representationoftsunamisingeneralizedhyperspace.ppt

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REPRESENTATION of TSUNAMIS in GENERALIZED

HYPERSPACE

Email: *linbfrank@gmail.com **kingkarn@ice.ci.ritsumei.ac.jp

Frank C. Lin*

University of Maryland Eastern Shore, Princess Anne, MD.

21801, U.S.A.and

Kingkarn Sookhanaphibarn**

Ritsumeikan University,Kusatsu, Shiga,525-8577, Japan

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PLAN of this TALK

I. First, we recapitulate a previous study* in which a new, reliable, unequivocal,

economical and instantaneous response method for DETECTING tsunamis at

birth using TIR images from geostationary satellites;

II. We show then the representations for tsunamis can be mapped into each other

by a linear transformation. *Lin,F.C., na Nakornphanom, K.Sookhanaphibarn and Lursinsap, C: “A New

Paradigm for Detecting Tsunamis by Remote Sensing”, International Journal of Geoinformatics, Vol.6, No.1, March, 2010, p.19-30

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Fig.1: The DART Method

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Shortcomings of the DART System

I.Time Delay: Mentawai (2010), Tohoku (2011);

II. Cost;

III. Reliability;

IV. Availability

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Fig.2: FY-2C 041226 0800 IR1

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MAIN EVENT

Fig.3: Signal along latitude 1067 (Banda Aceh) at 7 am

Fig.4: Signal along latitude 1067 (Banda Aceh) at 8 am

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Fig.5: Wavelet Decomposition at Latitude 1067, 7 am

Fig.6: Wavelet Decomposition at Latitude 1067, 8 am

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TABLE I.

Event Me Time (UTC) Latitude LAT in (pixels)

Longitude LON in (pixels)

Signal at Epicenter (pixels)

Mt (Eq.1)

1.Mainshock 8.9 00:58:51 3.298 1067 95.779 966 417 8.7039 2.Sumatra aftershock

5.9 02:59:12 3.177 1027 94.259 950 465 8.8611

3.Nicobar 6.5 09:20:01 8.867 1043 92.382 946 461 8.8486 4.Andaman-1 5.7 07:07:10 10.336 1012 93.756 958 477 8.8978 5.Andaman-2 5.8 07:38:25 13.119 978 93.051 958 none 6.Andaman-3 6.3 11:05:01 13.542 965 92.877 955 none

7.Andaman-4 5.7 06:21:58 10.336 1012 92.323 945 479 8.9039

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Fig.7: Earthquake Locations

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Fig.8: Signal from the Sumatra Aftershock at 09:00 a.m

0 500 1000 1500 2000 25000

50

100

150

200

250

300 Pixel Value (0-255) of FY2C IR1 20041226 T09:00 Line1067 Aftershock

Banda Aceh

0 500 1000 1500 2000 25000

50

100

150

200

250

300Pixel Value (0-255) of FY2C IR1 20041226 T10:00 Line1067 Aftershock

Banda Aceh

Fig.9: Signal from the Aftershock at 10:00 a.m

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Fig.10: Detail Decomposition of Aftershock Signal at 0900 and Latitude 1067

Fig 11 Detail : Decomposition of Aftershock Signal at 1000 and Latitude 1067

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NOAA Pathfinder V - TIR Images

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Declouded IR images from the NOAA V5 Pathfinder satellite

Fig 12: Detail Wavelet Decomposition of NOAA Night Image

Fig.13: Detail Wavelet Decomposition of NOAA Day Image

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4.The Nicobar Island: (Location 3):

Fig.14: Signal from the Nicobar Aftershock at 0900 LAT 1042

0 500 1000 1500 2000 25000

100

200

300Pixel Value (0-255) of FY2C IR1 20041226 T1000 LAT1042 Nicobar (Fig16)

Fig.15: Signal from the Nicobar Aftershock at 1000 LAT 1042

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Wavelet Decomposition,Nicobar

Fig.16: Wavelet Decomposition at Nicobar at 0900 LAT 1042

Fig.17: Wavelet Decomposition at Nicobar at 1000 LAT 1042

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CASE 1:ANDAMAN-1 and ANDAMAN-4 LAT 1012: (Location 4 &7):

FIG.18: ANDAMAN-1 & 4 Signal 0600 LAT 1012

Fig.19: Wavelet Decomposition of ANDAMAN-1 & 4 at 0600, LAT 1012

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ANDAMAN-4 0700 LAT 1012

Fig.:20: Signal for ANDAMAN-4 0700 LAT 1012

Fig.21: Wavelet Decomposition for ANDAMAN-4 0700 LAT 1012

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At 0800, another tsunami signal is detected at the

Andaman-1 epicenter

Fig.22: Signal for ANDAMAN-1 0800 LAT 1012

Fig.23: Wavelet Decomposition for ANDAMAN-1 0800 LAT 1012 LON 978

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CASE 2: ANDAMAN-2, LAT 978: (Location 5):

Fig.24: Satellite Photo of Epicenter for ANDAMAN-2 0800 LON 958

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No Tsunami Cases:

Fig.25: Signal for ANDAMAN-2 0700 LAT 978

Fig.26: Wavelet Decomposition of ANDAMAN-2 0700 LAT 978

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No Tsunami Cases:

Fig. 27: Signal of ANDAMAN-2 0800 LAT 978 LON 958

Fig.28: Wavelet Decomposition for ANDAMAN-2 0800 LAT 978

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CASE 3: ANDAMAN-3,LAT 965(Location 6):

Fig.29: Signal for ANDAMAN-3 10:56 LAT 965

Fig:30: Wavelet Decomposition for ANDAMAN-3 10:56 LAT 965

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ANDAMAN-3 Lat.965 11:29 (No Tsunami Signal)

Fig.31: Signal for ANDAMAN-3 11:29 LAT 965 LON 955

Fig.32: Wavelet Decomposition for ANDAMAN-3 11:29 LAT 965 LON 955

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Tsunami Magnitude & Intensity

Mt = log2 (S) (1)

where

• Mt = Infrared Tsunami Magnitude,

S = Tsunami Signal at the epicenter.

Intensity: It = log2(√2 * S) (2)

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Infrared Tsunami vs Earthquake Magnitude

Me = 9.2299 - 0.0592*log2(S) (3)

•

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Tsunami Index I

I = 1000*log2-1(S)-110 (4)

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Earthquake vs Infrared Tsunami Index at Epicenter

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System Modules

• Satellite Receiver Computer ↑

• PMEL

• Visualization Monitoring Alarm•

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Representations of Tsunamis:

• Signal Diagram (Canonical Representation);

• Wavelet Diagram;

• Vector Representation;

• Phase Space Representation (MOST etc.);

• Other.

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The Vector Representation

We can represent a tsunami by a vector , with the components x, y, z, t, Me, Mt and Px (pixel

brightness).

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Phase space (Iida) & Infrared Space (Lin) Representations

Iida vs Lin Representations

-20

-15

-10

-5

0

5

10

15

Me

Me

Mt Iida

Lin et al

Iida Equation:

Mt = 2.61*Me – 18.44 Lin et al :

Mt = 9.2299–0.0592*Me

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Linear Transformation

Define abbreviated vector vIR = (Me, MtIR, N) and vP

= (Me, MtP, N), while all other variables are held

constant, and N is an axis orthogonal to the Me-Mt plane. Then

vP = R * vIR + TMe + TMt

where

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CONCLUSION

The advantages of our method vis-à-vis DART are: its economy, its reliability,

its greater availability, and its instantaneous response time. Our procedure can be incorporated into an early warning system which potentially can save lives and property.

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Questions, Comments??