multisource least-squares reverse time migration
DESCRIPTION
Multisource Least-squares Reverse Time Migration. Wei Dai. Outline. Introduction and Overview Chapter 2: Multisource least-squares reverse time migration Chapter 3: Frequency-selection encoding LSRTM Chapter 4: Super-virtual inteferometric diffractions Summary. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/1.jpg)
Multisource Least-squares Reverse Time Migration
Wei Dai
![Page 2: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/2.jpg)
Outline• Introduction and Overview
• Chapter 2: Multisource least-squares reverse time
migration
• Chapter 3: Frequency-selection encoding LSRTM
• Chapter 4: Super-virtual inteferometric diffractions
• Summary
![Page 3: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/3.jpg)
Introduction: Least-squares Migration
• Seismic migration: Given: Observed data
modelling operator
Goal: find a reflectivity model to explain by solving
the equation
Direct solution: expensive
Conventional migration:
Iterative solution:
Migration velocity
![Page 4: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/4.jpg)
0 X (km) 60 X (km) 6
30
Z (k
m)
• Problems in conventional migration image
Introduction: Motivation for LSM
migration artifacts
imbalanced amplitude
![Page 5: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/5.jpg)
• Least-squares migration has been shown to
produce high quality images, but it is considered
too expensive for practical imaging.
• Solution: combine multisource technique and
least-squares migration (MLSM).
Problem of LSM
![Page 6: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/6.jpg)
Motivation for Multisource
Multisource LSMTo: Increase efficiency Remove artifacts Suppress crosstalk
• Problem: LSM is too slow
• Solution: multisource phase-encoding techniqueMany (i.e. 20) times slower than standard migration
Multisource Migration Image
Multisource Crosstalk
![Page 7: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/7.jpg)
Overview• Chapter 2 : Multisource least-squares reverse time
migration is implemented with random time-shift and
source-polarity encoding functions.
• Chapter 3: Multisource LSRTM is implemented with
frequency-selection encoding for marine data.
• Chapter 4: An interferometric method is proposed to
extract diffractions from seismic data and enhance its
signal-to-noise ratio.
![Page 8: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/8.jpg)
Outline• Introduction and Overview
• Chapter 2: Multisource least-squares reverse time
migration
• Chapter 3: Frequency-selection encoding LSRTM
• Chapter 4: Super-virtual inteferometric diffractions
• Summary
![Page 9: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/9.jpg)
Random Time Shift𝑳𝟏𝒎=𝒅𝟏
O(1/S) cost!
Encoding Matrix
Supergather
Random source time shifts
𝑳𝟐𝒎=𝒅𝟐
𝒅=𝑵𝟏𝒅𝟏+𝑵𝟐𝒅𝟐
Encoded supergather modeler
𝑳𝒎=[𝑵 ¿¿𝟏𝑳𝟏+𝑵𝟐𝑳𝟐]𝒎¿
![Page 10: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/10.jpg)
Random Time Shift𝑳𝟏𝒎=𝒅𝟏
Encoding Matrix
Supergather
𝑳𝟐𝒎=𝒅𝟐
𝒅=𝑵𝟏𝒅𝟏+𝑵𝟐𝒅𝟐
Encoded supergather modeler
𝑳𝒎=[𝑵 ¿¿𝟏𝑳𝟏+𝑵𝟐𝑳𝟐]𝒎¿
× (-1) × (+1)
![Page 11: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/11.jpg)
Conventional Least-squares
Find: an s.t. min
Given: &
Direct solution:
Iterative solution:
Note: subscripts agree
If is too big
In general, hugedimension matrix
![Page 12: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/12.jpg)
Problem: Each prediction is a FD solve
Solution: Multisource technique
Conventional Least-squares
![Page 13: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/13.jpg)
Multisource Least-squares
Find: an s.t. min
Given: &
Direct solution:
In general, smalldimension matrix
If is too big
Iterative solution:
+ crosstalk
![Page 14: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/14.jpg)
0 X (km) 18
0Z
(km
)7.
