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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