Time-reversal acoustics, virtual source imaging, and seismic interferometry
Haijiang Zhang
University of Science and Technology of China
Time-reversal acoustics
Fink, 1997
Time-reversal and super resolution
More heterogeneous and scattered the medium between the source and the TRM, the more focused the time-reversed signal.
Time-reversed seismic location
– No picking required
– Automatic (real-time) location
– Using full waveforms
Virtual source method
Bakulin and Calvert, 2006
Sources Sk on the surface
Receivers in the borehole
The goal is to construct seismic record from virtual source to receivers.
Synthetic velocity models
Virtual source gather (at 900 m) Real source gather (at 900 m)
Constructing virtual source (VS) data
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Ska (t) = wk (t) ˜ S ka (t)
Bakulin and Calvert, 2006
Problem: Overburden+statics defocus VSP migration
Redatum sources below overburdenLocal VSP migration
Solution: VSP -> SWP Transform (Calvert, Bakulin)
Applications
VSPVSP SWP
Shuster, SEG 09
VSP Geometry
Offset (m)0 1000
Depth (m)
1500
3500 Time (s)
0
3
Reflection wavefield
(He , 2006)
VSP Geometry
Offset (m)0 1000
Depth (m)
1500
3500
(He , 2006)
Time (s)
0
3
Reflection wavefield
superresolution
China
VSP Salt Flank Imaging (Hornby & Yu, 2006)
? 98 geophones
120 shots
Overburden
Poor image of flank by standard migration
Interferometric Migration Result
Seismic Interferometry
• Interferometry is a family of techniques in which waves, are superimposed in order to extract information about the waves (from wikipedia).
• Seismic Interferometry involves cross correlating and stacking diffusive waves to extract Green’s functions.
Cross-correlation and stacking
Gsa(t): Green’s function from source s to a.e(t): Source time function.
Cross-correlation
Stacking: source averaging
Homogeneous medium
Circular sources
a) τ= -3T0
b) τ= -T0
c) Τ=10T0
Larose et al., 2005
Homogeneous medium
800 sources (partially covered)
a) τ= -3T0
b) τ= -T0
c) Τ=10T0
Heterogeous medium
800 sources (partially covered)
a) first-part coda b) late coda
Time-reversal interpretation of the correlation process
Treat a as the virtual source
(Weaver and Lobkis, Ultrasonics, 40, 435-439, 2002)
20 30 40 50 60 70 80 90 100 110-4500
-4000-3500-3000-2500
-2000-1500-1000
-500
0500
100015002000
-0.5-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.91.01.1
time (microseconds)
Pulse/echo
noiseautocorrelation
(Weaver and Lobkis, Ultrasonics, 40, 435-439, 2002)