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

€

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)