Demonstration of Super-Resolution and Super-Stacking Properties of Time Reversal Mirrors in Locating Seismic Sources Weiping Cao, Gerard T. Schuster, Ge Zhan Chaiwoot Boonyasiriwat, and Sherif M. Hanafy

Outline ■ Motivation ■ Theory ■ Detecting Trapped Miners using Time Reversal Mirrors (TRM) ■ Validation of Super-Resolution and Super-Stacking ■ Conclusions

Outline ■ Motivation ■ Theory ■ Detecting Trapped Miners using Time Reversal Mirrors (TRM) ■ Validation of Super-Resolution and Super-Stacking ■ Conclusions

Why Work on Time-? Hydro-Frac Monitoring – Time reversal mirrors (TRM) approach has super stack property – No velocity model is required – Small aperture width gives good results If we have the exact velocity model – Reverse time migration (RTM) has both super- stack and super-resolution properties. Increasing the RTM resolution by 3-7 times deserves the effort of finding the exact velocity model.

Why Work on Time Reversal Mirrors (TRM)? ■ Advantages of TRM Super-resolution and super-stack; No velocity model needed; Small receiving aperture can provide good results. ■ TRM = Poststack Reverse Time Migration (RTM) with the exact velocity model. Properties of TRM can be achieved for RTM. ■ Locating hydro-fracs with TRM

Outline ■ Motivation ■ Theory ■ Detecting Trapped Miners using Time Reversal Mirrors (TRM) ■ Validation of Super-Resolution and Super-Stacking ■ Conclusions

Time Time Multiples Primary Primary Multiples TRM Imaging Forward ModelingTRM Imaging TRM = Poststack Reverse Time Migration

Backpropagation = Crosscorrelation TRM: Time Multiples Primary Backpropagation Crosscorrelation TimeMultiplesPrimary

Time Time Multiples Primary Primary Primary Migration vs TRM Migration Super- Stacking Multiples vs. Super-Resolution and Super-StackingSuper-Resolution Rayleigh.

Trial Time Shift Problem: unknown source excitation time Solution: trial time shift

Trial Time Shift Time Shift Amplitude Zero lag

Outline ■ Motivation ■ Theory ■ Locating Trapped Miners by Time Reversal Mirrors (TRM) ■ Validation of Super-Resolution and Super-Stacking ■ Conclusions

Locating Trapped Miners Migrating the seismic signal from the trapped miners

Locating Trapped Miner by TRMAirOverburden Coal Mine Tunnel TRM with time shift Record Green’s function g(g, t | x, 0) Correlation with time shift Record miner’s signal d(g, t | s, 0)

Locating Trapped Miners: Sythetic Test 201 shot gathers ( Calibration g(g, t | x, 0) ) Synthetic Test: Take Shot # 101 as miner’s signal d(g, t|s, 0), apply TRM Z (km) X (km) Air Overburden Coal Mine Tunnel

TRM with Correct Source Excitataion Times 02.0 X (km) Air Overburden Coal Mine Tunnel

Unknown shooting time: Trial time shift TRM Image with Trial Time Shift

Locating Trapped Miners by TRM Strong background noise Z (km) Air Overburden Coal Mine Tunnel Strong white noise Noise-free data d(g|s) Data d(g|s) with strong white noise: S/N =1/996

Strong Background Noise Strong white noise Noise-free data d( g, t | s, 0) Data d(g, t|s, 0) with strong white noise: S/N =1/996 Z (km) X (km) Air Overburden Coal Mine Tunnel

TRM Image with Trial Time Shift: S / N = 1 / 996 Strong Background Noise

02.0 X (km) Section with Correct Source Shooting Time: S/N = 1/996 Strong Background Noise

Outline ■ Motivation ■ Theory ■ Locating Trapped Miners by Time Reversal Mirrors (TRM) Validation of Super-Resolution and Super-Stacking ■ Conclusions

Super-Resolution and Super-Stacking Super-Resolution: time Multiples Primary Synthetic tests on resolution Scattered vs. direct waves Super-Stacking: Synthetic tests validate Rayleigh resolution limit

Rayleigh Resolution Limit Super-Resolution z0z0 L

Super-Resolution: Synthetic Tests Velocity Model and Source-Receiver Geometry Z (km) X (km) V back. =2.2 km/s V sc. =4.0 km/s

TRM Imaging by Backpropagation 1 3 Time (s) 13X (km) 1 3 Time (s) 13X (km) Original GatherScattered Gather Z (km) X (km) Z (km) X (km)

Effect of Receiving Aperture 1 3 Time (s) 13X (km) 1 3 Time (s) 13X (km) Original GatherScattered Gather Z (km) X (km) Z (km) X (km)

Quantitative Resolution Comparison Lateral resolutions different wavs, apertures Scattered gather full aperture: 67 m Scattered gather half aperture: 67 m Original gather full aperture: 382 m Rayleigh, full aperture: 557 m Rayleigh, half aperture: 1147 m Original gather half aperture: 652 m

Super-Stacking ValidateEnhancement of the Signal : the number of traces : recording time of a trace : dominant period Plot the vs.curve, enhancement should give linear trend.

X (km) Z (km) X (km) Time (s) 028 Validation of Super-Stacking SIGSBEE 2B Salt ModelSynthetic RVSP Shot Gather Obtain TRM Images and compute S/N in the images; Plot vs. curve. Validation:

Obtain TRM Images Validation of Super-Stacking S N Compute S/N in the images Add random noise to a RVSP gather, take it as the data Migrate the noisy RVSP gather with TRM.

Super-Stacing: Synthetic Tests Numerical result Theoretical prediction The vs. curve

Outline ■ Motivation ■ Theory ■ Locating Trapped Miners by Time Reversal Mirrors (TRM) ■ Validation of Super-Resolution and Super-Stacking Conclusions

TRM can reliably image the trapped miner’s location. Super-resolution of TRM beats the Rayleigh resolution limit. Super-stacking enhancement of validated.

Implications TRM = Poststack RTM with the exact velocity model Locating hydro-fracs with TRM Find the exact velocity model and achieve super- resolution and super-stacking property for RTM. Small receiving aperture still gives good results.

We thank the 2007 UTAM sponsors for the support. Acknowledgments