Mathematical models of elastic waves and their inverse problems
Project/Area Number 
17540145

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Basic analysis

Research Institution  Ibaraki University 
Principal Investigator 
SOGA Hideo IBARAKI University, the College of Education, Professor, 教育学部, 教授 (40125795)

CoInvestigator(Kenkyūbuntansha) 
KAIZU Satoshi IBARAKI University, the College of Education, Professor, 教育学部, 教授 (80017409)
NOZAKI Hideaki IBARAKI University, the College of Education, Professor, 教育学部, 教授 (60208337)
CHIBA Yasuo IBARAKI University, Center of University Education, Assistant Professor, 大学教育センター, 講師 (90400598)
NAKAMURA Gen HOKKAIDO University, the College of Science, Professor, 理学研究科, 教授 (50118535)
ITO Hiroya University of ElectroCommunication, Department of Mathematics, Associate Professor, 電気通信学部, 助教授 (30211056)

Project Period (FY) 
2005 – 2006

Project Status 
Completed (Fiscal Year 2006)

Budget Amount *help 
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)

Keywords  mathematical physics / inverse problems / elastic equations / seismic waves / scattering theory / Rayleigh wave / wave equations / partial differential equations / 偏微分方程 
Research Abstract 
In this research project we aimed initially (i) to examine scattering of surface waves (e.g. the Rayleigh wave, etc) and investigate inverse problems to extract the situations of the surface from the data of those waves ; (ii) to set up some mathematical model corresponding the seismic probe and study inverse problems to know the shape of stratums from the data of reflected waves for artificial incident waves ; (iii) to solve the above inverse problems numerically under typical conditions and make softwares of personal computers for exhibition of the propagation of the waves in the display. About (i) : We have constructed a scattering theory of the Rayleigh wave and its asymptotic solution useful for solving the inverse problem, and a representation of the scattering kernel expressing the situations of the boundary. Furthermore, using these results, we have solved the inverse problem to get the information of the boundary from the date of the Rayleigh wave. About (ii) : We have made an appropriate mathematical setup of the inverse problem of seismic waves and have developed the methods applied to it under some assumptions. But we have not been able to accomplish completely what we intended initially. About (iii) : We have obtained a numerical algorism of optimal shape problems which seems applicable to the inverse problem. We have made a software of personal computers for exhibition of the propagation of the waves in the display. This will be developed to the one to show the situations of various setting of the inverse problem.

Report
(3 results)
Research Products
(1 results)