Figure 1.
(a) RTM of scenario 1 using smoothed background velocity. (b) RTM of scenario 4 using true velocity as the input with multiple reflections. (c) RTM of scenario 3 using smoothed velocity with multiple energy. (d) Shot illumination of scenario 1. (e) Shot illumination of scenario 4. (f) Shot illumination of scenario 3.
Figure 1.
(a) RTM of scenario 1 using smoothed background velocity. (b) RTM of scenario 4 using true velocity as the input with multiple reflections. (c) RTM of scenario 3 using smoothed velocity with multiple energy. (d) Shot illumination of scenario 1. (e) Shot illumination of scenario 4. (f) Shot illumination of scenario 3.
Figure 2.
Pluto example: (a) background reflectivity, (b) true reflectivity, (c) RTM image without multiple energy, (d) RTM image with multiple energy, (e) RTMM with true band-limited reflectivity, and (f) true velocity model.
Figure 2.
Pluto example: (a) background reflectivity, (b) true reflectivity, (c) RTM image without multiple energy, (d) RTM image with multiple energy, (e) RTMM with true band-limited reflectivity, and (f) true velocity model.
Figure 3.
Detailed workflow of the U-net architecture. Each blue box represents a multichannel feature. The yellow boxes stand for the concatenated copied features from the encoder part. The arrows between boxes correspond to the different operations, as shown in the right legend. The number of channels is located on top of the box and the image dimensionality is denoted on the left or right edge.
Figure 3.
Detailed workflow of the U-net architecture. Each blue box represents a multichannel feature. The yellow boxes stand for the concatenated copied features from the encoder part. The arrows between boxes correspond to the different operations, as shown in the right legend. The number of channels is located on top of the box and the image dimensionality is denoted on the left or right edge.
Figure 4.
Neural network model plan for four scenarios.
Figure 4.
Neural network model plan for four scenarios.
Figure 5.
Canadian Foothills model results: (a) reflectivity from the background velocity, (b) true band-limited reflectivity, (c) RTM image without multiple reflections, (d) RTM image with multiple reflections, (e) model R1 result based on workflow 1, (f) model R3 result based on workflow 3, (g) model R4 result based on workflow 4, (h) true Foothills velocity, and (i) LSRTM result after 15 iterations. The boxes indicate areas shown in detail in the next figures.
Figure 5.
Canadian Foothills model results: (a) reflectivity from the background velocity, (b) true band-limited reflectivity, (c) RTM image without multiple reflections, (d) RTM image with multiple reflections, (e) model R1 result based on workflow 1, (f) model R3 result based on workflow 3, (g) model R4 result based on workflow 4, (h) true Foothills velocity, and (i) LSRTM result after 15 iterations. The boxes indicate areas shown in detail in the next figures.
Figure 6.
Amplitude spectrum comparison between models R1, R3, and R4 results for the Canadian Foothills example.
Figure 6.
Amplitude spectrum comparison between models R1, R3, and R4 results for the Canadian Foothills example.
Figure 7.
Foothills red box No. 1 results: (a) reflectivity from the background velocity, (b) true windowed band-limited reflectivity, (c) RTM image without multiple energy, (d) RTM image with multiple energy, (e) model R1 result based on workflow 1, (f) model R3 result based on workflow 3, (g) model R4 result based on workflow 4, and (h) true windowed velocity.
Figure 7.
Foothills red box No. 1 results: (a) reflectivity from the background velocity, (b) true windowed band-limited reflectivity, (c) RTM image without multiple energy, (d) RTM image with multiple energy, (e) model R1 result based on workflow 1, (f) model R3 result based on workflow 3, (g) model R4 result based on workflow 4, and (h) true windowed velocity.
Figure 8.
Foothills red box No. 2 results: (a) reflectivity from the background velocity, (b) true windowed band-limited reflectivity, (c) RTM image without multiple energy, (d) RTM image with multiple energy, (e) model R1 result based on workflow 1, (f) model R3 result based on workflow 3, (g) model R4 result based on workflow 4, and (h) true windowed velocity.
Figure 8.
Foothills red box No. 2 results: (a) reflectivity from the background velocity, (b) true windowed band-limited reflectivity, (c) RTM image without multiple energy, (d) RTM image with multiple energy, (e) model R1 result based on workflow 1, (f) model R3 result based on workflow 3, (g) model R4 result based on workflow 4, and (h) true windowed velocity.
Figure 9.
Crossplots for the Canadian Foothills example: the true band-limited reflectivity against the predicted reflectivity by using models R1 and R3, respectively.
Figure 9.
Crossplots for the Canadian Foothills example: the true band-limited reflectivity against the predicted reflectivity by using models R1 and R3, respectively.
Figure 10.
Overthrust model results: (a) reflectivity from the background velocity, (b) true band-limited reflectivity, (c) RTM image without multiple energy, (d) RTM image with multiple energy, (e) model R1 result based on workflow 1, (f) model R3 result based on workflow 3, (g) model R4 result based on workflow 4, and (h) true Overthrust velocity.
Figure 10.
