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

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

Resolution  x~ /2 L Z ΔxΔx Depth Rayleigh Resolution: Abbe Resolution: Super Resolution?:  x = z 4L 2  x << 2 ΔxΔx KAUST yacht

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

Transmission+Reflection Wavepaths (Woodward, 1992)  x RTM Resolution:  x= Rayleigh,  z= / 4 RTM smile  FWI Resolution:  FWI rabbit ears Z X d

Transmission+Reflection Wavepaths (Woodward, 1992) FWI Resolution: FWI rabbit ears d Z X

3 Transmission+Reflection Wavepaths (Woodward, 1992) FWI Resolution: FWI rabbit ears X x x x x  x diff  x diff d Benefit: Diffractions transform SSP  Xwell or VSP Data Liability: SNR diff << SNR spec

3 Summary FWI rabbit ears Benefit: Diffractions transform SSP  Xwell or VSP Data Liability: SNR diff << SNR spec

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

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

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

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

Mig(z) Far-field Propagation  -limited Resolution e i  xg r G(g|x)= Time

Mig(z) Near-field Propagation  /20 Resolution e i  xg r G(g|x)= Time Note: Time delay unable to distinguish 2 scatterers, but near-field amplitude changes can:  x=  20 Mig(z) r Evanescent energy

Near-field Propagation  /20 Resolution e i  xg r G(g|x)= Time Note: Time delay unable to distinguish 2 scatterers, but near-field amplitude changes can:  x=  20 Mig(z) r Evanescent energy If source is in farfield of scatterers & geophones in nearfield, superresolution possible

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

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

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

Near-Field Scatterer Images  x ~  x ~  x ~

 z ~ Near-Field Scatterers Image

Migration image at superresolution

25 Near-Field Scatterers Image

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

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

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

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

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

TRM Profiles

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

Summary Workflow 1. Collect Shot gathers G(g|s ), separate scattered field 2. m(s’) =  G(g,t|s’)* G(g,t|s ) 3. TRM profiles Synthetic Results  x~ /10 Limitations Either src or rec in nearfield of subwavelength scatterer Scattered field separated from specular fields is Big Challenge

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

Subduction zone TRM Profile Earthquakes along a Fault Detect Fault Roughness

Subduction zone Earthquakes US Array Detect Near Surface TRM Profile