5
4.5
1.5
km/s
Size: 1800 x 750Grid interval: 10 mSource number: 1800Receiver number: 1800
FD kernel: 2-4 staggered gridSource: 15 Hz
HESS VTI Model
![Page 15: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/15.jpg)
HESS VTI ModelDelta and Epsilon Models
0Z
(km
)7.
5
1.5
0
0 X (km) 18
0Z
(km
)7.
5
2.5
0
Delta
Epsilon
![Page 16: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/16.jpg)
Migration Velocity and Reflectivity
0Z
(km
)7.
5
4.5
1.5
0 X (km) 18
0Z
(km
)7.
5
0.2
-0.4
km/sMigration Velocity
Reflectivity
![Page 17: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/17.jpg)
RTM VS Multisource LSRTM
0 X (km) 18
0Z
(km
)7.
5
0 X (km) 18
0Z
(km
)7.
5
8 supergather30 iterationsSpeedup: 3.75
Standard RTM
Multisource LSRTM, 1 Supergather Multisource LSRTM, 4 Supergather Multisource LSRTM, 8 Supergather
Artifacts removed
Resolution Enhanced
![Page 18: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/18.jpg)
Signal-to-noise Ratio
SNR ∞
![Page 19: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/19.jpg)
3D SEG/EAGE Model400 Shots Evenly Distributed
Size: 676 x 676 x 201Grid interval: 20 mReceiver: 114244
Source: 5.0 hz
13.5 km
4.0 km 13.5 km
![Page 20: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/20.jpg)
Smooth Migration Velocity
20
13.5 km
4.0 km 13.5 km
Obtained by 3D boxcar smoothing
![Page 21: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/21.jpg)
Conventional RTM
13.5 km
4.0 km13.5 km
400 Shots, Migrated One by One
![Page 22: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/22.jpg)
13.5 km
4.0 km13.5 km
LSRTM400 Shots, 25 Shots/Supergather
![Page 23: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/23.jpg)
13.5 km
4.0 km13.5 km
Conventional RTM100 Shots
![Page 24: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/24.jpg)
13.5 km
4.0 km13.5 km
LSRTM100 Shots, 10 Shots/Supergather
![Page 25: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/25.jpg)
Chapter 2: Conclusions• MLSM can produce high quality images efficiently.
LSM produces high quality image.
Multisource technique increases computational
efficiency.
SNR analysis suggests that not too many iterations
are needed.
![Page 26: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/26.jpg)
• Random encoding is not applicable to marine streamer data.
Fixed spread geometry (synthetic) Marine streamer geometry (observed)
6 traces 4 traces
Mismatch between acquisition geometries will dominate the misfit.
Chapter 2: Limitations
![Page 27: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/27.jpg)
Outline• Introduction and Overview
• Chapter 2: Multisource least-squares reverse time
migration
• Chapter 3: Frequency-selection encoding LSRTM
• Chapter 4: Super-virtual inteferometric diffractions
• Summary
![Page 28: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/28.jpg)
28
observeddata
simulateddata
misfit = erroneous
misfit
Problem with Marine Data
![Page 29: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/29.jpg)
29
Solution• Every source is encoded with a unique
signature.
observed simulated
• Every receiver acknowledge the contribution from the ‘correct’ sources.
![Page 30: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/30.jpg)
4 shots/group
R(w)
Group 1
Nw frequency bands of source spectrum:
Frequency Selection
2 km
wAccommodate up to Nw shots
![Page 31: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/31.jpg)
Single Frequency Modeling
(𝜵𝟐+𝝎𝟐
𝒗𝟐 )~𝑷=−𝐖 (𝝎 )𝛅(𝒙 −𝒔)
Helmholtz Equation
(𝜵𝟐− 𝟏𝒗𝟐
𝝏𝟐𝝏𝟐 𝒕 )𝐏=−𝐑𝐞 {𝐖 (𝝎 )𝐞𝐱𝐩 (−𝒊𝝎𝒕 )}𝛅(𝒙−𝒔)
Acoustic Wave Equation
• Advantages: Lower complexity in 3D case. Applicable with multisource technique.
