Application of the inversion method to a GPS network for estimating the stress increment in Japan

SUMMARY This paper examines the applicability of an inversion method of identifying stress distribution to the Japanese Islands, whose deformation is measured by the nationwide GPS array. The present inversion method is different from ordinary inversion, which requires a parametrization of constitutive relations, even though it is applicable only in the 2‐D state. It is rigorously shown that stress can be found without using constitutive relations, and the validity and usefulness are verified by carrying out a numerical simulation and a model experiment for a certain class of materials. For the GPS data, the inversion method can predict the stress increment distribution that is associated with the measured displacement increment. Under assumptions of a plane stress state for the incremental deformation and no volumetric inelastic deformation, the stress increment is computed from the GPS array data measured during 1997 and 1998; from the viewpoint of numerical analysis, the validity of the solutions is examined by changing the discretization scale, boundary conditions and other parameters. Regional constitutive relations are deduced from relations between the measured strain increment and the inverted stress increment. While further studies are definitely needed, the results of the numerical simulation suggest the potential usefulness of the present inversion method. The limitations of the inversion method when applied to the Japanese Islands are discussed, and necessary modifications are mentioned.