Representation for Horizontal Crustal Deformation by Means of Chebychev Polynomials.

The Geographical Survey Institute has repeated the first order triangulations and trilaterations with high precision and high density since Meiji era in Japan. Many studies have been done in regard to horizontal strains of the crust by using these data. In those papers, they assume homogeneous strain fields in each triangle formed by three neighbouring triangulation stations. As a result, these triangles produce apparently discontinuous strain fields and are not convenient to elucidate spatial patterns and regional features. In this paper, we present a method to obtain continuous distributions of horizontal displacements and strains of the crust by means of triangulation and trilateration data in order to compare with other geophysical data sets. Weemploy two-dimensional Chebychev polynomials to interpolate horizontal displacements and strains at regularly distributed grid points. We applied the method for the first order triangulation and trilateration data in two regions in Japan to clearly reveal the regional features.