1. Statistical identification of faults in 3D seismic volumes using a machine learning approach
Antoine Guitton, Geophysics Department, CSM
Hua Wang, Computer Science Department, CSM
Whitney Trainor-Guitton, Geophysics Department, CSM

2. 3D Field data example: flat cube view
Time slice
Xline
Inline

3. 3D Field data example: flat cube view
Fault locations with Hale’s approach
Fault locations with MLA
≈P(faults) 1

4. Why MLA for faults?
MLAs can work well for interpretation tasks where Experience/Training matters
MLAs can work in any dimension
Codes yield reliable, reproducible, unbiased estimates
MLAs can be constantly improved (learn from mistakes, more data or features)
Fault imaging IS a classification problem
Tons of libraries

5. Machine learning in a nutshell
Outcome vector
Classifier
Matrix of feature vectors

6. Machine learning in a nutshell
Outcome vector
Classifier
Matrix of feature vectors

7. Machine learning in a nutshell
Outcome vector
Classifier
Matrix of feature vectors

8. Features - Predictors Histograms of Oriented Gradients (HOG)
2D only
Scale Invariant Feature Transform (SIFT)
Seismic amplitudes
Software available at:

9. Features - Predictors Histogram of Oriented Gradients (HOG):
Build local histograms of gradient orientation

10. Features - Predictors Scale Invariant Feature Transform (SIFT):
Identify features independent of scale, noise, illumination, orientation

11. Machine learning in a nutshell
Outcome vector
Classifier
Matrix of feature vectors

12. Training data - Outcome vector
Labels built with Hale’s java toolkit
≈P(faults) 1

13. Training data - Outcome vector
Labels built with Hale’s java toolkit
≈P(faults) 1

14. Training data - Outcome vector
Labels built with Hale’s java toolkit
≈P(faults) 1

15. Building outcome vector with patching1
(c)
y1=1
y7=0
y3=0
y9=0
(b)
Scatter
(a)

16. Building outcome vector with patching1
y1=1
y7=0 ≈ 4 3 1 2
y3=0
y9=0
(a)
(c)
Merge

17. Building data with patching
HOG/SIFT 1 X1 . . X= X2 . . X3 . X9
(a)
(b)
(c)
Scatter

18. Fault Imaging Workflow
Build fault labels
Patch of class labels and seismic data
Compute HOG and SIFT features for each patch
Train SVM classifier on training set
Predict on test set
Reassemble labeled data from test set to form fault image
Analyze result (confusion matrix)

19. Fault Imaging Workflow
Build labels
Patch of class labels and seismic data
Compute HOG and SIFT features for each patch
Train SVM classifier on training set
Predict on test set
Reassemble labeled data from test set to form fault image
Analyze result (confusion matrix)

20. Example: Synthetic test
Training with 40,000 feature vectors (10,000 used for crossvalidation for SVM parameters)
Testing with 200,000 vectors

21. Test data Seismic volume Estimate fault locations with Hale’s library
≈P(faults) 1

22. Test data “true” fault location after patching
Estimate fault locations with Hale’s library
≈P(faults) 1

23. Building outcome vector with patching1
y1=1
y7=0 ≈
Merge 4 3 1 2
y3=0
y9=0

24. Synthetic example
4: Train the MLA (SIFT/HOG) with 768 predictors: 91.5% accurate
30137
75.3%
2551
6.4%
True -
False -
856
2.1%
6456
16.1%
88.3%
11.7%
False +
True +
Precision
91.5%
8.5%
Overall
fit/error

25. Synthetic example 5&6: Apply on test data (SIFT+HOG) and reassemble
“true” fault locations
Predicted fault locations
≈P(faults) 1

26. Synthetic example 7: Analyze results (SIFT+HOG): 91.5% accurate 152720
76.4%
10372
5.2%
True -
False -
6652
3.3%
30246
15.1%
81.9%
18.1%
False +
True +
Precision
91.5%
8.5%
Overall
fit/error

27. Synthetic example 5&6: Apply on test data (SIFT+HOG) and reassemble
“true” fault locations
Predicted fault locations
≈P(faults) 1

28. Synthetic example 5&6: Apply on test data (HOG only) and reassemble
“true” fault locations
Predicted fault locations
≈P(faults) 1

29. Field data example
128,000 training samples
147,000 test samples

30. Field data example
“true” fault locations
Test data
≈P(faults) 1

31. Field data example
Mislabeling is present in both training and test data
Faults are labeled as non-faults
Non-faults are labeled as faults
Training is done with mislabeled data
Comparison with labels of test data is hard

32. Field data example 4: Train the MLA (HOG+SIFT): 86.5 % accurate 100842
78.3%
16757
13.0%
True -
False -
584
0.5%
10568
8.2%
94.8%
5.2%
False +
True +
Precision
86.5%
13.5%
Overall
fit/error

33. Predicted fault locations with smoothing
Field data example
5&6: Apply on test data (HOG+SIFT) and reassemble
“true” fault locations
Predicted fault locations with smoothing
≈P(faults) 1

