Statistical analysis of the eigenspace components of the two‐dimensional, symmetric rank‐two strain rate tensor derived from the space geodetic measurements (ITRF92‐ITRF2000 data sets) in central Mediterranean and Western Europe

SUMMARY In the deformation analysis with a 2‐D (or planar and horizontal), symmetric rank‐two deformation tensor in geosciences (geodesy, geophysics and geology), the eigenspace components of these random deformation tensors (principal components, principal directions) are of focal interest. With the new development of space‐geodetic techniques, such as GPS, VLBI, SLR and DORIS, the components of deformation measures (such as the stress or strain tensor, etc.) can be estimated from their highly accurate regular measurement of positions and change rates and analysed by means of the proper statistical testing procedures. In this paper we begin with a review of the results of statistical inference of eigenspace components of the 2‐D symmetric, rank‐two random tensor (‘random matrix’), that is, the best linear uniformly unbiased estimation (BLUUE) of the eigenspace elements and the best invariant quadratic uniformly unbiased estimate (BIQUUE) of its variance–covariance matrix. Then the geodynamic setting of the Earth and especially the selected investigated region—the central Mediterranean and Western Europe will be discussed. Thirdly, the ITRF sites are selected according to the history and quality of the ITRF realization series, and the related incremental velocities of selected ITRF sites are computed. Fourthly, the methods of derivation for the 2‐D geodetic strain rates are introduced in order to obtain these strain rates from the incremental velocities. In the case study, both BLUUE and BIQUUE models as well as related hypothesis tests are applied to the eigenspace components of the 2‐D strain rate tensor observations in the area of the central Mediterranean and Western Europe, as derived from the ITRF92 to ITRF2000 sequential station positions and velocities. The interpretation and comparison of these results with the geodynamic feature are followed. Furthermore the statistical inference of the eigenspace components provides us with not only the confidence regions of these estimated, but also the visual presentation of the possible magnitude and the directions of the extension and contraction of the strain rate, which is important for the prediction of the tectonic activity including the possible deformation trend and directions.