Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 1
AFI(AVO Fluid Inversion)
Uncertainty in AVO:How can we measure it?
Dan Hampson, Brian RussellHampson-Russell Software, Calgary
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 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 3
AVO Uncertainty Analysis:The Basic Process
AVO ATTRIBUTEAVO ATTRIBUTEMAPSMAPSISOCHRONISOCHRONMAPSMAPS
!! GRADIENTGRADIENT!! INTERCEPTINTERCEPT!! BURIAL DEPTHBURIAL DEPTH
CALIBRATED:CALIBRATED:
STOCHASTIC STOCHASTIC AVOAVOMODELMODEL
GG
IIFLUIDFLUID
PROBABILITYPROBABILITYMAPSMAPS
!! PPBRIBRI
!! PPOILOIL
!! PPGASGAS
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 4
“Conventional” AVO Modeling: Creating 2 pre-stack synthetics
IO GO
IB GB
IN SITU = OILIN SITU = OIL
FRM = BRINEFRM = BRINE
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 5
Monte Carlo Simulation: Creating many synthetics
0
25
50
75
II--G DENSITY FUNCTIONS G DENSITY FUNCTIONS BRINE OIL GAS
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 6
We assume a 3-layer model with shale enclosing a sand (with various fluids).
Shale
Shale
Sand
The Basic Model
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 7
The Shales are characterized by:
P-wave velocity S-wave velocityDensity
Vp1, Vs1, r1
Vp2, Vs2, r2
The Basic Model
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 8
Each parameter has a probability Each parameter has a probability distribution:distribution:
Vp1, Vs1, r1
Vp2, Vs2, r2
The Basic Model
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 9
The Sand is characterized by:
Brine ModulusBrine DensityGas ModulusGas DensityOil ModulusOil DensityMatrix ModulusMatrix densityPorosityShale VolumeWater SaturationThickness
Each of these has a probability distribution.Each of these has a probability distribution.
Shale
Shale
Sand
The Basic Model
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 10
0500
100015002000250030003500400045005000
0.4 0.9 1.4 1.9 2.4 2.9 3.4DBSB (Km)
Some of the statistical distributions are determined from well log trend analyses:
Trend Analysis
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 11
Determining Distributions at Selected Locations
0500
100015002000250030003500400045005000
0.4 0.9 1.4 1.9 2.4 2.9 3.4DBSB (Km)
Assume a Normal distribution. Get the Mean and Standard Deviation from the trend curves for each depth:
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 12
Trend Analysis: Other Distributions
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0.4 0.9 1.4 1.9 2.4 2.9 3.4DBSB (Km)
Shale Velocity
1.01.2
1.41.6
1.82.0
2.22.4
2.62.8
3.0
0.4 0.9 1.4 1.9 2.4 2.9 3.4DBSB (Km)
Sand Density
1.01.21.41.61.82.02.22.42.62.83.0
0.4 0.9 1.4 1.9 2.4 2.9 3.4DBSB (Km)0%
5%
10%
15%
20%
25%
30%
35%
40%
0.4 0.9 1.4 1.9 2.4 2.9 3.4DBSB (Km)
Shale Density
Sand Porosity
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 13
Shale:Shale:VVpp Trend AnalysisTrend AnalysisVVss Castagna’sCastagna’s Relationship with % errorRelationship with % errorDensityDensity Trend AnalysisTrend Analysis
Sand:Sand:Brine ModulusBrine ModulusBrine DensityBrine DensityGas ModulusGas ModulusGas DensityGas DensityOil ModulusOil Modulus Constants for the areaConstants for the areaOil DensityOil DensityMatrix ModulusMatrix ModulusMatrix densityMatrix densityDry Rock Modulus Dry Rock Modulus Calculated from sand trend analysisCalculated from sand trend analysisPorosityPorosity Trend AnalysisTrend AnalysisShale VolumeShale Volume Uniform Distribution from Uniform Distribution from petrophysicspetrophysicsWater SaturationWater Saturation Uniform Distribution from Uniform Distribution from petrophysicspetrophysicsThicknessThickness Uniform DistributionUniform Distribution
Practically, this is how we set up the distributions:
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 14
Top Shale
Base Shale
Sand
From a particular model instance, calculate two synthetic traces at different angles.
0o 45o
Note that a wavelet is assumed known.
Calculating a Single Model Response
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 15
Top Shale
Base Shale
Sand
0o 45o
On the synthetic traces, pick the event corresponding to the top of the sand layer:
P1P2
Note that these amplitudes include interference from the second interface.
