Lithology Prediction using
Seismic Inversion Attributes
Dan Hampson
April 22, 2010
Overview
A new product will be released by Hampson-Russell, called
“LithoSI”.
LithoSI is used to predict lithology or “classified” well logs from
pre-stack inversion attributes.
This talk presents the theory behind LithoSI, followed by two
examples.
April, 2010
2
The basic problem
It is now routine to
invert pre-stack data.
P-Impedance
S-Impedance
Vp/Vs Ratio
That process transforms
angle gathers into elastic
volumes.
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The basic problem
The challenge is to
relate the derived
volumes back to the
well logs.
P-Impedance
S-Impedance
Vp/Vs Ratio
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The basic problem
One way to do this is to cross plot inversion attributes from the logs:
Vp/Vs Ratio
P-Impedance
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The basic problem
We can then highlight selected zones on
the cross plot:
Vp/Vs Ratio
Gas sand
P-Impedance
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The basic problem
The selected zone is plotted on the
inversion volume:
Gas sand
InvertedVp/Vs Ratio
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Interpreted Gas Sand
7
The basic problem
The problem is that the interpreted
area depends critically on the size of
the zone:
Gas sand
InvertedVp/Vs Ratio
April, 2010
Interpreted Gas Sand
8
The basic problem
The problem is that the interpreted
area depends critically on the size of
the zone:
Gas sand
InvertedVp/Vs Ratio
April, 2010
Interpreted Gas Sand
9
The basic problem
Instead of defining an arbitrary sharp
cutoff for the zone, we can define a
probability distribution:
Vp/Vs Ratio
P-Impedance
Gas sand
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The basic problem
This probability distribution is mapped
to the inversion volumes using
“Bayesian Classification:
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The basic problem
How to improve the basic cross plot zone method:
(1) Select multiple zones automatically using lithology logs.
(2) Generate probability distributions for each zone.
(3) Use cross-validation to check zones with seismic.
(4) When applying to the volume, calculate not only the best
zone, but also the probability of occurrence.
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LithoSI – Facies Classification
Lithology
Zp
2000 4000 60001.8
1200
1250
1300
1350
1400
1450
1500
1550
1600
Training set
Vp/Vs
2.2
2.6
Vp/Vs 1600
1700 1800 1900 2000 2100 2200 2300 2400
1600 1700 1800 1900 2000 2100 2200 2300 2400
2.5
2.5
2.4
2.4
2.3
2.3
2.2
2.2
2.1
2.1
2.0
2.0
1.9
1.9
1.8
1600 1700 1800 1900 2000 2100 2200
Extract cross plot
data at well locations.
Zp
2300 2400
1.8
2.5
2.5
2.4
2.4
2.3
2.3
2.2
2.2
2.1
2.1
2.0
2.0
1.9
1.9
1.8
1.8
1600 1700 1800 1900 2000 2100 2200 2300 2400
Compute probability
distributions.
Oil
Water
gas
p(Class i I p , PR)
April, 2010
Extract probabilities
for each class at
arbitrary locations.
13
Extracting the cross plot data
Each input well requires a
lithology log in addition to
desired rock properties curves:
Zp
Lithology
1600
1200
2000
Vp/Vs
2400 1.8
2.2
2.6
1600 1700 1800 1900 2000 2100 2200 2300 2400
2.5
2.5
2.4
2.4
2.3
2.3
2.2
2.2
1350
2.1
2.1
1400
2.0
2.0
1.9
1.9
1.8
1.8
1250
1300
1450
1500
1600 1700 1800 1900 2000 2100 2200 2300 2400
1550
1600
The lithology log defines the zones boundaries for
extracting the cross plot points.
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Bayes Theorem
Bayes Theorem calculates the probability we have a particular
class, given a particular set of seismic attributes:
p c| X
p (c ) p ( X | c )
p( X )
Where:
• c is a class (e.g. Sand).
• X is a seismic attributes Vector (e.g. X = (Zp, Vp/Vs)).
• p(c) is the a-priori probability for class c (e.g. probability of
getting sand in general).