34. Field data example 5: Analyze results (HOG+SIFT): 77.4% accurate
108401
73.7%
28857
19.6%
True -
False -
4298
2.9%
5444
3.7%
55.9%
44.1%
False +
True +
Precision
77.4%
22.6%
Overall
fit/error

35. Predicted fault locations with smoothing
Field data example
4: Apply on test data (HOG+SIFT)
“true” fault locations
Predicted fault locations with smoothing
≈P(faults) 1

36. Predicted fault locations with smoothing
Field data example
4: Apply on test data (HOG only)
“true” fault locations
Predicted fault locations with smoothing
≈P(faults) 1

37. Predicted fault locations with smoothing
Field data example
4: Apply on test data (HOG+SIFT)
“true” fault locations
Predicted fault locations with smoothing
≈P(faults) 1

38. Predicted fault locations with smoothing
Field data example
4: Apply on test data (HOG)
“true” fault locations
Predicted fault locations with smoothing
≈P(faults) 1

39. Conclusions
1st successful application of MLA for fault imaging of field data
Supervised-learning worflow includes:
Fault labeling
Patching
Building feature sets (HOG,SIFT)
Training of SVM classifier with Gaussian kernels
Possible improvements
Train on more data
Include more/better features (3D, smoothing, LASSO, etc…)
Use other classifiers (trees, neural nets/deep learning, etc…)
Use semi-supervised learning

40. Fault locations with MLA
Thank you! Questions?
Fault locations with Hale’s approach
Fault locations with MLA

42. Predicted fault locations with smoothing
Thank you !
“true” fault locations
Predicted fault locations with smoothing
≈P(faults) 1

43. Synthetic example
4: Train the MLA (SIFT) with 128 predictors: 84.7% accurate
29279
73.2%
4420
11.1%
True -
False -
1714
4.3%
4587
11.5%
72.8%
27.2%
False +
True +
Precision
84.7%
15.3%
Overall
fit/error
Recall

44. Synthetic example 4: Apply on test data (SIFT only)
“true” fault locations
Predicted fault locations
≈P(faults) 1

45. Synthetic example 5: Analyze results (SIFT): 84.3% accurate 146334
73.2%
18307
9.2%
True -
False -
13048
6.5%
22311
11.2%
63.1%
26.9%
False +
True +
Precision
84.3%
15.7%
Overall
fit/error

46. Features
Histograms of Oriented Gradients (HOGs) are used for object recognition. Computed as follows:
Compute gradients in x and z directions at all pixel locations
Compute unassigned/signed angles at all pixel locations
Compute histograms of angles within cells (1 cell=8x8 pixels, for instance)
Normalization across blocks of cells (1 block=2x2 cells)

47. Synthetic example
4: Train the MLA (HOG) with 740 predictors: 99.4% accurate
30991
77.5%
245
0.6%
True -
False - 2
0.0%
8762
21.9%
100.0%
0.0%
False +
True +
Precision
99.4%
0.6%
Overall
fit/error

48. Synthetic example 5&6: Apply on test data (HOG only) and reassemble
“true” fault locations
Predicted fault locations

49. Synthetic example 7: Analyze results (HOG) – 92.1% accurate 150583
75.3%
7091
3.5%
True -
False -
8799
4.4%
33527
16.8%
79.2%
20.8%
False +
True +
Precision
92.1%
7.9%
Overall
fit/error

50. Synthetic example 7: Analyze results (HOG) – 92.1% accurate 150583
75.3%
7091
3.5%
True -
False -
8799
4.4%
33527
16.8%
79.2%
20.8%
False +
True +
Precision
92.1%
7.9%
Overall
fit/error

51. Features Scale Invariant Feature Transform (SIFT) process:
Identify keepoints (involves scaling/blurring/DoG/extrema identification)
Around each keypoints, build a histogram of gradients (8 bins) for 16 blocks (1 block is 4x4 cells).

52. Features Scale Invariant Feature Transform (SIFT) process:
Each keypoint has 128 features (8bins x 16blocks)
Problem: # of keypoints is variable for each image
Solution: Clustering of SIFT features and build histogram of them for each image (some might be all zeroes).

53. Field data example
4: Train the MLA (HOG): 100 % accurate ! overfit!!!!
101426
78.8% 7
0.0%
True -
False -
0.0%
27318
21.2%
100.0%
0.0%
False +
True +
Precision
100.0%
0.0%
Overall
fit/error

54. Predicted fault locations with smoothing
Field data example
5&6: Apply on test data (HOG only) and reassemble
“true” fault locations
Predicted fault locations with smoothing
≈P(faults) 1

55. Field data example 7: Analyze results (HOG): 77% accurate 105801 26866
72.0%
26866
18.3%
True -
False -
6898
4.7%
7435
5.1%
51.9%
48.1%
False +
True +
Precision
77.0%
23.0%
Overall
fit/error

56. Field data example 5: Analyze results (HOG): 77% accurate 105801 26866
72.0%
26866
18.3%
True -
False -
6898
4.7%
7435
5.1%
51.9%
48.1%
False +
True +
Precision
77.0%
23.0%
Overall
fit/error

57. Features - Predictors