AFI (AVO Fluid Inversion)

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1 AFI (AVO Fluid Inversion) Uncertainty in AVO: How can we measure it? Dan Hampson, Brian Russell Hampson-Russell Software, Calgary Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 1

2 Overview AVO Analysis is now routinely used for exploration and development. But: all AVO attributes contain a great deal of uncertainty there is a wide range of lithologies which could account for any AVO response. In this talk we present a procedure for analyzing and quantifying AVO uncertainty. As a result, we will calculate probability maps for hydrocarbon detection. Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 2

3 AVO Uncertainty Analysis: The Basic Process CALIBRATED:! GRADIENT! INTERCEPT! BURIAL DEPTH G I STOCHASTIC AVO MODEL FLUID PROBABILITY MAPS AVO ATTRIBUTE MAPS ISOCHRON MAPS! P BRI! P OIL! P GAS Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 3

4 Conventional AVO Modeling: Creating 2 pre-stack synthetics IN IN SITU SITU = = OIL OIL I O G O FRM FRM = = BRINE BRINE I B G B Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 4

5 Monte Carlo Simulation: Creating many synthetics I-G G DENSITY FUNCTIONS BRINE OIL GAS Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 5

6 The Basic Model Shale We assume a 3-layer model with shale enclosing a sand (with various fluids). Sand Shale Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 6

7 The Basic Model The Shales are characterized by: V p1, V s1, r 1 P-wave velocity S-wave velocity Density V p2, V s2, r 2 Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 7

8 The Basic Model V p1, V s1, r 1 Each parameter has a probability distribution: V p2, V s2, r 2 Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 8

9 The Basic Model The Sand is characterized by: Shale Sand Shale Brine Modulus Brine Density Gas Modulus Gas Density Oil Modulus Oil Density Matrix Modulus Matrix density Porosity Shale Volume Water Saturation Thickness Each of these has a probability distribution. Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 9

10 Trend Analysis Some of the statistical distributions are determined from well log trend analyses: DBSB (Km) Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 10

11 Determining Distributions at Selected Locations Assume a Normal distribution. Get the Mean and Standard Deviation from the trend curves for each depth: DBSB (Km) Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 11

12 5000 Shale Velocity Trend Analysis: Other Distributions Sand Density Shale Density % Sand Porosity % % % % % 1.4 DBSB (Km) % % DBSB (Km) % DBSB (Km) DBSB (Km) Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 12

13 Practically, this is how we set up the distributions: Shale: V p V s Density Trend Analysis Castagna s Relationship with % error Trend Analysis Sand: Brine Modulus Brine Density Gas Modulus Gas Density Oil Modulus Oil Density Matrix Modulus Matrix density Dry Rock Modulus Porosity Shale Volume Water Saturation Thickness Constants for the area Calculated from sand trend analysis Trend Analysis Uniform Distribution from petrophysics Uniform Distribution from petrophysics Uniform Distribution Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 13

14 Calculating a Single Model Response From a particular model instance, calculate two synthetic traces at different angles. Note that a wavelet is assumed known. 0 o 45 o Top Shale Sand Base Shale Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 14

15 On the synthetic traces, pick the event corresponding to the top of the sand layer: Calculating a Single Model Response Note that these amplitudes include interference from the second interface. 0 o 45 o Top Shale Sand P 1 P 2 Base Shale Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 15

16 Calculating a Single Model Response Using these picks, calculate the Intercept and Gradient for this model: I = P 1 G = (P 2 -P 1 )/sin 2 (45) 0 o 45 o Top Shale P 1 P 2 Sand Base Shale Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 16

17 GAS Using Biot-Gassmann Substitution Starting from the Brine Sand case, the corresponding Oil and Gas Sand models are generated using Biot-Gassmann substitution. This creates 3 points on the I-G cross plot: BRINE OIL K GAS ρ GAS K OIL ρ OIL G I G I G I Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 17

18 Monte-Carlo Analysis By repeating this process many times, we get a probability distribution for each of the 3 sand fluids: G I Brine Oil Gas Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 18

19 The Results are Depth Dependent Because the trends are depth-dependent, so are the predicted m Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 19

20 The Depth-dependence can often be understood using Rutherford-Williams classification Impedance Class Class 1 6 Sand Shale Class 3 Burial Depth Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 20

