Fault Detection in Seismic Datasets
Using Hough transform
Zhen Wang and Ghassan AlRegib
Center for Energy and Geo Processing - CeGP
School of Electrical and Computer Engineering
Georgia Institute of Technology, Atlanta, GA, U.S.A.
{zwang313, alregib}@gatech.edu
Outline
Introduction Problem of Seismic Interpretation
Seismic Datasets
The Proposed Method Fault Points Highlighting
Hough Transform
False Feature Removal
Fault Line Labeling
Experimental Results Single Fault
Multiple Faults
Conclusion and Future Work2/25
Faults and Its Geological Features
Feature: Discontinuity on horizons
3/25
Triassic
Tertiary
Chalk
Lower Cretaceous
Rattray
volcanics
Undifferentiated Paleozoic
http://gsabulletin.gsapubs.org/content/112/9/1414/F5.large.jpg
Time Slice
Seismic Interpretation
Based on experience and visual cue
Time-consuming and labor-intensive
4/25
Seismic Section
http://steveholbrook.com/_Media/3d_from_opendtect.jpeg
Computer-aided Interpretation
Dataset
Netherlands Offshore F3 Block ─ 3D Seismic Dataset
Size: Crossline(X)*Inline(Y)*Depth(Z) = 251*226*176
http://www.opendtect.org/index.php/share-seismic-data/osr.html
X(crossline)
Z
Seismic Image
( , )S x z
6/25
Outline
Introduction Problem of Seismic Interpretation
Seismic Datasets
The Proposed Method Fault Points Highlighting
Hough Transform
False Feature Removal
Fault Line Labeling
Experimental Results Single Fault
Multiple Faults
Conclusion and Future Work7/25
Fault Detection Diagram
8/25
Fault Points
Highlighting
Hough
Transform
False Feature
Removal
Fault Line
Labeling
Seismic
Sections
Fault
Lines
Discontinuity:
Fault Points Highlighting
Horizon:
+
−
+
−
Faults:( , ) 0D x z ( , ) 0D x z
2
2
,
, ln
(2 1) ,
r r
j r i r
r r
j r i r
S x i z j
D x z
r S x i z j
Mask:
2 1r
2 1r
10/25
Fault Points Highlighting
Thresholding:
(a) Discontinuity Map (b) Highlighted Fault Points
Z
X(crossline)
0
1 if ,,
0 o.w.
D x z TB x z
11/25
Fault Points
Highlighting
Hough
Transform
False Feature
Removal
Fault Line
Labeling
Seismic
Sections
Fault
Lines
Fault Detection Diagram
12/25
Hough Transform
Mapping from image space to parameter space
13/25
0 0 0cos sinx y r
r
0r
x
y
Image Space Parameter Space
0
0 0,r
r
0r
x
y
Image Space Parameter Space
0
0 0cos sinx y r
0 0,x y
0 0 0cos sinx y r
r
0r
x
y
Image Space Parameter Space
0
1 1cos sinx y r
0 0cos sinx y r
0 0,x y
1 1,x y
Fault Detection Diagram
14/25
Fault Points
Highlighting
Hough
Transform
False Feature
Removal
Fault Line
Labeling
Seismic
Sections
Fault
Lines
Two types of false features:
1. Outlier
2. Neighboring group
Features can be represented by :
, the midpoint of :
False Feature Removal
, ,
, ,
b i b i
i
e i e i
x z
x z
I
, ,,b i b ix z
, ,,e i e ix z
iI
im
imiI
, , , ,,
2 2
b i e i b i e i
i
x x z z
m
iI
15/25
False Feature Removal
Define Two types of distance:
1. Absolute Distance(AD)
2. Lateral Distance(LD)
1 1,LD i i i m m v
1 2
1AD
2i i I I 1iI
iI
1l
2l
AD
LD
il
1il
im
1im1,i v
LD2 2
1 2
2
l l
16/25
False Feature Removal
Algorithm:
Outlier Removal
Neighboring Group
Merging
17/25
Fault Detection Diagram
18/25
Fault Points
Highlighting
Hough
Transform
False Feature
Removal
Fault Line
Labeling
Seismic
Sections
Fault
Lines
,c cx z
( ), ( )c ci ix z
Fault Line Labeling
0 0,x z
Discontinuity Map
( ), ( )
( ) arg max ,s c s c
m cx r i r i
i D x
x x
x z
19/25
( ( ), ( ))c ci ix z
sr
Fault Line Labeling
1 22 2ˆ arg min c m
x
x x x x x
mxcx x̂ 0x
20/27
1 20.2, 0.8
Outline
Introduction Problem of Seismic Interpretation
Seismic Datasets
The Proposed Method Fault Points Highlighting
Hough Transform
False Feature Removal
Fault Line Labeling
Experimental Results Single Fault
Multiple Faults
Conclusion and Future Work19/25
20/25
Experimental Results
Hough
Transform
False Feature
Removal
Fault Line
Labeling
(a) (b)
sr
(b) (c) (d) (a) (b) (c) (d)
Experimental Results
D. Hale, “Methods to compute fault images, extract fault surfaces,
and estimate fault throws from 3d seismic images,” GEOPHYSICS,
vol. 78, no. 2, pp. O33–O43, 2013. (b)(e)
Detected
Methods
Ground
Truth
(f)
(f)(b)(e)
(g) (h)
Experimental Results
Case of Multiple Faults
22/25
Outline
Introduction Problem of Seismic Interpretation
Seismic Datasets
The Proposed Method Fault Points Highlighting
Hough Transform
False Feature Removal
Fault Line Labeling
Experimental Results Single Fault
Multiple Faults
Conclusion and Future Work23/25
Conclusion and Future Work
24/25
Hough transform can be applied to detect fault
lines in seismic data
More sophisticated assessment methods need
to be proposed to evaluate the detected results
Automatically calculate parameters such as the
thresholds and parameters in Hough transform
25/25