3D Super-virtual Refraction Interferometry Kai Lu King Abdullah University of Science and Technology

Outline Introduction and Motivation Theory: conventional SVI with stationary phase integration Synthetic data example Field data example Conclusion Acknowledgement

Outline Introduction and Motivation Theory: conventional SVI with stationary phase integration Synthetic data example Field data example Conclusion Acknowledgement

B C A3 dt A2A1 dt 1.Stacked Refractions: + Stacking dt B C A Common Pair Gather (Dong et al., 2006) Benefit: SNR = N d AB AC ~ d BC A virtual ~ 2D Super-virtual Interferometry

2. Dedatum Virtual Refraction to Known Surface Point B C A A = * = * + d AB AC ~ d BC A src virtual real super-virtual d AB BC ~ d AC B rec supervirtual * virtual Raw traceVirtual trace (Calvert+Bakulin, 2004) Super-virtual trace B rec A src Datuming Dedatuming 2D Super-virtual Interferometry

Theory and workflow: Are first arrivals at far-offsets pickable ? Window around first arrivals and mute near offset Correlate and stack to generate virtual refractions Input Data Output Data Convolve and stack to generate Super-virtual refractions N Ʃ Ʃ Raw Data Super-virtual refraction Data Windowed Data Iterative SVI

Difficulties from 2D to 3D Difficulty to find locations of stationary sources and receivers S A1A1 Unknown Path Few sources and receiver available A2A2 Limited number of sources and receivers

Solution 2D: all traces are stationary 3D: stationary phase integration A B Virtual Trace S1S1 S2S2 S3S3 SnSn S*S*

Outline Introduction and Motivation Theory: conventional SVI with stationary phase integration Synthetic data example Field data example Conclusion Acknowledgement

Stationary Phase Integration Stationary phase analysis (Bleistein, 1984) applied to the line integral: Applied to SVI: Virtual trace AB A B S1S1 S2S2 S3S3 SnSn S*S*

Cross-correlation Type A B CRG A CRG B Cross-correlation Results Ʃ Correlation of S*A and S*B Virtual trace AB Source Time (s) 0 4 Source Source Amplitude 1 S1S1 S1S1 SnSn SnSn S*

Virtual Trace Stacking over Source Lines A B S1S1 S2S2 S3S3 SnSn     lineN line1 line2 2D: Stacking over sources: 3D: Stacking over source lines: C A1 B C B C B = A2 A3

Super Virtual Trace – Convolution Type A S B1B1 B2B2 B3B3 BnBn     lineN line1 line2 2D: Stacking over receivers: 3D: Stacking over receiver lines: C A B1 C A B C * = B2 B3

Workflow of 3D SVI Window around the targeted refraction Input Band-pass filtered Data Output Data Iterative SVI

Outline Introduction and Motivation Theory: conventional SVI with stationary phase integration Synthetic data example Field data example Conclusion Acknowledgement

Synthetic Test – Undulating Layer Model V 1 =1500m/s V 2 =3000m/s 151 receivers, 76 sources on every line 11 survey lines

Line1 Line11 Synthetic Result Original data Data with random noise Super-virtual refractionIterative Super-virtual Refraction Trace Time (s) Trace Time (s) Trace Time (s) Trace Time (s)

Outline Motivation: from 2D to 3D Theory: conventional SVI with stationary phase integration Synthetic data example Field data example Conclusion Acknowledgement

x [km] y [km] D OBS Survey Geometry m 50 m 5 m Sihil 3D OBS data – 234 OBS stations – 129 source-lines Irregular geometry. Map view

Field Results 1 Raw data Band-pass filtered data Super-virtual result Trace Time (s) Trace Time (s) Trace Time (s)

Zoom View Comparison Zoom view of band-pass filtered data Zoom view of super-virtual data Trace Time (s) Trace Time (s) Zoom view of super-virtual data Unpickable

Field Results 2 Raw data Super-virtual result Iterative Super-virtual result Trace Time (s) Trace Time (s) Trace Time (s)

Zoom View Comparison Raw data Super-virtual result Iterative Super-virtual result Trace Time (s) Trace Time (s) Trace Time (s) Unpickable

Outline Introduction and Motivation Theory: conventional SVI with stationary phase integration Synthetic data example Field data example Conclusion Acknowledgement

Conclusion We apply stationary phase integration method to achieve super-virtual refraction with enhanced SNR in 3D cases. Iterative method is an option to further improve SNR when super-virtual refraction is still noisy. Artifacts can be produced because of the limited aperture for integration as well as a coarse spacing of sources or receivers.

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