Overthrust model results: (a) reflectivity from the background velocity, (b) true band-limited reflectivity, (c) RTM image without multiple energy, (d) RTM image with multiple energy, (e) model R1 result based on workflow 1, (f) model R3 result based on workflow 3, (g) model R4 result based on workflow 4, and (h) true Overthrust velocity.
Figure 11.
Overthrust red box results: (a) reflectivity from the background velocity, (b) true windowed band-limited reflectivity, (c) RTM image without multiple energy, (d) RTM image with multiple energy, (e) model R1 result based on workflow 1, (f) model R3 result based on workflow 3, (g) model R4 result based on workflow 4, and (h) true windowed velocity.
Figure 11.
Overthrust red box results: (a) reflectivity from the background velocity, (b) true windowed band-limited reflectivity, (c) RTM image without multiple energy, (d) RTM image with multiple energy, (e) model R1 result based on workflow 1, (f) model R3 result based on workflow 3, (g) model R4 result based on workflow 4, and (h) true windowed velocity.
Figure 12.
SEAM model results: (a) reflectivity from the background velocity, (b) true band-limited reflectivity, (c) RTM image without multiple energy, (d) RTM image with multiple energy, (e) model R1 result based on workflow 1, (f) model R3 result based on workflow 3, (g) model R4 result based on workflow 4, and (h) true SEAM velocity.
Figure 12.
SEAM model results: (a) reflectivity from the background velocity, (b) true band-limited reflectivity, (c) RTM image without multiple energy, (d) RTM image with multiple energy, (e) model R1 result based on workflow 1, (f) model R3 result based on workflow 3, (g) model R4 result based on workflow 4, and (h) true SEAM velocity.
Figure 13.
SEAM Phase 1 red box results: (a) reflectivity from the background velocity, (b) true windowed band-limited reflectivity, (c) RTM image without multiple energy, (d) RTM image with multiple energy, (e) model R1 result based on workflow 1, (f) model R3 result based on workflow 3, (g) model R4 result based on workflow 4, and (h) true windowed velocity.
Figure 13.
SEAM Phase 1 red box results: (a) reflectivity from the background velocity, (b) true windowed band-limited reflectivity, (c) RTM image without multiple energy, (d) RTM image with multiple energy, (e) model R1 result based on workflow 1, (f) model R3 result based on workflow 3, (g) model R4 result based on workflow 4, and (h) true windowed velocity.
Figure 14.
Crossplots for the SEAM Phase 1 example: the true band-limited reflectivity against the predicted reflectivity by using the model R1 and R3, respectively.
Figure 14.
Crossplots for the SEAM Phase 1 example: the true band-limited reflectivity against the predicted reflectivity by using the model R1 and R3, respectively.
Figure 15.
(a) Model train loss and (b) validation loss comparison between different neural network models with fifty iterations.
Figure 15.
(a) Model train loss and (b) validation loss comparison between different neural network models with fifty iterations.
Table 1.
U-net architecture encoding.
Table 1.
U-net architecture encoding.
Layer Number | Type | Size | Output |
---|
1 | Input | | 256 × 256 × 2 |
2 | Conv2D | 16 filters | 256 × 256 × 16 |
3 | Batch Normalization | | 256 × 256 × 16 |
4 | Conv2D | 16 filters | 256 × 256 × 16 |
5 | Batch Normalization | | 256 × 256 × 16 |
6 | Conv2D | 16 filters | 256 × 256 × 16 |
7 | Batch Normalization | | 256 × 256 × 16 |
8 | Dropout | 20% | 256 × 256 × 16 |
9 | MaxPooling2D | 2 × 2 | 128 × 128 × 16 |
10 | Conv2D | 32 filters | 128 × 128 × 32 |
11 | Batch Normalization | | 128 × 128 × 32 |
12 | Conv2D | 32 filters | 128 × 128 × 32 |
13 | Batch Normalization | | 128 × 128 × 32 |
14 | Conv2D | 32 filters | 128 × 128 × 32 |
15 | Batch Normalization | | 128 × 128 × 32 |
16 | Dropout | 20% | 128 × 128 × 32 |
17 | MaxPooling2D | 2 × 2 | 64 × 64 × 32 |
18 | Conv2D | 64 filters | 64 × 64 × 64 |
19 | Batch Normalization | | 64 × 64 × 64 |
20 | Conv2D | 64 filters | 64 × 64 × 64 |
21 | Batch Normalization | | 64 × 64 × 64 |
22 | Conv2D | 64 filters | 64 × 64 × 64 |
23 | Batch Normalization | | 64 × 64 × 64 |
24 | Dropout | 20% | 64 × 64 × 64 |
25 | MaxPooling2D | 2 × 2 | 32 × 32 × 64 |
26 | Conv2D | 128 filters | 32 × 32 × 128 |
27 | Batch Normalization | | 32 × 32 × 128 |
28 | Conv2D | 128 filters | 32 × 32 × 128 |
29 | Batch Normalization | | 32 × 32 × 128 |
30 | Conv2D | 128 filters | 32 × 32 × 128 |
31 | Batch Normalization | | 32 × 32 × 128 |
32 | Dropout | 20% | 32 × 32 × 128 |
33 | MaxPooling2D | 2 × 2 | 16 × 16 × 128 |
34 | Conv2D | 256 filters | 16 × 16 × 256 |
35 | Batch Normalization | | 16 × 16 × 256 |
36 | Conv2D | 256 filters | 16 × 16 × 256 |
37 | Batch Normalization | | 16 × 16 × 256 |
38 | Dropout | 20% | 16 × 16 × 256 |
39 | MaxPooling2D | 2 × 2 | 8 × 8 × 256 |
40 | Conv2D | 512 filters | 8 × 8 × 512 |
41 | Batch Normalization | | 8 × 8 × 512 |
42 | Conv2D | 512 filters | 8 × 8 × 512 |
43 | Batch Normalization | | 8 × 8 × 512 |
44 | Dropout | 20% | 8 × 8 × 512 |
45 | MaxPooling2D | 2 × 2 | 4 × 4 × 512 |
Table 2.
