Comptes Rendus
Stress inversion method and analysis of GPS array data
Comptes Rendus. Mécanique, Volume 336 (2008) no. 1-2, pp. 132-148.

The stress inversion method is developed to find a stress field which satisfies the equation of equilibrium for a body in a state of plane stress. When one stress–strain relation is known and data on the strain distribution on the body and traction along the boundary are provided, the method solves a well-posed problem, which is a linear boundary value problem for Airy's stress function, with the governing equation being the Poisson equation and the boundary conditions being of the Neumann type. The stress inversion method is applied to the Global Positioning System (GPS) array data of the Japanese Islands. The stress increment distribution, which is associated with the displacement increment measured by the GPS array, is computed, and it is found that the distribution is not uniform over the islands and that some regions have a relatively large increment. The elasticity inversion method is developed as an alternative to the stress inversion method; it is based on the assumption of linear elastic deformation with unknown elastic moduli and does not need boundary traction data, which are usually difficult to measure. This method is applied to the GPS array data of a small region in Japan to which the stress inversion method is not applicable.

La méthode d'inversion est développée pour trouver un champ de contraintes satisfaisant les équations d'équilibre pour un corps en situation de contrainte plane. La relation entre contrainte et déformation étant connue et les données de distribution de déformation sur le corps et de traction sur le bord étant fournies, la méthode résout un problème bien posé, qui consiste en un problème aux limites linéaire pour la fonction de contrainte d'Airy, comprenant l'équation de Poisson et des conditions aux limites de type Neumann. La méthode d'inversion est appliquée aux données GPS (Global Positioning System) concernant les îles japonaises. Les incréments de contraintes associés aux incréments de déplacements mesurés par le système GPS sont calculés, et l'on trouve que leur distribution n'est pas uniforme sur les îles, certaines régions présentant un incrément relativement grand. La méthode d'inversion élastique est développée comme alternative à la méthode d'inversion des contraintes ; elle est fondée sur l'hypothèse d'une déformation linéaire élastique avec des coefficients d'élasticité inconnus, et ne requiert pas de données concernant les tractions au bord, généralement difficilement mesurables. La méthode est appliquée aux données GPS d'une petite région du Japon pour laquelle la méthode d'inversion des contraintes n'est pas utilisable.

Published online:
DOI: 10.1016/j.crme.2007.11.007
Keywords: Dynamical systems, Inverse analysis, Crustal deformation, GPS (Global Positioning System), Identification of local constitutive relation
Mot clés : Systèmes dynamiques, Analyse inverse, Déformation de la croûte, GPS (Global Positioning System), Identification de la relation constitutive locale

Muneo Hori 1; Takeshi Iinuma 2; Teruyuki Kato 1

1 Earthquake Research Institute, University of Tokyo, 1-1-1, Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan
2 Research Center for Prediction of Earthquakes and Volcanic Eruptions, Graduate School of Science, Tohoku University, 6-6 Aza-Aoba, Aramaki, Aoba-ku, Sendai 980-8578, Japan
@article{CRMECA_2008__336_1-2_132_0,
     author = {Muneo Hori and Takeshi Iinuma and Teruyuki Kato},
     title = {Stress inversion method and analysis of {GPS} array data},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {132--148},
     publisher = {Elsevier},
     volume = {336},
     number = {1-2},
     year = {2008},
     doi = {10.1016/j.crme.2007.11.007},
     language = {en},
}
TY  - JOUR
AU  - Muneo Hori
AU  - Takeshi Iinuma
AU  - Teruyuki Kato
TI  - Stress inversion method and analysis of GPS array data
JO  - Comptes Rendus. Mécanique
PY  - 2008
SP  - 132
EP  - 148
VL  - 336
IS  - 1-2
PB  - Elsevier
DO  - 10.1016/j.crme.2007.11.007
LA  - en
ID  - CRMECA_2008__336_1-2_132_0
ER  - 
%0 Journal Article
%A Muneo Hori
%A Takeshi Iinuma
%A Teruyuki Kato
%T Stress inversion method and analysis of GPS array data
%J Comptes Rendus. Mécanique
%D 2008
%P 132-148
%V 336
%N 1-2
%I Elsevier
%R 10.1016/j.crme.2007.11.007
%G en
%F CRMECA_2008__336_1-2_132_0
Muneo Hori; Takeshi Iinuma; Teruyuki Kato. Stress inversion method and analysis of GPS array data. Comptes Rendus. Mécanique, Volume 336 (2008) no. 1-2, pp. 132-148. doi : 10.1016/j.crme.2007.11.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.11.007/

[1] Geophysical Survey Institute, the Ministry of Construction, Japan, 2000. Home page, http://mekira.gsi-mc.go.jp/

[2] H.D. Bui Inverse Problem in the Mechanics of Materials: An Introduction, CRC Press, New York, 1994

[3] Y.E. Anikonov Multidimensional Inverse and Ill-Posed Problems for Differential Equations, VSP International Science Publishers, New York, 1995

[4] A. Kirsch An Introduction to the Mathematical Theory of Inverse Problems, Springer, New York, 1996

[5] Inverse Problems in Engineering Mechanics (M. Tanaka; G.S. Dulikravich, eds.), Elsevier, New York, 1998

[6] G. Eskin; J. Ralston On the inverse boundary value problem for linear isotropic elasticity, Inverse Problems, Volume 18 (2002), pp. 907-921

[7] G. Nakamura; G. Uhlmann Global uniqueness for an inverse boundary problem arising in elasticity, Invent. Math., Volume 118 (1994), pp. 457-474

[8] G. Nakamura; G. Uhlmann Inverse problems at the boundary for an elastic medium, SIAM J. Math. Anal, Volume 26 (1995), pp. 263-279

[9] M. Hori; T. Kameda Inversion of stress from strain without full knowledge of constitutive relations, J. Mech. Phys. Solids, Volume 49 (2001), pp. 1621-1638

[10] M. Hori; T. Kameda; T. Kato Application of stress inversion method to predict stress distribution in Japanese Islands, Geophys. J. Int., Volume 144 (2001), pp. 597-608

[11] T. Iinuma; T. Kato; M. Hori Inversion of GPS velocity and seismicity data to yield changes in stress in the Japanese Islands, Geophys. J. Int., Volume 160 (2005), pp. 417-434

[12] M. Hori Inverse analysis method to find local constitutive relations, Mech. Mater., Volume 35 (2003), pp. 1089-1105

Cited by Sources:

Comments - Policy