least-squares reverse time migration with frequency-selection encoding for marine data
DESCRIPTION
Least-squares Reverse Time Migration with Frequency-selection Encoding for Marine Data. Wei Dai, WesternGeco Yunsong Huang and Gerard T. Schuster , King Abdulla University of Science and Technology. Sep 26, 2013. Outline. Introduction and Overview. Theory Single frequency modeling - PowerPoint PPT PresentationTRANSCRIPT
Least-squares Reverse Time Migration with Frequency-selection
Encoding for Marine Data
Wei Dai, WesternGecoYunsong Huang and Gerard T. Schuster,
King Abdulla University of Science and Technology
Sep 26, 2013
Outlineβ’ Introduction and Overview
β’ Theory
Single frequency modeling
Least-squares migration
β’ Numerical Results
Marmousi2
Marine field data
β’ Summary
β’ Random encoding is not applicable to marine streamer data.
Fixed spread geometry (synthetic)
6 traces
Marine streamer geometry (observed)
4 traces
Mismatch between acquisition geometries will dominate the misfit.
Motivation of Freq. Select. Encoding
4
observeddata
simulateddata
misfit = erroneous
misfit
Marine Data
5
Solutionβ’ Every source is encoded with a unique
signature.
observed simulated
β’ Every receiver acknowledge the contribution from the βcorrectβ sources.
4 shots/group
R(w)
Group 1
Nw frequency bands of source spectrum:
Frequency Selection
2 km
wAccommodate up to Nw shots
Outlineβ’ Introduction and Overview
β’ Theory
Single frequency modeling
Least-squares migration
β’ Numerical Results
Marmousi2
Marine field data
β’ Summary
Single Frequency Modeling
(π΅π+ππ
ππ )~π·=βπ (π )π (π βπ)
Helmholtz Equation
(π΅πβ πππ
ππππ π )π=βππ {π (π )ππ±π© (βπππ )}π (πβπ)
Acoustic Wave Equation
β’ Advantages: Lower complexity in 3D case. Applicable with multisource technique.
Harmonic wave source
Single Frequency Modeling
(π΅πβ πππ
ππππ π )π=βππ {π (π )ππ±π© (βπππ )}π (πβπ)
Am
plitu
de
T T
Single Frequency ModelingA
mpl
itude
0 Frequency (Hz) 50
Am
plitu
de
20 Frequency (Hz) 30
11
Single Frequency Modeling
Where do the savings come from?
T
T
β π = 1π
Frequency sampling rate:
Smaller T larger less samples in frequency
domain
Estimated Frequency Sampling
ππππ
ππππ₯
β π πππ₯=1
ππππ₯βππππ
(Mulder and Plessix, 2004)
Theory: Least-squares Migrationπ (π )=π
πβπ³πβ~π βπ
β’ Misfit:
~π β’ Encoded Supergather:
only contains one frequency component for each shot, with
frequency-selection encoding.β’ Encoding functions are changed at every iteration.
Misfit function is redefined at every iteration.
β’ N frequency components N iterations.
πππ‘ ,ππ ,ππ ππ π ,ππ ,ππ π ππ ππ , ππ
Outlineβ’ Introduction and Overview
β’ Theory
Single frequency modeling
Least-squares migration
β’ Numerical Results
Marmousi2
Marine field data
β’ Summary
Marmousi2
0 X (km) 8
0Z
(km
)3.
5
4.5
1.5
km/s
β’ Model size: 8 x 3.5 kmβ’ Shots: 301
β’ Cable: 2km
β’ Receivers: 201
β’ Freq.: 400 (0~50 hz)
Marmousi2β’ Trace length: 8 sec = 0.125 Hz
β π πππ₯=1
ππππ₯βππππβ0.7π»π§
β’ According to the formula:
For the frequency bank 0~50 Hz, there are 400
frequency channels accommodate up to 400 shots
β’ We choose = 0.625 Hz. Each shot contains 80 frequency
components 80 iterations needed.
β’ At the first iteration, all 400 shots are randomly assigned with a
unique frequency . For next iteration,
0 X (km) 8
0Z
(km
)3.
5
0 X (km) 8
Z (k
m)
3.5
Conventional RTM0
LSRTM Image (iteration=1)LSRTM Image (iteration=20)LSRTM Image (iteration=80) Cost: 3.2
Frequency-selection LSRTM of 2D Marine Field Data
0 X (km) 18.7
0Z
(km
)2.
5
2.1
1.5
km/s
β’ Model size: 18.7 x 2.5 km β’ Freq: 625 (0-62.5 Hz) β’ Shots: 496 β’ Cable: 6kmβ’ Receivers: 480
Marine Field Dataβ’ Trace length: 10 sec = 0.1 Hz
β π πππ₯=1
ππππ₯βππππβ1π»π§
β’ According to the formula:
For the frequency bank 0~62.5 Hz, there are 625
frequency channels accommodate up to 625 shots
β’ Empirical tests suggest = 0.3 Hz 208 iterations.
One possible reason is the large shot spacing 37.5 m.
Conventional RTM
Frequency-selection LSRTM
Z (k
m)
2.5
0Z
(km
)2.
50
0 X (km) 18.7
Cost: 5
Freq. Select LSRTM
Conventional RTM Conventional RTM
Freq. Select LSRTM
Zoom Views
Summaryβ’ MLSM can produce high quality images efficiently.
LSM produces high quality image.
Frequency-selection encoding applicable to marine
data.
β’ Limitation:
High frequency noises are present. Sensitive to velocity error (5% errors in velocity led to
failure).
Thanks