367_AVO_Fluid_Inversion.pdf

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AFI

(AVO Fluid Inversion)

Uncertainty in AVO:

How can we measure it?

Dan Hampson, Brian Russell

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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.

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AVO Uncertainty Analysis:

The Basic Process

AVO ATTRIBUTE

MAPS

ISOCHRON

MAPS

!

GRADIENT

!

INTERCEPT

!

BURIAL DEPTH

CALIBRATED:

STOCHASTIC

AVO

MODEL

G

I

FLUID

PROBABILITY

MAPS

!

P

_BRI

!

P

_OIL

!

P

_GAS

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“Conventional” AVO Modeling:

Creating 2 pre-stack synthetics

I

_O

G

_O

I

_B

_G

B

IN SITU = OIL

FRM = BRINE

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Monte Carlo Simulation:

Creating many synthetics

0 25 50 75

I

-

G DENSITY FUNCTIONS

BRINE OIL GAS

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We assume a 3-layer model with

shale enclosing a sand (with

various fluids).

Shale

Sand

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The Shales are characterized by:

P-wave velocity

S-wave velocity

Density

V

_p1

, V

_s1

, r

₁

V

_p2

, V

_s2

, r

₂

(8)

Each parameter has a probability

distribution:

V

_p1

, V

_s1

, r

₁

V

_p2

, V

_s2

, r

₂

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The Sand is characterized by:

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.

Shale

Sand

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0

500 1000

1500

2000

2500

3000

3500

4000

4500

5000

0.4

0.9

1.4

1.9

2.4

2.9

3.4 DBSB (Km)

Some of the statistical distributions are determined from well log

trend analyses:

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Determining Distributions at

Selected Locations

0

500 1000

1500

2000

2500

3000

3500

4000

4500

5000

0.4

0.9

1.4

1.9

2.4

2.9

3.4 DBSB (Km)

Assume a Normal distribution. Get the Mean and Standard Deviation

from the trend curves for each depth:

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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

3.4 DBSB (Km)

Shale Velocity

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

0.4

0.9

1.4

1.9

2.4

2.9

3.4 DBSB (Km)

Sand Density

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

0.4

0.9

1.4

1.9

2.4

2.9

3.4 DBSB (Km)

0%

5%

10%

15%

20%

25%

30%

35%

40%

0.4

0.9

1.4

1.9

2.4

2.9

3.4 DBSB (Km)

Shale Density

Sand Porosity

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Shale:

V

_p_p

Trend Analysis

V

_s_s

Castagna’s

Relationship with % error

Density

Trend Analysis

Sand:

Brine Modulus

Brine Density

Gas Modulus

Gas Density

Oil Modulus

Constants for the area

Oil Density

Matrix Modulus

Matrix density

Dry Rock Modulus

Calculated from sand trend analysis

Porosity

Trend Analysis

Shale Volume

Uniform Distribution from

petrophysics

Water Saturation

Uniform Distribution from

petrophysics

Thickness

Uniform Distribution

Practically, this is how we set up the

distributions:

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Top Shale

Base Shale

Sand

From a particular model instance,

calculate two synthetic traces at

different angles.

0 o

45 o

Note that a wavelet is assumed

known.

Calculating a Single Model

Response

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Top Shale

Base Shale

Sand

0 o

45 o

On the synthetic traces, pick the

event corresponding to the top of

the sand layer:

P

₁

P

2 Note that these amplitudes include

interference from the second interface.