Calculating a Single Model Response
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 16
Top Shale
Base Shale
Sand
0o 45o
P1P2
Using these picks, calculate the Intercept and Gradient for this model:
I = P1G = (P2-P1)/sin2(45)
Calculating a Single Model Response
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 17
GI
GI
GI
OILOIL
KKOILOIL
ρρOILOIL
GASGAS
KKGASGAS
ρρGASGAS
BRINEBRINE
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:
Using Biot-Gassmann Substitution
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 18
I
G
BrineOilGas
By repeating this process many times, we get a probability distribution for each of the 3 sand fluids:
Monte-Carlo Analysis
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 19
@ 1000m@ 1000m @ 1200m@ 1200m @ 1400m@ 1400m
@ 1600m@ 1600m @ 1800m@ 1800m @ 2000m@ 2000m
Because the trends are depth-dependent, so are the predicted distributions:
The Results are Depth Dependent
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 20
The Depth-dependence can often be understood using Rutherford-Williams
classification
SandSand
Burial DepthBurial Depth
Impe
danc
eIm
peda
nce ShaleShale
1
1
2
2
3
3
4
4
5
5
6
6
Class 3
Class 2Class 1
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 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):
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 kk FPFGIp
FPFGIpGIFP
*,
)~(*~,,~
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 22
How Bayes’ Theorem works in a simple case:
VARIABLEVARIABLE
OC
CU
RR
ENC
EO
CC
UR
REN
CE
Assume we have these distributions:
Gas Oil
Brine
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 23VARIABLEVARIABLE
OC
CU
RR
ENC
EO
CC
UR
REN
CE
100%
50%
This is the calculated probability for (gas, oil, brine).
How Bayes’ Theorem works in a simple case:
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 24
When the distributions overlap, the probabilities decrease:
VARIABLEVARIABLE
OC
CU
RR
ENC
EO
CC
UR
REN
CE
100%
50%
Even if we are right on the “Gas” peak, we can only be 60% sure we have gas.
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 25
This is an example simulation result, assuming that the wet shale VS and VP are related by Castagna’s equation.
Showing the Effect of Bayes’ Theorem
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 26
This is an example simulation result, assuming that the wet shale VS and VP are related by Castagna’s equation.
This is the result of assuming 10% noise in the VS calculation
Showing the Effect of Bayes’ Theorem
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 27
Note the effect on the calculated gas probability
0.0
0.5
1.0
Gas Probability
By this process, we can investigate the sensitivity of the probability distributions to individual parameters.
Showing the Effect of Bayes’ Theorem
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 28
Example Probability Calculations
Gas Oil Brine
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 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, Sglobal and Sgradient, this way:
Iscaled = Sglobal *IrealGscaled = Sglobal * Sgradient * Greal
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 30
Fitting 6 Known Zones to the Model
1
4
2
3
56
1
4
2
3
56
1 2
4 5 6
3
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 31
This example shows a real project from West Africa, performed byone 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.
Real Data Example – West Africa
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 32
Near Angle Stack0-20 degrees
Far Angle Stack20-40 degrees
One Line from the 3D Volume
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 33
Near Angle Stack0-20 degrees
Far Angle Stack20-40 degrees
Shallow producing zone
Deeper target zone
One Line from the 3D Volume
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 34
Near Angle Stack0-20 degrees
Far Angle Stack20-40 degrees
AVO Anomaly
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 35
Near Angle Stack0-20 degrees
Far Angle Stack20-40 degrees
-3500
+189
Amplitude Slices Extracted fromShallow Producing Zone
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 36
Trend AnalysisSand and Shale Trends
1000
1500
2000
2500
3000
3500
4000
4500
5000
500 700 900 1100 1300 1500 1700 1900
VELO
CIT
Y
1.50
1.75
2.00
2.25
2.50
2.75
3.00
500 700 900 1100 1300 1500 1700 1900
DEN
SITY
1000
1500
2000
2500
3000
3500
4000
500 700 900 1100 1300 1500 1700 1900 2100 2300 2500
BURIAL DEPTH (m)
VELO
CIT
Y
1.50
1.75
2.00
2.25
2.50
2.75
3.00
500 700 900 1100 1300 1500 1700 1900
BURIAL DEPTH (m)
DEN
SITY
Sand velocity
Shale velocity
Sand density
Shale density
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 37
Monte Carlo Simulations at 6 Burial Depths
-1400 -1600 -1800
-2000 -2200 -2400
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 38
Near Angle Amplitude Map Showing Defined Zones
Wet Zone 1
Wet Zone 2
Well 6
Well 7Well 3 Well 5
Well 1
Well 2
Well 4
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 39
Calibration Results at Defined Locations
Wet Zone 1
Wet Zone 2
Well 2
Well 5
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 40
Well 3
Well 4
Well 6
Well 1
Calibration Results at Defined Locations
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 41
.30
.60
1.0
Probability of Oil.80
Near Angle Amplitudes
Using Bayes’ Theorem at Producing Zone: OIL
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 42
.30
.60
1.0
Probability of Gas.80
Near Angle Amplitudes
Using Bayes’ Theorem at Producing Zone: GAS
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 43
Near angle amplitudes of second event
.30
.60
1.0
.80Probability of oil on second event
Using Bayes’ Theorem at Target Horizon
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 44
Verifying Selected Locationsat Target Horizon
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 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 allthe underlying probability distributions.