• p(X|c) is the probability of attributes X knowing we are in
class c (e.g. distribution of (Zp, Vp/Vs) in sand).
• p(X) is the probability of attributes X.
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Pdf computation
The cross plot is convolved with a smooth kernel function:
p c| X
p (c ) p ( X | c )
p( X )
x
xi
(e.g., Zp)
The kernel estimate of a 1-D PDF is given by:
fˆ ( x )
1
nh
n
i 1
x xi
K(
)
h
Kernel function K
2h
This user parameter controls the smoothing of the distribution
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Effect of the smoothing parameter
Vp/Vs
Small “h”
Zp
April, 2010
Large “h”
17
Probability cube computation
p c| X
P
p (c ) p ( X | c )
p( X )
Density functions weighted
by a priori class proportions
Normalisation
X
1
Probabilities:
Class A
0.34
0.10
N/A
Class B
0.22
0.46
N/A
Class C
0.44
N/A
0
x3
April, 2010
x1
x2
18
Confusion matrix
Thanks to Brian Russell and Wikipedia:
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Confusion matrix
Thanks to Brian Russell and Wikipedia:
Diagonals show successful classification.
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Confusion matrix
Thanks to Brian Russell and Wikipedia:
Off-diagonals show “confusion”.
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Validation using the Confidence matrix
Zp
Lithology Log
Classified
Inversion trace
SHALES
HC SAND
SAND
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Validation using the Confidence matrix
Zp
Lithology Log
Classified
Inversion trace
How often do we get a HC Sand when
there is actually a HC sand present? – 83%
SHALES
HC SAND
SAND
April, 2010
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Validation using the Confidence matrix
Zp
Lithology Log
Classified
Inversion trace
How often do we get a shale when there
is actually a sand present? – 27%
SHALES
HC SAND
SAND
April, 2010
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Workflow overview
Zp
Vp/Vs
1600 2000 24001.8
2.2
1600 1700 1800 1900 2000 2100 2200 2300 2400
2.6
Vp/Vs
2.5
2.5
2.4
2.4
1300
2.3
2.3
1350
2.2
2.2
1400
2.1
2.1
1200
1250
1450
2.0
1500
1.9
1550
1.8
1600
Input data
2.0
Zp
1.9
1.8
1600 1700 1800 1900 2000 2100 2200 2300 2400
Extraction of training set
from wells
Compute
multivariate
PDFs
1600 1700 1800 1900 2000 2100 2200 2300 2400
1.0
0.0
Oil
Water
gas
p(Class i I p , PR)
Compute probability litho-cubes
April, 2010
2.5
2.5
2.4
2.4
2.3
2.3
2.2
2.2
2.1
2.1
2.0
2.0
1.9
1.9
1.8
1.8
1600 1700 1800 1900 2000 2100 2200 2300 2400
Extract litho-class probabilities
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Example: West Africa
Inline Direction
Crossline Direction
Hz 1
500 ms
Hz 2
Hz 3
Time
1 km
Deep offshore west Africa
Well3
Well3
Complex turbiditic deposit
environment
35 sqkm
12.5x12.5m bin size – 4ms
Several targets in 800ms
time window
April, 2010
Well1
Well1
Well2
Well2
Hz 1 time map
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AVA response and lithology / fluid
discrimination
0.5
GR
VP
VS
RHO
AVA
VSH
SW
PHIE
VSH
0
0
3000
P Impedance
1
11000
S Impedance
100 ms
Poisson’s ratio
6000
SAND
SHALE
SW
0
1500
April, 2010
3000
P Impedance
1
11000
27
Seismic data quality and frequency
bandwidth
Near
Far Ultra Far
Extracted wavelets
500 ms
Near: 12-20° (2-23/28-60Hz)
Near
Far: 20-36°(2-17/25-55 Hz)
90
Far
Ultra Far
Seismic Power spectra
NEAR
FAR
ULTRA
FAR
Ultra far: 36-50°(2-12/17-37 Hz)
30
0
April, 2010
Hz
100
28
Simultaneous Elastic Inversion in Stratigraphic
Framework
Initial Layered Model
Structural Framework
Synthetic Angle Stacks
Initial Model
Real Angle Stacks
Difference
Simulated Annealing
Model Perturbation
Vp, Vs, and t
<
?