21 Bayes Theorem Bayes Theorem is used to calculate the probability that any new (I,G) point belongs to each of the classes (brine, oil, gas): P ~ ( F I, G ) = p k ( ~ ) I, G F p ( I, G F )* P ( F ) where: P(Fk) represent a priori probabilities and Fk is either brine, oil, gas; p(i,g Fk) are suitable distribution densities (eg. Gaussian) estimated from the stochastic simulation output. * k ~ P ( F ) k Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 21

22 How Bayes Theorem works in a simple case: Assume we have these distributions: Gas Oil Brine OCCURRENCE VARIABLE Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 22

23 How Bayes Theorem works in a simple case: This is the calculated probability for (gas, oil, brine). 100% OCCURRENCE 50% VARIABLE Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 23

24 When the distributions overlap, the probabilities decrease: Even if we are right on the Gas peak, we can only be 60% sure we have gas. 100% OCCURRENCE 50% VARIABLE Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 24

25 Showing the Effect of Bayes Theorem This is an example simulation result, assuming that the wet shale V S and V P are related by Castagna s equation. Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 25

26 Showing the Effect of Bayes Theorem This is an example simulation result, assuming that the wet shale V S and V P are related by Castagna s equation. This is the result of assuming 10% noise in the V S calculation Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 26

27 Showing the Effect of Bayes Theorem Note the effect on the calculated gas probability Gas Probability 0.0 By this process, we can investigate the sensitivity of the probability distributions to individual parameters. Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 27

28 Example Probability Calculations Gas Oil Brine Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 28

29 Real Data Calibration # In order to apply Bayes Theorem to (I,G) points from a real seismic data set, we need to calibrate the real data points. # This means that we need to determine a scaling from the real data amplitudes to the model amplitudes. # We define two scalers, S global and S gradient, this way: I scaled G scaled = S global *I real = S global * S gradient * G real One way to determine these scalers is by manually fitting multiple known regions to the model data. Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 29

30 Fitting 6 Known Zones to the Model Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 30

31 Real Data Example West Africa This example shows a real project from West Africa, performed by one of the authors (Cardamone). There are 7 productive oil wells which produce from a shallow formation. The seismic data consists of 2 common angle stacks. The object is to perform Monte Carlo analysis using trends from the productive wells, calibrate to the known data points, and evaluate potential drilling locations on a second deeper formation. Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 31

32 One Line from the 3D Volume Near Angle Stack 0-20 degrees Far Angle Stack degrees Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 32

33 One Line from the 3D Volume Near Angle Stack 0-20 degrees Shallow producing zone Deeper target zone Far Angle Stack degrees Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 33

34 AVO Anomaly Near Angle Stack 0-20 degrees Far Angle Stack degrees Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 34

35 Amplitude Slices Extracted from Shallow Producing Zone Near Angle Stack 0-20 degrees Far Angle Stack degrees Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 35

36 Trend Analysis Sand and Shale Trends VELOCITY Sand velocity DENSITY Sand density VELOCITY Shale velocity DENSITY Shale density BURIAL DEPTH (m) BURIAL DEPTH (m) Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 36

37 Monte Carlo Simulations at 6 Burial Depths Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 37

38 Near Angle Amplitude Map Showing Defined Zones Wet Zone 1 Well 6 Well 7 Well 3 Well 5 Well 1 Well 2 Well 4 Wet Zone 2 Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 38

39 Calibration Results at Defined Locations Wet Zone 1 Well 2 Wet Zone 2 Well 5 Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 39

40 Calibration Results at Defined Locations Well 3 Well 6 Well 4 Well 1 Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 40

41 Near Angle Amplitudes Using Bayes Theorem at Producing Zone: OIL 1.0 Probability of Oil Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 41

42 Near Angle Amplitudes Using Bayes Theorem at Producing Zone: GAS 1.0 Probability of Gas Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 42

43 Using Bayes Theorem at Target Horizon Near angle amplitudes of second event 1.0 Probability of oil on second event Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 43

44 Verifying Selected Locations at Target Horizon Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 44

45 Summary By representing lithologic parameters as probability distributions we can calculate the range of expected AVO responses. This allows us to investigate the uncertainty in AVO predictions. Using Bayes theorem we can produce probability maps for different potential pore fluids. But: The results depend critically on calibration between the real and model data. And: The calculated probabilities depend on the reliability of all the underlying probability distributions. Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 45

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