Super-virtual Interferometric Separation and
Enhancement of Back-scattered Surface Waves
Bowen Guo*, Sherif Hanafy, Gerard Schuster
King Abdullah University of Science and Technology
Outline
 Motivation
 Theory
 Numerical results
 Conclusion and future work
fault
Motivation
 Back-scattered surface waves (BSWs)
can be migrated to detect nearsurface structures
 Problem: weak amplitude,
masked by incident surface
waves, so that difficult to be
separated
 Solution: super-virtual
interferometry (Bharadwaj et
al., 2011; Dai et al., 2011)
to separate and enhance BSWs
Shot
Virtual
BSWsWaves
Shot Gather
ofGather
Surface
0.0
0.0
0.5
0.0
0.0
1.6 km/s
0.3
0.3
0
500.0
X (m)
X 2.2
(m)km/s
150
1.6 km/s
(m)(Yu et al., 2014) 300
300
XX (m)
Outline
 Motivation
 Theory
 Numerical results
 Conclusion and future work
Theory: super-virtual interferometry by
cross-correlation
 Case 1: 𝑔 ∈ 𝑙1
𝑔
𝑠′
𝑠
𝑙1
𝑙2
fault
𝑙3
𝐺(𝑔|𝑠)𝑏𝑎𝑐𝑘
𝑔∊𝑙1
𝐺(𝑔|𝑠 ′ )𝑖𝑛𝑐
𝒃𝒂𝒄𝒌
𝐺(𝑠
𝑮(𝒔′ |𝑠)
|𝒔)𝑏𝑎𝑐𝑘
𝐼𝑚[𝐺 𝑠 ′ 𝑠
𝑏𝑎𝑐𝑘 ]
𝐺(𝑔|𝑠)𝑏𝑎𝑐𝑘 ⊗ 𝐺(𝑔|𝑠 ′ )𝑖𝑛𝑐
≈ 2k
𝑔∈𝑙1
Theory: super-virtual interferometry by
cross-correlation
 Case 2: 𝑔 ∈ 𝑙2
𝑠
𝑙1
𝑔
𝑙2
𝑠′
fault
𝑙3
𝐺(𝑔|𝑠)𝑏𝑎𝑐𝑘
𝑔∊𝑙2
𝐺(𝑔|𝑠 ′ )𝑖𝑛𝑐
𝑏𝑎𝑐𝑘
𝑮(𝒔
𝐺(𝑠′ |𝒔)
|𝑠)𝒃𝒂𝒄𝒌
𝐼𝑚[𝐺 𝑠 ′ 𝑠
𝑏𝑎𝑐𝑘 ]
𝐺(𝑔|𝑠)𝑏𝑎𝑐𝑘 ⊗ 𝐺(𝑔|𝑠 ′ )𝑖𝑛𝑐
≈ 2k
𝑔∈𝑙1
Theory: artifacts from the cross-correlation
 Artifacts in Cases 1 and 2
𝑠
𝑔 fault
𝑠′
𝐺(𝑔|𝑠)𝑏𝑎𝑐𝑘
𝑔∊𝑙2
𝐺(𝑔|𝑠 ′ )𝑖𝑛𝑐
Artifacts
Artifacts can be muted because they arrive
earlier than incident surface waves
Theory: super-virtual interferometry by
convolution
 Case 3: 𝑔 ∈ 𝑙3
𝑠′
𝑠
𝑙1
𝑔
fault
𝑙3
𝑙2
𝐺(𝑔|𝑠)𝑏𝑎𝑐𝑘
*
𝑔∊𝑙3
* ′)𝑖𝑛𝑐
𝐺(𝑔|𝑠
𝒃𝒂𝒄𝒌
𝐺(𝑠 ′ |𝒔)
|𝑠)𝑏𝑎𝑐𝑘
𝑮(𝒔
Work Flow
Step 1: Mute body waves.
No need to be Step 2: Retain incident surface waves
and mute other events.
accurate
Step 3: Retain BSWs and mute other
events.
𝐺(𝑔|𝑠 ′ )𝑖𝑛𝑐
𝐺(𝑔|𝑠)𝑏𝑎𝑐𝑘
Step 4: Use SVI to calculate virtual BSWs 𝑮(𝒔′ |𝒔)𝒃𝒂𝒄𝒌
Outline
 Motivation
 Theory
 Numerical results
 Conclusion and future work
Synthetic Example
0
S-wave Velocity
m/s
800
CSGNoise
CSG with
0
Scattered Surface Wave with Noise
0
𝑮(𝒈|𝒔)𝒃𝒂𝒄𝒌
𝑮(𝒈|𝒔′ )𝒊𝒏𝒄
500
60
0
500
X (m)
0
300 1.2
0
X (m)
500
Virtual BSWs by
Convolution
0
Virtual BSWs by
Correlation
1.2
0
X (m)
500
Trace Comparison
0.7
Artifacts
Noised
BSWs
BSWs
True Data
BSWs by
Correlation
1.2
0
X (m)
500
1.2
0
X (m) 500
1.2
0 Normalized 1
Amplitude
BSWs by
Convolution
Field Data Example
0.0
Common Shot Gather (CSG)
Gulf of Aqaba Data in Saudi
Arabia
 120 shots and 120
receivers
t(s)
 Source/receiver sampling
interval 2.4 m
0.3
0
X (m)
300
Field
Data
Example
CSG 30
Mute Body Waves
0.0
0.0
𝑮(𝒈|𝒔)𝒃𝒂𝒄𝒌
0.3
0
X (m)
300
Incident Surface Waves
0.0
0.3
0
0.0
X (m)
300
X (m)
300
Virtual BSWs
𝑮(𝒈|𝒔′ )𝒊𝒏𝒄
0.3
0
X (m)
300
0.3
0
Field Data Example
0.0
0.3
0
0.0
0.3
0
CSG 38
X (m)
300
CSG 40
X (m)
Virtual BSWs 38
0.0
0.3
0
0.0
300
0.3
0
X (m)
300
Virtual BSWs 40
X (m)
300
Field Data Example
Virtual BSWs 38
0.0
Velocity Tomogram
0
40
0
150 (m)
400
0.3
0
0.0
X (m)
Virtual BSWs 40
Resistivity Tomogram
40
0
300
300 (m)
150 (m)
1
X (m)
2800
300
0
0.3
0
Velocity (m/s)
300 (m)
Resistivity (Ohm.m)
500
Outline
 Motivation
 Theory
 Numerical results
 Conclusion and future work
Conclusions
 Back-scattered surface waves can be enhanced and separated by SVI
 No need for velocity, robust
Future Work
 2D
3D
Acknowledgement
We would like to thank King Abdullah University
of Science and Technology for their support
Thank you for your attention