Calculating a Single Model

Response

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Top Shale

Base Shale

Sand

0 o

45 o

P

₁

P

2 Using these picks, calculate the Intercept and Gradient for this model:

I

= P

₁

G =

(P

₂

-P

₁

)/sin

2 (45)

Calculating a Single Model

Response

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G

I

G

I

G

I

OIL

K

KOIL

OIL

ρ

OIL

GAS

K

KGAS

GAS

ρ

GAS

BRINE

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:

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I

G

Brine

Oil

Gas

By repeating this process many times, we get a probability distribution for

each of the 3 sand fluids:

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@ 1000m

@ 1200m

@ 1400m

@ 1600m

@ 1800m

@ 2000m

Because the trends are depth-dependent, so are the predicted

distributions:

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The Depth-dependence can often be

understood using Rutherford-Williams

classification

Sand

Burial Depth

Im

pe

da

nc

e

Im

pe

da

nc

e

Shale

1

2

3

4

5

6

6 Class 3

Class 2

Class 1

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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(F

k

)

represent a priori probabilities and F

k

is either brine, oil, gas;

• p(I,G|F

k

)

are suitable distribution densities (eg. Gaussian) estimated

from the stochastic simulation output.

(

)

=

_∑

(

₍

)

₎

_{( )}

k

p

I

G

F

k

P

F

k

F

P

F

G

I

p

G

I

F

P

*

,

)

~

(

*

~

,

~

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How Bayes’ Theorem works in a

simple case:

VARIABLE

OCCURRENCE

Assume we have these distributions:

Gas

Oil

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VARIABLE

OCCURRENCE

100%

50%

This is the calculated probability for

(

gas

,

oil

,

brine

).

How Bayes’ Theorem works in a

simple case:

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When the distributions overlap, the

probabilities decrease:

VARIABLE

OCCURRENCE

100%

50%

Even if we are right on the “Gas”

peak, we can only be 60% sure we

have gas.

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This is an example simulation

result, assuming that the wet

shale V

_S

and V

_P

are related by

Castagna’s equation.

Showing the Effect of Bayes’

Theorem

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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

Showing the Effect of Bayes’

Theorem

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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

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Example Probability Calculations

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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

= S

_global

*I

_real

G

_scaled

= S

_global

* S

_gradient

* G

_real

One way to determine these scalers is by manually fitting multiple

known regions to the model data.

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Fitting 6 Known Zones to the Model

1

4

2

3

5

6

1

4

2

3

5

6

1

2

4

5

6

3

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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.

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Near Angle Stack

0-20 degrees

Far Angle Stack

20-40 degrees

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Near Angle Stack

0-20 degrees

Far Angle Stack

20-40 degrees

Shallow producing zone

Deeper target zone

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Near Angle Stack

0-20 degrees

Far Angle Stack

20-40 degrees

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Near Angle Stack

0-20 degrees

Far Angle Stack

20-40 degrees

-3500

+189

Amplitude Slices Extracted from

Shallow Producing Zone

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Trend Analysis

Sand and Shale Trends

1000 1500 2000 2500 3000 3500 4000 4500 5000 500 700 900 1100 1300 1500 1700 1900

VELO

C

ITY

1.50 1.75 2.00 2.25 2.50 2.75 3.00 500 700 900 1100 1300 1500 1700 1900

DENSITY

1000 1500 2000 2500 3000 3500 4000 500 700 900 1100 1300 1500 1700 1900 2100 2300 2500

BURIAL DEPTH (m)

VELO

C

ITY

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)

DENSITY

Sand velocity

Shale velocity

Sand density

Shale density

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Monte Carlo Simulations at 6 Burial

Depths

-1400

-1600

-1800

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Near Angle Amplitude Map Showing

Defined Zones

Wet Zone 1

Wet Zone 2

Well 6

Well 7

Well 3

_{Well 5}

Well 1

Well 2

Well 4

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Calibration Results at Defined

Locations

Wet Zone 1

Wet Zone 2

Well 2

Well 5

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Well 3

Well 4

Well 6

Well 1

Calibration Results at Defined

Locations

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.30

.60

1.0 Probability of Oil

.80

Near Angle Amplitudes

Using Bayes’ Theorem at Producing Zone:

OIL

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.30

.60

1.0 Probability of Gas

.80

Near Angle Amplitudes

Using Bayes’ Theorem at Producing Zone:

GAS

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Near angle amplitudes of second event

.30

.60

1.0 .80

Probability of oil on second event

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Verifying Selected Locations

at Target Horizon

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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.