Match filtering a time-lapse data set utilizing the surface-consistent method

Mahdi Almutlaq and Gary Margrave

9th March, 20129 March, 2012

CREWES Technical talk

OutlineOutline

• Surface-consistent hypothesisSurface consistent hypothesis

• What’s a surface-consistent matching filter?

l• Examples

• Conclusions & FW

• Acknowledgements

Surface-consistent hypothesisSurface consistent hypothesis

h f d l

( ) ( )* ( )* ( )* ( )d t t t h t t

The surface-consistent model:the seismic trace can be modeled as

(1)( ) ( )* ( )* ( )* ( )ij i j k ld t s t r t h t y t≈

whereo d : seismic trace

(1)

o dij : seismic traceo si : source response at location io rj : receiver response at location jo hk: offset response at location k; k=|i-j|o hk: offset response at location k; k |i j|o yl: subsurface response at l; l=(i+j)/2

FACT : the model is reasonable approximation of the seismic trace that is easy to compute.

Forward modelingInput model (4-components) Data

shots receivers offsets midpoints

( )* ( )* ( )* ( ) ( )i j k l ijs t r t h t y t d t≈

Forward model

Inverse modelingPredicted model (4-components) Data

shots receivers offsets midpoints

( )* ( )* ( )* ( ) ( )i j k l ijs t r t h t y t d t≈T

i j k l

Gx d

x s r h y

=

= Inverse model

FACT : Seismic data geometry matrix has no unique inverse due to singularity of h i GTG h G i h i i f f

1( )

j

T Tx G G G d−

=

the square matrix GTG, where G contains the positions of four-components above.

DifferenceSeismic traces

1 5 10 1 5 10

Input traces

d d

Difference( )rms base monitor −Predicted traces ( )200

( ) ( )rms base monitorNRMS

rms base rms monitor −= +

NRMS vs. Time shiftNRMS vs. Time shift

1( ) sin(2 )D t a ftπ=1

2

1 2

( ) ( )( ) sin(2 ( )( ) ( ) ( ) (2 )cos(2 )

fD t a f t tD t D t D t a f t ft

π δδ π δ π

= += − =

[ ][ ] [ ]

[ ]

(2 ) cos(2 )200

. sin(2 ) . sin(2 ( ))

(%) 100 2

a f t RMS ftNRMS

a RMS ft a RMS f t t

NRMS f t

π δ ππ π δ

δ

= + +

[ ](%) 100 2NRMS f tπ δ=

F (Hz) Time shift δt (ms)

NRMS (%)δt (ms)

50 0.001 31.4

50 0.002 62.8

NRMS vs. AmplitudeNRMS vs. Amplitude

1( ) sin(2 )D t ftπ=1

2

1 2

( ) s ( )( ) (1 )sin(2 )( ) ( ) ( ) sin(2 )

t ftD t b ftD t D t D t b ft

ππ

δ π= += − =(%) 100*NRMS b≈ Assuming amplitude change is small

a b NRMS (%)

1.0 0.1 9.5

1.0 0.6 46

Small amplitude differenceLarge amplitude difference

Surface-consistent matching filters ( )(SCMF)

For two repeated data sets, their surface-consistent model is:

( ) ( )* ( )* ( )* ( )

( ) ( )* ( )*2 2 2 2 ( )* ( )

1 1 1

2

1 1ij i j k l

ij i j k l

d t s t r t h t y t

d t s t r t h t y t

≈

≈

(2)

(3)j j

Q. Can we design a matching filter for these two data sets?

Matching filter concept:Matching filter concept:

1 2*m s s=Fourier domain

2

1

( )( )( )

SMS

ωωω

= (4)

1( )Spectral ratio is an exact matching filter, but it is unstable in presence of noise.

Alternatively: solve the time domain in LSQ & FT the solution which is aAlternatively: solve the time-domain in LSQ & FT the solution which is a good approx to the spectral ratio.

Surface-consistent matching filters ( ’)(cont’)

2. Compute LSQ match filter in time for each trace1. Define filter length

Filter length (static section)

Dynamic layer

3. Take the Fourier transform

4. Spectral decomposition

Shot component Receiver componentAfterDiff Base Before

5. Apply filters to monitor trace and difference from base trace.

7. Else, use your matched traces and iterate until goal is

h d NO

Offset component Midpoint component6. If NRMS value is within your

reached.

YES

NO

yspec. range (0 to 0.2) then stop. -

OutlineOutline

• Surface-consistent hypothesisSurface consistent hypothesis

• What’s a surface-consistent matching filter?

l• Examples

• Conclusions & FW

• Acknowledgements

Two earth models

Near-surfNear-surf

ReservoirReservoir

Other non-repeatable parametersOther non repeatable parameters

tion

Att

enua

t

Raw shot: before match filtering

Avg NRMS =41%

Difference = Baseline – monitor (before match filtering)Difference = Baseline – monitor (before match filtering)

Raw shot: after match filtering

Avg NRMS =25%

Difference = Baseline – monitor (after match filtering)Difference = Baseline – monitor (after match filtering)

Raw stack: before match filtering

Mean NRMS =70%

Stack: after match filtering

Mean NRMS =28%

Stack: After match filtering & statics

Mean NRMS =16%

Not: 3rd iteration of statics was not necessary. Match filtering was iterated 2 times.Not: 3rd iteration of statics was not necessary. Match filtering was iterated 2 times.

NRMS values: GOM vs. MGM

0.8

0.9

0 5

0.6

0.7

GOM example

M l0.3

0.4

0.5

Fast Track

Co-Processing

SCMF

NRM

S

My example (MGM)

0.1

0.2

SCMF

0 Perfectly repeated survey

(modified plot from Helgerud et al., TLE 2011)

ConclusionsConclusions

• Surface-consistent matching filter is analogous to other g gsurface-consistent methods (decon, statics , ...), exceptthe data term is spectral ratio of 2 surveys.W t MF i ti i LSQ & FT th lt hi h i• We compute MF in time in LSQ & FT the result which is an approx to spectral ratio.

• Spectral decomposition of trace-by-trace MF intoSpectral decomposition of trace by trace MF into surface-consistent operators; and

• small NRMS values balanced amplitude, equalized phase & bandwidth, and small or no time-shifts

• we have a SCMF that can significantly reduce the non-repeatability observed in TL data setsnon-repeatability observed in TL data sets.

Future workFuture work

Walkway PP VSP data from the observation well ( Alshuhail, et al., 2008)Walkway PP VSP data from the observation well ( Alshuhail, et al., 2008)Violet Grove Violet Grove

( Chen & Lawton, 2005)( Chen & Lawton, 2005)

AcknowledgementsAcknowledgements

• CREWES & all the sponsorsCREWES & all the sponsors

i l h k S di f h i• A special thanks to Saudi Aramco for their sponsorship

• Faranak for the good discussion on the SC resid statics, & Rolf for his help w/ the VG data set.