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