Applications of deformation analysis in geodesy and geodynamics

Abstract

The role of deformation analysis is discussed with respect to its existing or possible future applications in geodesy and geodynamics. Expressions for strain tensors are given in the more general case of Riemannian spaces and specialized for Euclidean spaces and the case of infinitesimal deformation. Among the various applications, special emphasis is given to the study of crustal deformations of the earth, deformations of the gravity field, and gravity field related deformations. Other applications are also considered.

Statistical analysis of geodetic deformation (strain rate) derived from the space geodetic measurements of BIFROST Project in Fennoscandia

“…For the infinitesimal strain rate, we have the strain rate tensor T = (L + L T )/2 and the rotation rate tensor R = (L − L T )/2 (Dermanis and Liveratos, 1983).…”

Three-dimensional strain tensor estimation by GPS observations: methodological aspects and geophysical applications

“…The estimation of the strain tensor components by geodetic networks has been stressed in the past by many authors (Frank, 1966;Bibby, 1975;Borre, 1979;Brunner, 1979;Cohen and Cook, 1979;Livieratos, 1980;Brunner et al, 1981;Dermanis and Livieratos, 1983;Liu, 1998;Dong et al, 1998;Crespi et al, 2000;Kahle et al, 2000;Bos et al, 2003;Jimenez-Munt et al, 2003).…”

“…at each point of the medium. Since geodetic observations are usually discrete, it is necessary to interpolate the displacement field; consequently, the geodetic estimated strain may depend not only on the observations but also on the chosen interpolation technique (Dermanis and Livieratos, 1983). Concerning the two mentioned data processing strategies, in the first one a kind of interpolation is just needed, since the strain tensor is estimated within each triangle but it is not defined how it varies shifting from a triangle to another; in the global estimation approach, on the contrary, the interpolation is not necessary because the strain field is supposed homogeneous.…”

GeoStrain: An open source software for calculating crustal strain rates

“…If the interpolation technique considers the physical reality of the earth crust more, the computed strain filed is closer to the real one. There is an additional problem for calculating the strain for the points on the crust surface: mathematically interpolation techniques predict displacements even outside the medium, but in the physical reality, displacements are not defined outside the medium and boundary conditions should be introduced (Dermanis and Livieratos, 1983). If the strain calculation depends on such predictions, it does not reflect the physical reality.…”