Final Model
t
Final model
April, 2010
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Initial model for simultaneous inversion
100 ms
1 Km
1.6
Vp/Vs
2.6
Property filling of the Vp, Vs and density attributes performed by kriging within
layers of the corresponding 5-10Hz low pass filtered logs
March, 2010
LithoSI Presentation
30
Inverted Vp/Vs attribute
100 ms
1 Km
Vp/Vs
1.6
2.6
Near seismic residuals (Real Seismic – Synthetic Seismic) and VpVs attribute
April, 2010
1.6
Vp/Vs
2.6
31
Inversion QC and validation at well 1
VSH
1
VP/VS
5000
IP
10000
IS
12-20°
0
20-36°
0
36-60°
0
0
SW
1
100 ms
0
Seismic wavelets :
1.4
2.8
2000
Well log
Initial model
Final inverted model
April, 2010
6000
Real seismic trace
Synthetic trace from well
Synthetic trace from inversion results
32
Training Set Computation at Different Scales
Upscaled Logs
Logs
11x11 traces
P-Impedance
P-Impedance
Poisson Ratio
PR
Poisson Ratio
Zp
Poisson Ratio
Litho
Inverted attributes
extracted near wells
P-Impedance
Effect of Smoothing Parameter
h= 6
h=3
h= 10
0
Poisson’s Ratio
Poisson’s Ratio
0.5
3000
P impedance
11000
Kernel function K
2h
April, 2010
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Kernel Density Estimate for Lithology
Prediction
VS
RHO
IP
IS
SHALE
April, 2010
SW
VSH
PR VP/VS
0.5
Poisson Ratio
100 ms
VP
OIL-SAND
WATER-SAND
0
3000
P impedance
11000
35
Kernel Density Estimate for Lithology
Prediction
VS
RHO
IP
IS
SW
VSH
PR VP/VS
0.5
Poisson Ratio
100 ms
VP
p(Z p , PR oil sand )
SHALE
April, 2010
OIL-SAND
WATER-SAND
0
3000
P impedance
11000
36
Validation: Input data
VS
RHO
IP
IS
SW
VSH
PR
VP/VS
100 ms
VP
SHALES
HC SAND
April, 2010
SAND
Logs colored by Litho log
37
Validation: Classification result at
Well Locations
VS
RHO
IP
IS
SW
VSH
PR
VP/VS
100 ms
VP
SHALES
HC SAND
April, 2010
SAND
Logs colored by most probable facies derived
from seismic attribute at well location
38
Litho Probability Cubes
Probability of Water Sand
100 ms
1 Km
Probability of Shales
0
VSH SW
Probability of HC Sand
0
April, 2010
0
1
1
1
Most Probable Facies
LITHO log
SHALES
HC SAND
SAND
39
3-D Visualization of HC Sands
p( HC Sand I p , PR) 80%
1.6
April, 2010
Vp/Vs
2.6
HC sand probability
0
1
40
Example 2: Brazeau area, Alberta
2005 study
2003 study
Brazeau
River
Brazeau
South
Primary Targets:
2007 study
Clastics
Belly River, Cardium,
Viking
 Carbonates
Elkton/Shunda, Nisku

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Example 2 dataset
Area - ~100 km2
1 relocated well (A) with a log set on the full
inversion window, used for the low frequency
initial model.
2 productive gas wells (P,E), used for the inversion
QC and the lithological interpretation.
