IMA NEWS - Jan. 2002

Motto: We challenge risk boldly, deduce conclusion rapidly, create new business chance and contribute to revitalization of Japanese economy.

IMA (Institute of Mathematical Analysis) news is delivered every month. 

My company's fundamental strategy on high precision measurements of crust deformation at sea bottom

This time, the author would like to explain the high precision measurements of crust deformation at sea bottom. A GPS observation network called GEONET of Geographical Survey Institute of Japan monitors precisely the crust deformation on land. However, observation of crust deformation at sea bottom around the Japanese archipelagos is also very important to a country like Japan. It goes without saying that the crust deformation at sea bottom can't be measured directly by GPS in contrast to that on land. Furthermore, the precision of centimeters is required for the purpose of the measurements of crust deformation. The underwater measurements utilize acoustic signals. And the underwater acoustic velocity changes from hour by hour.

Although it is a very significant problem, the difficulty of the problem is unprecedented. Ordinary people would never challenge it. Nobody would like to be a Don Quixote. However, the world is wide. There is a people who challenged this problem. They are people of Scripps Institution of Oceanography. Their method is as follows. Let us assume that three transponder on the sea surface, for an example, are placed on a circle with its center at the bottom transponder, and the acoustic velocity does not change horizontally and changes only vertically, so-called horizontal stratification. The effect of ray deformation due to inhomogeneous distribution of acoustic velocity may be cancelled. The bottom transponder locates at the geometrical center of the surface transponder. On the other hand, the positions of the surface transponders are determined precisely by the high precision GPS measurements. Namely, the horizontal position of the bottom transponder can be determined very precisely.

In Japan too, a group of Maritime Safety Agency and a group of Tohoku University are developing the observation system. However, the practicability of the method seems doubtful to the author. It may be very difficult to place the surface transponder in such a convenient way. The method should be more flexible.

How about making not only the position of the bottom transponder but also the distribution of the underwater acoustic velocity as unknowns and solving them simultaneously? Assuming that the acoustic velocity is forming a horizontal stratification, the acoustic velocities on each layers are made unknowns. If there exists current, the current is also made unknowns. 

Mathematically, it is a kind of tomography. The author has been studying the problem for three years, and the results are presented at The Geodetic Society of Japan, The Society of Naval Architects of Japan and Underwater Technology Symposium. A result is obtained that the effects of making the underwater environments unknowns is crucial. At present, the author is plugging away alone and is hoping that the research is appreciated justly.
When a paper was read at Underwater Technology 2000, Prof. Emeritus N. Nasu of the former director of Ocean Research Institute, the University of Tokyo was listening to the presentation. Prof. Nasu advised me to send my paper to Prof. W. Munk of Scripps Institution of Oceanography who is the founder of Ocean Acoustic Tomography. So, the author is always sending papers on this topic to Prof. Munk. Prof. Munk always gives me warm encouragements.

Jobs in December

(1) Experiment on Underground GPS and completion of a report
(2) Proposal for practical use of a high sensitivity GPS receiver
(3) Proposal for R&D of a high precision GPS
(4) Application of a paper for the Society of Naval Architects of Japan and  preparation of a paper
        http://www.snaj.or.jp
(5) Preparation of a paper for ION NTM 2002
        http://www.ion.org/meetings/ntm2002abstractlist.html

Schedule in and after January

(1) Proposal for practical use of an Underground GPS
(2) Proposal for R&D of a high precision GPS
(3) Proposal for R&D of a high sensitivity GPS
(4) Proposal for an experimental system of Modulation/Demodulation
Experiment
(5) Presentation of a paper on an underground GPS at ION2002 NTM (Jan., San Diego)
        http://www.ion.org/meetings/ntm2002program.html#sessions
(6) Presentation of a paper on GPS Acoustics at UT2002 (April, Tokyo)
        http://underwater.iis.u-tokyo.ac.jp/ut02/Welcome.html
(7) Presentation of a paper at the Spring Meeting for the Society of Naval Architects of Japan
        http://www.snaj.or.jp
(8) Presentation a paper on a new method in wave tank experiments at OMAE Symposium (June, Oslo)
        http://www.asmeconferences.org/omae02/Author/NewAbstract.cfm

Essay: Children of Afghanistan

Since the terrorist attacks on Sept. 11 last year, suffering of Afghan people escaping from retaliation attacks by USA is reported every day. Eventually it may result in the liberation from the rule of Tariban and Al Kaida. So, the present pain may be rewarded certainly. However, the suffering may exceed our imagination. It's really hard to see children in pain.

The author was born in December 1940. So, I was four years eight months when Japan accepted the unconditional surrender at World War II. The living of Japanese people at the time was really miserable, since Japan had exhausted the national wealth to the war. Above all, for people in cities, it was very hard to get daily foods. The ration of food was completely insufficient. The author's memory in his infancy is penetrated through hunger. Thanks to love from his parent and food aid from USA, he survived barely.

The author is 165 cm in height. The height is the average of people belonging to the same generation, but it is a few centimeter lower than that of people belonging to prior and post generations. The hard living of the day is memorized in the height of the children.

Since the author has this kind of experience in his infancy, the suffering of Afghan children revive the memory in his infancy. It makes him feel as if it were his own affair. Why innocent children must suffer the misery? They should be given enough food and spend happy life. Why are they forced to live in hunger and terror? It's really unreasonable!

Nobody doubts that the war is wrong. However, there still exist wars. When does mankind overcome the war?