Invariant geodynamical information in geometric geodetic measurements

Summary Repeated geodetic measurements have been used to extract geodynamical quantities such as displacements, velocities of movement and crustal strains. Historical geodetic networks, especially those established before the space geodetic era, were, and still are, very important in providing a unique insight into the (local or regional) historical deformation state of the Earth. For the geodetic network without a tie to an external reference frame, free network adjustment methods have been widely applied to derive geodynamical quantities. Currently, it is commonly accepted that absolute displacements cannot be uniquely determined from triangulation/trilateration measurements, but relative displacements can be found uniquely if the geodetic network is geometrically overdetermined (see e.g. Segall & Matthews 1988). Strain tensors were derived using the coordinate method and were reported to be uniquely determined. We have carried out a theoretical analysis of invariant geodynamical information in geometric geodetic observations and concluded: (1) that relative displacements are not invariant quantities and thus cannot be uniquely determined from the geodetic network without a tie to an external reference frame; and (2) the components of the strain tensors are not all invariant and thus cannot individually be determined uniquely from the network. However, certain combinations of strain components are indeed invariant and can be uniquely determined from geometric geodetic measurements. The theory of invariant information is then applied to the analysis of the Tokai first-order triangulation/trilateration network spanning an interval of more than 100 yr. The results show that the normal and principal strains are significantly affected by the unknown scaling biases and orientation differences; thus any attempt at geophysical interpretation of these quantities must be exercised with great care. If the scaling bias and the orientation difference are small, the shear strain is shown to be practically invariant. The invariant analysis of the Tokai network has also shown that a belt near Shizuoka has been significantly deformed in the past 100 yr; this has not been seen in any previous analysis of displacements and/or strains.