 |
151.0 |
5963.7055 |
152.0 |
5939.4989 |
153.0 |
5913.9657 |
154.0 |
5887.1352 |
155.0 |
5859.0401 |
156.0 |
5829.7167 |
157.0 |
5799.2058 |
158.0 |
5767.5531 |
159.0 |
5734.8104 |
160.0 |
5701.0359 |
161.0 |
5666.2964 |
162.0 |
5630.6681 |
163.0 |
5594.2389 |
164.0 |
5557.1106 |
165.0 |
5519.4023 |
166.0 |
5481.2538 |
167.0 |
5442.8306 |
168.0 |
5404.3296 |
169.0 |
5365.9866 |
170.0 |
5328.0849 |
171.0 |
5290.9659 |
172.0 |
5255.0399 |
173.0 |
5220.7981 |
174.0 |
5188.8210 |
175.0 |
5159.7804 |
176.0 |
5134.4274 |
177.0 |
5113.5586 |
178.0 |
5097.9530 |
179.0 |
5088.2812 |
180.0 |
5085.0026 |
181.0 |
5088.2812 |
182.0 |
5097.9530 |
183.0 |
5113.5586 |
184.0 |
5134.4274 |
185.0 |
5159.7804 |
186.0 |
5188.8210 |
187.0 |
5220.7981 |
188.0 |
5255.0399 |
189.0 |
5290.9659 |
190.0 |
5328.0849 |
191.0 |
5365.9866 |
192.0 |
5404.3296 |
193.0 |
5442.8306 |
194.0 |
5481.2538 |
195.0 |
5519.4023 |
196.0 |
5557.1106 |
197.0 |
5594.2389 |
198.0 |
5630.6681 |
199.0 |
5666.2964 |
200.0 |
5701.0359 |
201.0 |
5734.8104 |
202.0 |
5767.5531 |
203.0 |
5799.2058 |
204.0 |
5829.7167 |
205.0 |
5859.0401 |
206.0 |
5887.1352 |
207.0 |
5913.9657 |
208.0 |
5939.4989 |
209.0 |
5963.7055 |
210.0 |
5986.5592 |
211.0 |
6008.0363 |
212.0 |
6028.1154 |
213.0 |
6046.7773 |
214.0 |
6064.0048 |
215.0 |
6079.7826 |
216.0 |
6094.0969 |
217.0 |
6106.9356 |
218.0 |
6118.2881 |
219.0 |
6128.1450 |
220.0 |
6136.4986 |
221.0 |
6143.3422 |
222.0 |
6148.6704 |
223.0 |
6152.4793 |
224.0 |
6154.7657 |
225.0 |
6155.5281 |
226.0 |
6154.7657 |
227.0 |
6152.4793 |
228.0 |
6148.6704 |
229.0 |
6143.3422 |
230.0 |
6136.4986 |
231.0 |
6128.1450 |
232.0 |
6118.2881 |
233.0 |
6106.9356 |
234.0 |
6094.0969 |
235.0 |
6079.7826 |
236.0 |
6064.0048 |
237.0 |
6046.7773 |
238.0 |
6028.1154 |
239.0 |
6008.0363 |
240.0 |
5986.5592 |
241.0 |
5963.7055 |
242.0 |
5939.4989 |
243.0 |
5913.9657 |
244.0 |
5887.1352 |
245.0 |
5859.0401 |
246.0 |
5829.7167 |
247.0 |
5799.2058 |
248.0 |
5767.5531 |
249.0 |
5734.8104 |
250.0 |
5701.0359 |
251.0 |
5666.2964 |
252.0 |
5630.6681 |
253.0 |
5594.2389 |
254.0 |
5557.1106 |
255.0 |
5519.4023 |
256.0 |
5481.2538 |
257.0 |
5442.8306 |
258.0 |
5404.3296 |
259.0 |
5365.9866 |
260.0 |
5328.0849 |
261.0 |
5290.9659 |
262.0 |
5255.0399 |
263.0 |
5220.7981 |
264.0 |
5188.8210 |
265.0 |
5159.7804 |
266.0 |
5134.4274 |
267.0 |
5113.5586 |
268.0 |
5097.9530 |
269.0 |
5088.2812 |
270.0 |
5085.0026 |
271.0 |
5088.2812 |
272.0 |
5097.9530 |
273.0 |
5113.5586 |
274.0 |
5134.4274 |
275.0 |
5159.7804 |
276.0 |
5188.8210 |
277.0 |
5220.7981 |
278.0 |
5255.0399 |
279.0 |
5290.9659 |
280.0 |
5328.0849 |
281.0 |
5365.9866 |
282.0 |
5404.3296 |
283.0 |
5442.8306 |
284.0 |
5481.2538 |
285.0 |
5519.4023 |
286.0 |
5557.1106 |
287.0 |
5594.2389 |
288.0 |
5630.6681 |
289.0 |
5666.2964 |
290.0 |
5701.0359 |
291.0 |
5734.8104 |
292.0 |
5767.5531 |
293.0 |
5799.2058 |
294.0 |
5829.7167 |
295.0 |
5859.0401 |
296.0 |
5887.1352 |
297.0 |
5913.9657 |
298.0 |
5939.4989 |
299.0 |
5963.7055 |
300.0 |
5986.5592 |
301.0 |
6008.0363 |
302.0 |
6028.1154 |
303.0 |
6046.7773 |
304.0 |
6064.0048 |
305.0 |
6079.7826 |
306.0 |
6094.0969 |
307.0 |
6106.9356 |
308.0 |
6118.2881 |
309.0 |
6128.1450 |
310.0 |
6136.4986 |
311.0 |
6143.3422 |
312.0 |
6148.6704 |
313.0 |
6152.4793 |
314.0 |
6154.7657 |
315.0 |
6155.5281 |
316.0 |
6154.7657 |
317.0 |
6152.4793 |
318.0 |
6148.6704 |
319.0 |
6143.3422 |
320.0 |
6136.4986 |
321.0 |
6128.1450 |
322.0 |
6118.2881 |
323.0 |
6106.9356 |
