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
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
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
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
Monte Carlo Simulation: Creating many synthetics I-G G DENSITY FUNCTIONS BRINE OIL GAS 75 50 25 0 Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 5
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
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
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
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
Trend Analysis Some of the statistical distributions are determined from well log trend analyses: 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0 0.4 0.9 1.4 1.9 2.4 2.9 3.4 DBSB (Km) Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 10
Determining Distributions at Selected Locations Assume a Normal distribution. Get the Mean and Standard Deviation from the trend curves for each depth: 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0 0.4 0.9 1.4 1.9 2.4 2.9 3.4 DBSB (Km) Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 11
5000 Shale Velocity Trend Analysis: Other Distributions 4500 4000 3.0 Sand Density 3500 2.8 3000 2.6 3.0 Shale Density 2500 2.4 2.8 40% 2.6 2000 2.2 Sand Porosity 2.4 35% 1500 2.0 2.2 30% 1000 1.8 2.0 500 1.6 25% 1.8 0 1.4 20% 1.6 0.4 1.2 0.9 1.4 1.9 2.4 2.9 3.4 15% 1.4 DBSB (Km) 1.0 1.2 10% 0.4 0.9 1.4 1.9 2.4 2.9 3.4 1.0 5% DBSB (Km) 0.4 0.9 1.4 1.9 2.4 2.9 3.4 0% DBSB (Km) 0.4 0.9 1.4 1.9 2.4 2.9 3.4 DBSB (Km) Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 12
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
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
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
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
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
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
The Results are Depth Dependent Because the trends are depth-dependent, so are the predicted distributions: @ 1000m @ 1200m @ 1400m @ 1600m @ 1800m @ 2000m Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 19
The Depth-dependence can often be understood using Rutherford-Williams classification 2 4 6 5 1 3 Impedance 1 2 3 Class 2 4 5 Class 1 6 Sand Shale Class 3 Burial Depth Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 20
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
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
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
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
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
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
Showing the Effect of Bayes Theorem Note the effect on the calculated gas probability 1.0 0.5 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
Example Probability Calculations Gas Oil Brine Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 28
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
Fitting 6 Known Zones to the Model 4 5 6 4 5 6 1 3 1 3 2 2 1 2 3 4 5 6 Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 30
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
One Line from the 3D Volume Near Angle Stack 0-20 degrees Far Angle Stack 20-40 degrees Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 32
One Line from the 3D Volume Near Angle Stack 0-20 degrees Shallow producing zone Deeper target zone Far Angle Stack 20-40 degrees Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 33
AVO Anomaly Near Angle Stack 0-20 degrees Far Angle Stack 20-40 degrees Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 34
Amplitude Slices Extracted from Shallow Producing Zone Near Angle Stack 0-20 degrees +189-3500 Far Angle Stack 20-40 degrees Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 35
Trend Analysis Sand and Shale Trends 3.00 5000 VELOCITY 4500 4000 3500 3000 2500 2000 Sand velocity DENSITY 2.75 2.50 2.25 2.00 Sand density 1500 1.75 1000 500 700 900 1100 1300 1500 1700 1900 1.50 500 700 900 1100 1300 1500 1700 1900 4000 VELOCITY 3500 3000 2500 2000 Shale velocity DENSITY 3.00 2.75 2.50 2.25 2.00 Shale density 1500 1.75 1000 500 700 900 1100 1300 1500 1700 1900 2100 2300 2500 BURIAL DEPTH (m) 1.50 500 700 900 1100 1300 1500 1700 1900 BURIAL DEPTH (m) Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 36
Monte Carlo Simulations at 6 Burial Depths -1400-1600 -1800-2000 -2200-2400 Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 37
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
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
Calibration Results at Defined Locations Well 3 Well 6 Well 4 Well 1 Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 40
Near Angle Amplitudes Using Bayes Theorem at Producing Zone: OIL 1.0 Probability of Oil.80.60.30 Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 41
Near Angle Amplitudes Using Bayes Theorem at Producing Zone: GAS 1.0 Probability of Gas.80.60.30 Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 42
Using Bayes Theorem at Target Horizon Near angle amplitudes of second event 1.0 Probability of oil on second event.80.60.30 Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 43
Verifying Selected Locations at Target Horizon Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 44
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