Using neural networks for porosity prediction from seismic attributes

1. Using neural networks for porosity prediction from seismic attributes Daniel Hampson, Todor Todorov and Adrian Smith Hampson-Russell Software Services Ltd.

2. Outline • Deterministic vs data-driven approaches • Methodology • linear multi-regression analysis • neural networks • Blackfoot field example • Conclusions • Acknowledgments

3. Deterministic methodology • We derive (or assume) a theoretical relationship between a log property and the seismic attributes, and we invert the attributes to get the log property. • Example • forward: trace = wavelet * reflectivity • inverse: reflectivity = decon(trace,wavelet)

4. Data-driven (statistical) methodology We aim to derive a statistical relationship between a log property and some seismic attributes: P(x, y, t) = F[A1(x, y, t), A2(x, y, t), …, AM(x, y, t)] where: P(x, y, t) : log property as a function of x, y, t F[…] : functional relationship Ai : seismic attribute, i = 1, …, M

5. The EMERGE analysis can be thought of as an extension of cross plotting. This display shows a cross plot of the target log against the attribute STRATA Inversion. The cross-correlation and prediction error are printed at the top of the display. Simple linear fit

6. It is sometimes possible to improve the correlation by using a non-linear transform on either the target log, the attribute or both. The non-linear transforms are: - natural logarithm - 1/x - square - square root Improved fit with non-linear

7. Linear multi-regression analysis P1 = W1A11 + W2A21 + … + WMAM1 + C P2 = W1A12 + W2A22 + … + WMAM2 + C … PN = W1A1N + W2A2N + … + WMAMN + C where: Pk : measured porosity samples in time, k = 1, …, N Aik : seismic attributes, i = 1, …, M, k = 1, …, N Wi : weights to be determined, i = 1, …, M C : constant

8. Example using three seismic attributes well log seismic attributes w1 w2 w3

9. Replacing weights with convolution P1 = W1*A1 + W2*A2 + … + WM*AM + C P2 = W1*A1 + W2*A2 + … + WM*AM + C … PN = W1*A1 + W2*A2 + … + WM*AM + C where: Pk : measured porosity samples in time, k = 1, …, N Ai : seismic attributes, i = 1, …, M Wi : convolution operator, i = 1, …, M C : constant

10. Example using 5-point convolution operator well log seismic attributes

11. Adding multiple attributes in EMERGE is like fitting a set of points with an increasingly higher order polynomial. The higher order polynomial always fits better, but there is a danger of over-fitting. More attributes = increased accuracy?

12. Determine non-linear relationship • apply non-linear transform prior to least- • squares optimization • neural networks

13. Basic neural network architecture Input layer Hidden layer Output layer A1 A2 output A3 A4

14. Multi-Layer Feed Forward Network • Traditional network - back propagation • Weights, nodes, hidden layers, etc • Conjugate gradient and 3D simulated • annealing • Accurate but easily over trained

15. Probabilistic Neural Network • Mathematical interpolation using neural • network architecture • Less black box • Calculates optimum smoothers (si) • Better stability at expense of runtime

16. Neural network training flow chart start train test add a neuron yes improved ? no end

17. Overfitting the training data w e l l l o g seismic attribute - training data set - test/validation data set

18. Blackfoot 3-D • location: Southern Alberta, Canada • recorded: October, 1995 • target: the Glauconitic member of the • Mannville group • reservoir: sand channel at depth of 1550 m. • 13 wells in dataset

19. Blackfoot 3-D: location map

20. Blackfoot 3-D seismic inline

21. Porosity log, seismic trace and inversion

22. Single-attribute list using 5-point convolution operator Attributes Correlation inversion -0.69 Derivative 0.36 Integrated trace -0.34 Amplitude Weighted Phase -0.26 Instantaneous Phase -0.23

23. The predicted porosity logs using the best single attribute. Single attribute prediction

24. Multi-attribute list using 5-point convolution operator Attributes RMS error(%) 1 / inversion 4.09 Derivative Instantaneous Amplitude 3.91 Average Frequency 3.84 Second Derivative Ins. Amplitude 3.76 Integrated Absolute Amplitude 3.70 Amplitude Weighted Cosine Phase 3.62 Apparent Polarity 3.58

25. RMS error vs number of seismic attributes

26. Predicted porosity logs using multi-regression

27. Validation result

28. Results from the neural network training Data Correlation RMS error Records % All 0.87 2.47 566 100 0.88 Train 2.33 396 70 Test 0.84 2.79 170 30

29. Predicted porosity logs using neural network

30. A comparison between multi-linear regression and Neural Network prediction. Note the enhanced high-frequency resolution with the Neural Network. Linear vs Neural • Linear • Neural

31. Predicted porosity using multi-regression

32. Predicted porosity using neural network

33. Porosity slice, multi-regression

34. Porosity slice, neural net

35. Conclusions • Statistical methods successfully derive porosity • log from seismic attributes • Cross-validation tests find meaningful • attributes • Convolution operators can improve results • Highest correlation is achieved using a neural • network • High porosity correlates with sand channel

36. Acknowledgments • The CREWES Project, University of Calgary • for the Blackfoot data set • Mobil Expl. and Prod. Technology, Dallas • MENI, MEEG • Hampson-Russell Software Developers