Harmonic wave source
![Page 32: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/32.jpg)
Single Frequency Modeling
(𝜵𝟐− 𝟏𝒗𝟐
𝝏𝟐𝝏𝟐 𝒕 )𝐏=−𝐑𝐞 {𝐖 (𝝎 )𝐞𝐱𝐩 (−𝒊𝝎𝒕 )}𝛅(𝒙−𝒔)
Am
plitu
de
T T
![Page 33: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/33.jpg)
Single Frequency ModelingA
mpl
itude
0 Freqency (Hz) 50
Am
plitu
de
20 Freqency (Hz) 30
![Page 34: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/34.jpg)
Marmousi2
0 X (km) 8
0Z
(km
)3.
5
4.5
1.5
km/s
• Model size: 8 x 3.5 km• Shots: 301
• Cable: 2km
• Receivers: 201
• Freq.: 400 (0~50 hz)
![Page 35: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/35.jpg)
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: 2.4
![Page 36: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/36.jpg)
Frequency-selection LSRTM of 2D Marine Data
0 X (km) 18.7
0Z
(km
)2.
5
2.1
1.5
km/s
• Model size: 18.7 x 2.5 km • Freq: 625 (0-62.5 Hz) • Shots: 496 • Cable: 6km• Receivers: 480
![Page 37: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/37.jpg)
Conventional RTM
Frequency-selection LSRTM
Z (k
m)
2.5
0Z
(km
)2.
50
0 X (km) 18.7
![Page 38: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/38.jpg)
Freq. Select LSRTM
Conventional RTM Conventional RTM
Freq. Select LSRTM
Zoom Views
![Page 39: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/39.jpg)
Chapter 3: Conclusions• MLSM can produce high quality images efficiently.
LSM produces high quality image.
Frequency-selection encoding applicable to marine
data.
• Limitation:
High frequency noises are present.
![Page 40: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/40.jpg)
Outline• Introduction and Overview
• Chapter 2: Multisource least-squares reverse time
migration
• Chapter 3: Frequency-selection encoding LSRTM
• Chapter 4: Super-virtual inteferometric diffractions
• Summary
![Page 41: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/41.jpg)
Chapter 4: Super-virtual inteferometric diffractions
• Diffracted energy contains valuable
information about the subsurface structure.• Goal: extract diffractions from seismic data
and enhance its SNR.
![Page 42: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/42.jpg)
Rotate
Guide Stars
![Page 43: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/43.jpg)
Step 1: Virtual Diffraction Moveout + Stacking
y zw3
dt
w2 w1 y z
y’
dt
dt
dt
w
y z
y’
=
Super-virtual stacking theory
![Page 44: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/44.jpg)
Step 2: Redatum virtual refraction to known surface position
y z
y’
y zx y zx
=*
y z x x
=
y z
i.e.y’
Super-virtual stacking theory
![Page 45: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/45.jpg)
Step 3: Repeat Steps 1&2 for a Different Master Trace
y z
y’
y zx y zx
=*
y z x x
=
y z
i.e.y’
Super-virtual stacking theory
![Page 46: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/46.jpg)
Stacking Over Master Trace Location
x zDesired shot/
receiver combination
Common raypaths
Super-virtual stacking theory
![Page 47: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/47.jpg)
Super-virtual Diffraction Algorithm
=w z
=
+
*
1. Crosscorrelate and stack to generate virtual diffractions
2. Convolve to generate super-virtual diffractions
3. Stack super-virtual diffractions to increase SNR
w
w z w z
w z
Virtual srcexcited at -tzz’ z’
w z
w z w z w z
+
![Page 48: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/48.jpg)
Synthetic Results: Fault Model
0 X (km) 6
0Z (k
m)
3
3.4
1.8
km/s
![Page 49: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/49.jpg)
Synthetic Shot Gather: Fault Model
0 Offset (km)
6
0tim
e (s
)3
Diffraction
![Page 50: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/50.jpg)
Synthetic Shot Gather: Fault Model0.
