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Superresolution Imaging Techniques in Geophysics: Extracting High-Frequency Information

This study explores advanced techniques for extracting 200 Hz information from 50 Hz data in geophysical contexts. We discuss the significance of resolution—differentiating between diffraction and specular resolution—and the implications it has for accurate imaging. Through field tests and theoretical analysis, we delve into concepts like Evanescence Resolution and the potential for superresolution under various conditions. Our findings highlight the challenge of separating scattered fields and the importance of signal-to-noise ratios, thereby informing future applications in subsurface imaging and anomaly detection.

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Superresolution Imaging Techniques in Geophysics: Extracting High-Frequency Information

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  1. Extracting 200 Hz Information from 50 Hz Data G. Schuster, S. Hanafy, and Y. Huang, KAUST Sinc function Spiking function Rayleigh Resolution Profile Superresolution Profile

  2. Outline • Motivation: Why Resolution Matters • Diffraction vs Specular Resolution: Example • Evanescence Resolution • Field Test • Conclusions

  3. Resolution Dx~l/2 L Z Depth Δx Rayleigh Resolution: Δx KAUST yacht Abbe Resolution: Super Resolution?: Dx = Dx = Dx << lz l l 2 2 4L

  4. Geophysical Resolution 0 km 3 km ? (Jianhua Yu) 0 km 7 km 0 km 7 km

  5. Transmission+ReflectionWavepaths (Woodward, 1992) FWI rabbit ears d RTM smile Z RTM Resolution: Dx=Rayleigh, Dz=l/4 FWI Resolution: ? X

  6. Transmission+ReflectionWavepaths (Woodward, 1992) FWI rabbit ears d Z FWI Resolution: X FWI Resolution: Dx= 2ld (Williamson, 1991)

  7. Transmission+ReflectionWavepaths (Woodward, 1992) Diff. FWI Resolution: Dxdiff= ld FWI rabbit ears d 3 FWI Resolution: Benefit: Diffractions transform SSPXwellor VSP Data Liability: SNRdiff << SNRspec X FWI Resolution: Dx= 2ld (Williamson, 1991) Dx =2 Dxdiff

  8. Summary Diff. FWI Resolution: Dxdiff= ldvsSpecular FWI Resolution: Dx = Benefit: Diffractions transform SSPXwellor VSP Data Liability: SNRdiff << SNRspec FWI rabbit ears 3

  9. Outline • Motivation: Why Resolution Matters • Diffraction vs Specular Resolution: Example • Evanescence Resolution • Field Test • Conclusions

  10. Diffraction Waveform Modeling 0 time (s) Born Modeling 4.0 Distance (km) 0 3.8 Scattered CSG Velocity 0 Depth (km) 1.2 Reflectivity 0 Depth (km) 1.2 0 Distance (km) 3.8

  11. Diffraction Waveform Inversion True Velocity 0 Depth (km) 1.2 0 Distance (km) 3.8 Initial Velocity Inverted Velocity 0 0 Depth (km) Depth (km) 1.2 1.2 Estimated Reflectivity 0 Depth (km) 1.2 0 Distance (km) 3.8

  12. Outline • Motivation: Why Resolution Matters • Diffraction vs Specular Resolution: Example • Evanescence Resolution • Field Test • Conclusions

  13. Far-field Propagation  l-limited Resolution eiwtxg G(g|x)= r Mig(z) l Time

  14. Near-field Propagation  l/20 Resolution eiwtxg G(g|x)= r r Evanescent energy Mig(z) Mig(z) Note: Time delay unable to distinguish 2 scatterers, but near-field amplitude changes can: Dx=l/20 l Time

  15. Near-field Propagation  l/20 Resolution eiwtxg G(g|x)= r r Evanescent energy Mig(z) Note: Time delay unable to distinguish 2 scatterers, but near-field amplitude changes can: Dx=l/20 If source is in farfield of scatterers & geophones in nearfield, superresolution possible l Time

  16. Summary 1. Near-field Propagation  l/20 Resolution Mig(z) If source is in farfield of scatterers & geophones in nearfield, superresolution possible reciprocity If source is in nearfield of scatterers & geophones in farfield, superresolution possible l Time

  17. Summary 1. Near-field Propagation  l/20 Resolution CRG Mig(z) If source is in farfield of scatterers & geophones in nearfield, superresolution possible reciprocity If source is in nearfield of scatterers & geophones in farfield, superresolution possible l Time

  18. Outline • Motivation: Why Resolution Matters • Diffraction vs Specular Resolution: Example • Evanescence Resolution • Field Test • Conclusions

  19. Dx ~ Dx ~ 0.1 0.01 0.7 Dx ~  Near-Field Scatterer Images     

  20. D z ~ 0.1 25 Near-Field Scatterers Image  

  21. 25 Near-Field Scatterers Image  Migration image at superresolution

  22. 25 Near-Field Scatterers Image

  23. 25 Near-Field Scatterers Image

  24. Elastic Tunnel Test: 6 Near-Field Scatterers S wave P wave Vp=1.5 km/s Vs=0.75 km/s 40 m Vp=3.0 km/s Vs=1.5 km/s 100 m

  25. Elastic Tunnel Test: 6 Near-Field Scatterers S wave P wave Vp=1.5 km/s Vs=0.75 km/s No scatterer data scattered data 40 m Vp=3.0 km/s Vs=1.5 km/s 100 m

  26. Outline • Motivation: Why Resolution Matters • Diffraction vs Specular Resolution: Example • Evanescence Resolution • Field Test • Conclusions

  27. Experimental Setup (Not to Scale) Superresolution Test Goal: Test superresolution imaging by seismic experiment Experiment: Data with and without a scatterer l=1.6 m

  28. Experimental Setup (Not to Scale) Superresolution Test Goal: Test superresolution imaging by seismic experiment Experiment: Data with and without a scatterer l=1.6 m 0.2 m 0.6 m

  29. TRM Profiles

  30. l/4 Resolution (110 Hz) 0.5 m w/o scatterer with scatterer l/8 Resolution (55 Hz) Theory l with scatterer 0.5 m 220 Hz information from 55 Hz data

  31. Summary Diff. FWI Resolution: Dxdiff= ldvsSpecular FWI Resolution: Dx = • Workflow • 1. Collect Shot gathers G(g|s ), separate scattered field • 2. m(s’) = S G(g,t|s’)* G(g,t|s ) • 3. TRM profiles • Synthetic Results Dx~l/10 • Limitations • Either src or rec in nearfield of subwavelength scatterer • Scattered field separated from specular fields is Big Challenge

  32. Possible Applications SSP: Detect local anomalies, faults, and scatterer points around surface VSP: Find local anomalies, faults, and scatterer points around boreholes in VSP data Farfield? Ground Borehole

  33. Earthquakes along a Fault Detect Fault Roughness Subduction zone TRM Profile

  34. Earthquakes US Array Detect Near Surface Subduction zone TRM Profile

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