324.0 |
6094.0969 |
325.0 |
6079.7826 |
326.0 |
6064.0048 |
327.0 |
6046.7773 |
328.0 |
6028.1154 |
329.0 |
6008.0363 |
330.0 |
5986.5592 |
331.0 |
5963.7055 |
332.0 |
5939.4989 |
333.0 |
5913.9657 |
334.0 |
5887.1352 |
335.0 |
5859.0401 |
336.0 |
5829.7167 |
337.0 |
5799.2058 |
338.0 |
5767.5531 |
339.0 |
5734.8104 |
340.0 |
5701.0359 |
341.0 |
5666.2964 |
342.0 |
5630.6681 |
343.0 |
5594.2389 |
344.0 |
5557.1106 |
345.0 |
5519.4023 |
346.0 |
5481.2538 |
347.0 |
5442.8306 |
348.0 |
5404.3296 |
349.0 |
5365.9866 |
350.0 |
5328.0849 |
351.0 |
5290.9659 |
352.0 |
5255.0399 |
353.0 |
5220.7981 |
354.0 |
5188.8210 |
355.0 |
5159.7804 |
356.0 |
5134.4274 |
357.0 |
5113.5586 |
358.0 |
5097.9530 |
359.0 |
5088.2812 |
360.0 |
5085.0026 |
Anisotropic materials can also be defined using a stifness tensor and density of the material. This is done using the add_materials() function which will generate a table of velocities. Alternatively for orthotropic materials, velocities can be calculated at run time using the parameter stif_den which has the stifness tensor and density at all grid points. All stifness tensors using this method must be input using MPa not Pa and have type np.int64, which is used to aviod overflow errors. Any points not using this method will not be used and so can be left as zeros.
Tip
Using stif_den is prefered for anisotropic materials as it gives more accurate velocities.
Assigning Materials
There are four variables which define the materials at each grid point.
velnis the anisotropic orientations at each grid point i.e rotation of the velocity curve.
velpnis the material index of each grid point, with 0 being a grid point where the velocity is calculated at run time usingstif_denand others being the column in the velocity tables for that material.
vel_mapis the velocity scaling of each grid point. This is often set to 1 for most anisotropic materials, however for isotropic materials this parameter defines the velocity at a grid point (when used with a material with velocity of 1 in tables of velocities).
stif_denis the stifness tensors and density at grid points which is only used when the material index is 0.
Calculating Traveltime Fields
Travel time fields can be calculated through three different functions:
update_i()calculates the travel time field for a single source.
update()calculates travel time fields for all sources unless specific ones are selected through thesourcesparameter.
update_parallel()is the same asupdate(), however parallelisation is used to speed up computation.
Calculating Ray Paths
Ray paths can be calculated using find_all_TTF_rays() or in parrallel using find_all_TTF_rays_parallel(). These functions will calculate the nessessary travel time fields and perform ray tracing through them. The parameter trans_pairs defines which source reciever pairs have ray paths calculated. If ray paths are saved into the class they can be retrieved using the ray_path() function.
Tip
Travel times of ray paths are identical when traveling forward or backwards along the ray. Swapping the source and receivers using the paramter trans_pairs so that less recievers are used will result in faster computation as less travel time fields are required.
Example
Both values of trans_pairs use the same source/receiver pairs, however using a single reciever with three sources is computationally cheaper than one source and three receivers
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |