1)Earthquake Administration of Fujian Province,Fuzhou 350003;2)Xianmen Research Centre of Earthquake Surveying,Xiamen 361021;3)Faculty of Science, Kobe University, Rokkotaimachi 1-1,Nada,Kobe 6578501, Japan
Abstract：On the basis of deducing the universal expressions in an orthogonal curvilinear coordinate system of the displacement gradient matrix and the strain tensor matrix of displacement vectors, we further derive the universal expression of the conversional matrix between two partial coodinates in random different orthogonal curvilinear coordinate systems,meanwhile, indicats that this conversional matrix also belongs to the orthogonal matrixes so that the strain tensor matrixes are similar matrixes. With this understanding,the after deply analysis of the geometric and physical natures of the strain tensor matrixes, discovers the invariant code mystery of crustal deformation hidden in these matrixes, which is, whatever the orthogonal curvilinear coordinate system is, the strain tensor matrix has a unique and invariant principle strain characteristic polynomial and by its corresponding strain eigenvalue equation we can derive the principle strains with their directions at any crustal particle,then the matrix can be turned into a diagonal matrix by putting the principle strains values as its diagonal elements, and the matrix trace equals the body strain, the matrix determinant equals a product of the principe strains. All these geometric and physical quantities are the crustal deformation invariants at the spot.