April, 2010
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Petrophysical Analysis - Viking
SP
-160
MV
GR_1
0
GAPI
MM
200
400
BS
150
MM
K/M3
100 0.5
DEN_1
CALI_1
150
WIRE.PHIE_RHOG_1
DRHO
-400
40
1950
DEPTH
METRES 0.45
400
K/M3
NPHI
500
V/V
2950 0
TOPS
-0.15 1950
10 0.2
2950 0.2
K/M3
OHMM
2000 0
2000 0
OHMM
OHMM
0
V/V
1
VOL_QUARTZ_6
SFL_1
2950 0.2
V/V
COAL_1
ILM
WIRE.DEN_1
100 1950
1
ILD_1
WIRE.DEN_4
K/M3
PHIE_RHOG_1
0
WIRE.BADHOLE_1
DT_1
US/M
V/V
V/V QUARTZ
Viking Sand – Oil (Class I)
Gas (Class IIp)
1
VSH_2
2000 0
V/V
1
2519.8
2525
LCRET
2530
2535
2540
VIK
2545
2550
2555
VIKSND
2560
2565
2570
2576.0
April, 2010
VIKSSB
JFOU
Angle
MANN
43
CDP Stack through well locations
Well P
Well E
Viking
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5 degree Angle Stack
Angle Stack
April, 2010
Synthetic Angle Stack
45
12 degree Angle Stack
Angle Stack
April, 2010
Synthetic Angle Stack
46
20 degree Angle Stack
Angle Stack
April, 2010
Synthetic Angle Stack
47
28 degree Angle Stack
Angle Stack
April, 2010
Synthetic Angle Stack
48
36 degree Angle Stack
Angle Stack
April, 2010
Synthetic Angle Stack
49
Inversion Results Well-P Location
- GR Well Log
- IP Well Log
- IS Well Log
- Rhob Well Log
- Seismic Trace
- Seismic Trace
- Seismic Trace
- Seismic Trace
- Seismic Trace
- upscaled Log
- upscaled Log
- upscaled Log
- Inverted IP
- Inverted IS
- Inverted Rhob
- Inverted
Synthetic
- Inverted
Synthetic
- Inverted
Synthetic
- Inverted
Synthetic
- Inverted
Synthetic
ANGLE 05
ANGLE 12
ANGLE 20
ANGLE 28
ANGLE 36
Viking
April, 2010
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Inversion Results Well-E Location
- GR Well Log
- IP Well Log
- IS Well Log
- Rhob Well Log
- Seismic Trace
- Seismic Trace
- Seismic Trace
- Seismic Trace
- Seismic Trace
- upscaled Log
- upscaled Log
- upscaled Log
- Inverted IP
- Inverted IS
- Inverted Rhob
- Inverted
Synthetic
- Inverted
Synthetic
- Inverted
Synthetic
- Inverted
Synthetic
- Inverted
Synthetic
ANGLE 05
ANGLE 12
ANGLE 20
ANGLE 28
ANGLE 36
Viking
April, 2010
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Section through the wells - Initial Model – Zp
SE
P
E
NW
High
Viking
Nordegg
Wabamun
Nisku
Ireton
Low
April, 2010
52
Section through the wells – Elastic Inversion – Zp
SE
P
E
NW
High
Viking
Nisku
Low
April, 2010
53
Section through the wells – Elastic Inversion –
Density
SE
P
E
NW
High
Viking
Nisku
Low
April, 2010
54
LithoLogs computation
VSH
RHOB
GR
XPLOT QC
LithoLogs
A E P
GR
VSH
April, 2010
55
3D Xplot – Wells points – Viking – Mannville
interval
Rho
Vp
Vs
Rho
Vp
April, 2010
Vs
Sand:
Shale:
56
Distribution Functions computation
Validation at wells:
E
P
Rho
Vp
Vs
Rho
Vp
April, 2010
Vs
Sand:
Shale:
57
Section through the wells
E
1
P
E
Carb
P
Sand
Shale
Viking
0
E
E
P
Sand
Probability
0
April, 2010
Sand probability
P
1
Most probable facies
58
3D Visualization - VIKING Horizon
April, 2010
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3D Visualization of Sand Probability
Sand
Probability
1
0.2
April, 2010
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CE9 Release of LithoSI
LithoSI is
scheduled to
be released
with the CE9
update in
Q4/2010.
April, 2010
61
Summary
A new product will be released by Hampson-Russell, called
“LithoSI”.
LithoSI is used to predict lithology or “classified” well logs from
pre-stack seismic inversion attributes.
LithoSI will be released as a part of the general HRS-9
release in early 2011.
This talk has presented the theory behind LithoSI, followed by
two examples.
April, 2010
62