Locating Trapped Miners Using Time Reversal Mirrors

Sherif M. HanafyWeiping Cao Kim McCarter

Gerard T. Schuster

November 12, 2008

• Motivation• RTM Methodology• Field Examples• Practical Problems • Super-resolution Tests• Summary and Conclusions

Outline

• Motivation• RTM Methodology• Field Examples• Practical Problems • Super-resolution Tests• Summary and Conclusions

Outline

MotivationProblem:

Miners are lost in a mine collapse, death could happens

Proposed Solution:

Time Reversal Mirror (TRM) with super resolution and super stacking properties

• Motivation• RTM Methodology• Field Examples• Practical Problems • Super-resolution Tests• Summary and Conclusions

Outline

Step # 1: before the collapse

G1 …………………………………… Gn

Receiver Line

Ground Surface

Subsurface Mine

3 Step RTM Methodology

• Geophones are planted on the ground surface above the mine.

• Select some communication points inside the mine

• From each communication point a band-limited natural Green’s function is recorded

Step # 2: get the SOS call

Receiver Line

Ground Surface

Subsurface Mine

After a collapse occurs,

G1 G2 G3

trapped miners should go to the nearest communication point and hit the mine wall at this point

This (SOS) call will be recorded by the geophones on the ground surface

3 Step RTM Methodology

Does the recorded SOS looks like one of our previously recorded band-limited calibration Green’s functions?

G1 G2 G3 ………. Gn

Recorded SOS

NO NO Yes NO

The location of the trapped miners is the location of the calibration Green’s functions that best match the recorded SOS

We can use a pattern matching approach between the recorded SOS and the calibration Green’s function gathers

Step # 3: where are the trapped miner(s)?

3 Step RTM Methodology

Mathematically, better match means higher d & g dot product value

t g

isourcei gtxgtstgdtxm )0,|,(),|,(),(

Dot product results

Recorded SOS call

Band-limited Green’s function

Refers to the location of the communication point

3 Step RTM Methodology

Time Reversal Mirror equation

Post Stack Migration

……....... ………....... …………Subsurface

Mine

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

D ista n ce (m )

-1

-0 .5

0

0 .5

1N

orm

aliz

ed A

mp

litu

de

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

D ista n ce (m )

-1

-0 .5

0

0 .5

1N

orm

aliz

ed A

mp

litu

de

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

D ista n ce (m )

-1

-0 .5

0

0 .5

1N

orm

aliz

ed A

mp

litu

de

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

D ista n ce (m )

-1

-0 .5

0

0 .5

1N

orm

aliz

ed A

mp

litu

de

Location of trapped miners

G1 G2 G3

3 Step RTM Methodology

• Motivation• RTM Methodology• Field Examples• Practical Problems • Super-resolution Tests• Summary and Conclusions

Outline

• Number of receivers = 120 @ 1m interval

•Number of communication points = 25

• Comm. point interval;

• Points 1- 6 & 20 – 25 = 4 m

• Points 6 – 20 = 0.5 m

• Distance from receiver line to tunnel = 35 m

3 m

2 .5 m

S tea m -T u n n el P ro jectio n

S tea m -T u n n el

G ro u n d S u rfa ce1 2 0 m

R eceiver L in e

3 5 m

U of U Test

Field Examples

T u n n el a t leve l 2(3 0 m from grou n d )

T u n n el a t leve l 3(4 5 m from grou n d )

Sh

aft G ro u n d S u rface3 0 m

1 5 m

N

S h o t lo ca tio n

R ece iv e r lo ca tio n

S h aft en tran ce

• Number of receivers = 120 @ 0.5 m interval

•Number of communication points = 25 @ 0.5 & 0.75 m intervals

• Distances from receiver-line to tunnel are 30 & 45 m, respectively

Tucson, AZ Test

Generating both Green’s function and SOS call

U of U Test

Tucson, Arizona Test

Generating both Green’s function and SOS call

Sample results from U of U and Tucson Tests

Dot Product Results

X (m) X (m)

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8D istan ce (m )

-0 .4

-0 .2

0

0 .2

0 .4

0 .6

0 .8

1

Nor

mal

ized

Am

pli

tud

e

F in d T ra p p ed M in ers, S O S ca ll # 1 1 a t X = 7 .5m , T u n n el # 3

A rro w sh o w s lo ca tio n o f tra p p ed m in ersNor

mal

ized

m(x

,0)

X (m)

Nor

mal

ized

m(x

,0)

Nor

mal

ized

m(x

,0)

• Motivation• RTM Methodology• Field Examples• Practical Problems • Super-resolution Tests• Summary and Conclusions

Outline

Amplitude

Tim

e S

hift

Unknown SOS Excitation Time

We use a simple time shift test

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0

Tim

e (m

s)

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0

Tim

e (m

s)0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0

Tim

e (m

s)0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0

Tim

e (m

s)

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0

Tim

e (m

s)

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0

Tim

e (m

s)

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0

Tim

e (m

s)

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0

Tim

e (m

s)

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0

Tim

e (m

s)

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0

Tim

e (m

s)

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0T

ime

(ms)

Excitation Time

-0.2-0.1

00.1

0.2

Tim

e Shift

-0.8

-0.6

-0.4

-0.2 0

0.2

0.4

0.6

0.8 1

N o rm a lized A m p litu d e

Unknown SOS Excitation Time

Excitation Time

Location of Trapped Miner

-0.25

0.25 0

45

-1

1

X (m)Time Shift (ms)