5tim
e (s
)1.
5Raw Data
0 Offset (km) 6
0.5
time
(s)
1.5
0 Offset (km) 6
Our Method
0.5
time
(s)
1.5
Median Filter
![Page 51: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/51.jpg)
Estimation of Statics
0 Offset (km) 6
0.5
time
(s)
1.0
Picked Traveltimes
Predicted Traveltimes
Estimate statics
![Page 52: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/52.jpg)
Experimental Cross-well Data
0 Depth (m) 300
0.3
time
(s)
1.0
180 Depth (m) 280
0.6
time
(s)
0.9
Picked Moveout0.
6tim
e (s
)0.
9
180 Depth (m) 280
![Page 53: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/53.jpg)
Experimental Cross-well Data
180 Depth (m) 280
0.6
time
(s)
0.9
180 Depth (m) 280
0.6
time
(s)
0.9
Median Filter
Time Windowed
180 Depth (m)
0.6
time
(s)
0.9
280
Super-virtual Diffractions
![Page 54: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/54.jpg)
Experimental Cross-well Data
0 Depth (m) 300
0.3
time
(s)
1.0
180 Depth (m) 280
0.6
time
(s)
0.9
Super-virtual Diffraction0.
6tim
e (s
)0.
9
Median Filtered
180 Depth (m) 280
![Page 55: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/55.jpg)
• Super-virtual diffraction algorithm can greatly improve
the SNR of diffracted waves..
Limitation• Dependence on median filtering when there are other coherent
events.• Wavelet is distorted (solution: deconvolution or match filter).
Chapter 4: Conclusions
![Page 56: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/56.jpg)
Outline• Introduction and Overview
• Chapter 2: Multisource least-squares reverse time
migration
• Chapter 3: Frequency-selection encoding LSRTM
• Chapter 4: Super-virtual inteferometric diffractions
• Summary
![Page 57: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/57.jpg)
Chapter 2: Multisource LSRTM• Multisource LSRTM is implemented with random encoding
functions.
LSM produces high quality image. Multisource technique increases computational
efficiency.Multisource LSRTM, 8 Supergather
![Page 58: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/58.jpg)
Chapter 2: Frequency-selection LSRTM
• Multisource LSRTM is implemented with frequency-
selection encoding functions.
Applicable to marine data.
Frequency-selection LSRTM
![Page 59: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/59.jpg)
• Super-virtual diffraction algorithm can extract diffraction
waves and greatly improve its SNR.
Chapter 4: Super-virtual inteferometric diffractions
Before Before After
![Page 60: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/60.jpg)
Acknowledgements
I thank the sponsors of CSIM consortium for their financial support.
I thank my advisor Prof. Gerard T. Schuster and other committee members for the supervision
over my program of study.
I thank my fellow graduate students for the collaborations and help over last 4 years.
![Page 61: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/61.jpg)
WorkflowRaw data
Pick a master trace
Cross-correlate all the traces with the master trace
Repeat for all the shots and stack the result to give virtual diffractions
Convolve the virtual diffractions with the master trace to restore original traveltime
Stack to generate Super-virtual Diffractions
![Page 62: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/62.jpg)
Diffraction Waveform Modeling
BornModeling
0 Distance (km) 3.8
0D
epth
(km
)1.
20
Dep
th (k
m)
1.2
0tim
e (s
)4.
0
0 Distance (km) 3.8
Velocity
Reflectivity
![Page 63: Multisource Least-squares Reverse Time Migration](https://reader030.vdocument.in/reader030/viewer/2022012905/56815e06550346895dcc5252/html5/thumbnails/63.jpg)
Diffraction Waveform Inversion
0 Distance (km) 3.8
0D
epth
(km
)1.
20
Dep
th (k
m)
1.2
Initial Velocity
Estimated Reflectivity
0D
epth
(km
)1.
2
Inverted Velocity
0 Distance (km) 3.8
0D
epth
(km
)1.
2
True Velocity