U-net architecture decoding.
Table 2.
U-net architecture decoding.
Layer Number | Type | Size | Output |
---|
1 | Conv2D Transpose | 256 filters | 8 × 8 × 256 |
2 | Batch Normalization | | 8 × 8 × 256 |
3 | Concatenate | | 8 × 8 × 768 |
4 | Conv2D Transpose | 256 filters | 8 × 8 × 256 |
5 | Batch Normalization | | 8 × 8 × 256 |
6 | Conv2D Transpose | 256 filters | 8 × 8 × 256 |
7 | Batch Normalization | | 8 × 8 × 256 |
8 | Conv2D Transpose | 256 filters | 16 × 16 × 256 |
9 | Batch Normalization | | 16 × 16 × 256 |
10 | Concatenate | | 16 × 16 × 512 |
11 | Conv2D Transpose | 256 filters | 16 × 16 × 256 |
12 | Batch Normalization | | 16 × 16 × 256 |
13 | Conv2D Transpose | 256 filters | 16 × 16 × 256 |
14 | Batch Normalization | | 16 × 16 × 256 |
15 | Conv2D Transpose | 128 filters | 32 × 32 × 128 |
16 | Batch Normalization | | 32 × 32 × 128 |
17 | Concatenate | | 32 × 32 × 256 |
18 | Conv2D Transpose | 128 filters | 32 × 32 × 128 |
19 | Batch Normalization | | 32 × 32 × 128 |
20 | Conv2D Transpose | 128 filters | 32 × 32 × 128 |
21 | Batch Normalization | | 32 × 32 × 128 |
22 | Conv2D Transpose | 64 filters | 64 × 64 × 64 |
23 | Batch Normalization | | 64 × 64 × 64 |
24 | Concatenate | | 64 × 64 × 128 |
25 | Conv2D Transpose | 64 filters | 64 × 64 × 64 |
26 | Batch Normalization | | 64 × 64 × 64 |
27 | Conv2D Transpose | 64 filters | 64 × 64 × 64 |
28 | Batch Normalization | | 64 × 64 × 64 |
29 | Conv2D Transpose | 32 filters | 128 × 128 × 32 |
30 | Batch Normalization | | 128 × 128 × 32 |
31 | Concatenate | | 128 × 128 × 64 |
32 | Conv2D Transpose | 32 filters | 128 × 128 × 32 |
33 | Batch Normalization | | 128 × 128 × 32 |
34 | Conv2D Transpose | 32 filters | 128 × 128 × 32 |
35 | Batch Normalization | | 128 × 128 × 32 |
36 | Conv2D Transpose | 16 filters | 256 × 256 × 16 |
37 | Batch Normalization | | 256 × 256 × 16 |
38 | Concatenate | | 256 × 256 × 32 |
39 | Conv2D Transpose | 16 filters | 256 × 256 × 16 |
40 | Batch Normalization | | 256 × 256 × 16 |
41 | Conv2D Transpose | 16 filters | 256 × 256 × 16 |
42 | Batch Normalization | | 256 × 256 × 16 |
43 | Concatenate | | 256 × 256 × 16 |
44 | Conv2D | 1 filter | 256 × 256 × 1 |
Table 3.
PSNR (dB) comparison for Foothills example.
Table 3.
PSNR (dB) comparison for Foothills example.
Prediction | Model R1 | Model R3 | Model R4 |
---|
Total Foothills | 24.84 | 25.80 | 20.59 |
Example 1 | 20.88 | 22.58 | 16.40 |
Example 2 | 19.16 | 20.18 | 17.03 |
Table 4.
PSNR (dB) comparison for Overthrust example.
Table 4.
PSNR (dB) comparison for Overthrust example.
Prediction | Model R1 | Model R3 | Model R4 |
---|
Total Overthrust | 24.09 | 24.61 | 20.61 |
Example 1 | 19.06 | 20.11 | 15.99 |
Table 5.
PSNR (dB) comparison for SEAM example.
Table 5.
PSNR (dB) comparison for SEAM example.
Prediction | Model R1 | Model R3 | Model R4 |
---|
Total SEAM | 24.58 | 26.32 | 23.75 |
Example 1 | 21.52 | 22.88 | 20.14 |