Nor

mal

ized

A

mp

litu

de

0.0

45.0

0.0

45.0

U of U Test Tucson, AZ Test

Mine Depth = 35 m Mine Depth = 45 m

Low S/N ratio of the SOS call• We generated a random noise CSG• This random-noise CSG is added to the recorded SOS• The results are then used in our calculations

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D istan ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0

Tim

e (m

s)

S O S C a ll # 6 + R a n d o m N o iseS /N = 1 :1 7 3 8

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0

Tim

e (m

s)

S O S C a ll # 6 + R a n d o m N o iseU n iv ersity o f U ta h T est - S /N = 1 :1 7 3 8

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0

Tim

e (m

s)

S O S C a llA fter b an d -p a ss filter

+ =

Results with Random Noise

Results without adding noise Results with adding noise New S/N

U of U 1:1738

Tucson 1:2670

Nor

mal

ized

m(x

,0)

X (m)

Nor

mal

ized

m(x

,0)

X (m)

Nor

mal

ized

m(x

,0)

X (m)

Nor

mal

ized

m(x

,0)

X (m)

• Motivation• RTM Methodology• Field Examples• Practical Problems • Super-resolution Tests• Summary and Conclusions

Outline

Rayleigh Spatial Resolution

Spatial resolution is defined by Sheriff

(1991) as the ability to separate two features

that are very close together, i.e., the

minimum separation of two bodies before

their individual identities are lost.

Ground Surface2L

Z

L

Zx

2

x

Expected Spatial Resolution

U of U TestTucson Test

Tunnel # 1 Tunnel # 2

10 m 10 m 10 m

Z 35 m 30 m 45 m

L 60 m 30 m 30 m

x

L

Zx

2

Rayleigh resolution

3 m 5 m 7.5 m

Can Scatterers Beat the Resolution Limit?Recorded shot gathers (SOS & G) are divided into:

- Full aperture & direct arrivals - Full aperture & scattered arrivals

- Half aperture & direct arrivals - Half aperture & scattered arrivals

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0T

ime

(ms)

G reen 's F u n ctio nA fter b an d -p a ss filter

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0

Tim

e (m

s)

G reen 's F u n ctio nA fter b an d -p a ss filter

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0

Tim

e (m

s)

G reen 's F u n ctio nA fter b an d -p a ss filter

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0

Tim

e (m

s)

G reen 's F u n ctio nA fter b an d -p a ss filter

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0

D ista n ce (m )

0 .5

0 .4

0 .3

0 .2

0 .1

0

Tim

e (m

s)

G reen 's F u n ctio nA fter b an d -p a ss filter

Super-Resolution

1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6 2 8 3 0D ista n ce (m )

-0 .2

0

0 .2

0 .4

0 .6

0 .8

1

Nor

mal

ized

Am

pli

tud

e

1. Spatial resolution of correlating traces with scatterer-only events is much higher.

2. Spatial resolution of correlating traces with direct-only events depends on the aperture width.

X (m)

L

Zx

2

Results using traces with only

- Direct waves, full aperture width

- Direct waves, half aperture width

- Scattered waves, full aperture width

- Scattered waves, half aperture width

Expected Spatial Resolution

U of U TestTucson Test

Tunnel # 1 Tunnel # 2

10 m 10 m 10 m

Z 35 m 30 m 45 m

L 60 m 30 m 30 m

x 3 m 5 m 7.5 mRayleigh resolution

0.5 m 0.5 m 0.75 mScatterers resolution

Our approach shows a resolution 6 – 10 times better than the expected Rayleigh resolution limit.

• Motivation• RTM Methodology• Field Examples• Practical Problems • Super-resolution Tests• Summary and Conclusions

Outline

• We have successfully introduced a TRM method to locate trapped miners in a collapsed mine

• Two field tests are made to validate the proposed TRM method

• Field tests show that TRM can successfully locate trapped miners with signal-to-noise ratio as low as

0.0005

Summary and Conclusions

Summary and Conclusions

• Super Resolution

– Using traces with scatterer only improve data resolution 6-10 times

– Aperture width does not change the scatterer only results, while direct only waves is highly affected by the aperture width

To the best of our knowledge, our work is the first time super-stack and super-resolution properties are validated with field seismic data.

Summary and Conclusions

For the first time in EM waves, Lerosey et al. (2007) succeeded to get a resolution of /30

Implication

• 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.

Thank You

• Motivation and Introduction • Methodology• Field Examples

– University of Utah test– Tucson, Arizona test

• Practical Problems – Time shift test– Super-stack results– Trapped between two communication points– Two groups are trapped– Complex example

• Super-resolution Tests• Summary and Conclusions

Outline

CPSOS

Miners are trapped between two CP

CPSOS

CPSOS

CPSOS

Example from U of U test

• Motivation and Introduction • Methodology• Field Examples

– University of Utah test– Tucson, Arizona test

• Practical Problems – Time shift test– Super-stack results– Trapped between two communication points– Two groups are trapped– Complex example

• Super-resolution Tests• Summary and Conclusions

Outline

Two groups of miners sending SOS call

CP

SOS 1 SOS 2

Example from U of U test

• Motivation and Introduction • Methodology• Field Examples

– University of Utah test– Tucson, Arizona test

• Practical Problems – Time shift test– Super-stack results– Trapped between two communication points– Two groups are trapped– Complex example

• Super-resolution Tests• Summary and Conclusions

Outline