representationoftsunamisingeneralizedhyperspace.ppt

07/29/11 IGARSS'11 SENDAI/VANCOUVER 1

REPRESENTATION of TSUNAMIS in GENERALIZED

HYPERSPACE

Email: *[email protected] **[email protected]

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

mailto:[email protected]


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


Fig.1: The DART Method


Shortcomings of the DART System

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

II. Cost;

III. Reliability;

IV. Availability


Fig.2: FY-2C 041226 0800 IR1


MAIN EVENT

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

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


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

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


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


Fig.7: Earthquake Locations


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


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

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


NOAA Pathfinder V - TIR Images


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


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


Wavelet Decomposition,Nicobar

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

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


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


ANDAMAN-4 0700 LAT 1012

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

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


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


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

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


No Tsunami Cases:

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

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


No Tsunami Cases:

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

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


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


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


Tsunami Magnitude & Intensity

Mt = log2 (S) (1)

where

• Mt = Infrared Tsunami Magnitude,

S = Tsunami Signal at the epicenter.

Intensity: It = log2(√2 * S) (2)


Infrared Tsunami vs Earthquake Magnitude

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

•


Tsunami Index I

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


Earthquake vs Infrared Tsunami Index at Epicenter


System Modules

• Satellite Receiver Computer ↑

• PMEL

• Visualization Monitoring Alarm•


Representations of Tsunamis:

• Signal Diagram (Canonical Representation);

• Wavelet Diagram;

• Vector Representation;

• Phase Space Representation (MOST etc.);

• Other.


The Vector Representation

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

brightness).


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


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


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.


Questions, Comments??

representationoftsunamisingeneralizedhyperspace.ppt

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