An attempt to determine areas with homogeneous vertical soil movement

Abstract

An algorithm is given for determining vertical soil movements from all available height determinations. The interpretation of the results will attempt to delimit tectonic plates and to give homogeneous vertical movements (tilts) for each tectonic plate. All available levelling data and trigonometric height determinations are divided into partial nets. All simultaneous observations of possible ratios of motion are put together into one partial net. These partial nets are adjusted in the common, free, static pattern by the well-known solutions of an adjustment of observation equations. The precision of the partial nets may be investigated for geometric levelling as well as for trigonometric levelling without disturbance by real movements. By bringing the partial nets together, a general system for the vertical point movements is formulated. The observations of this followup adjustment are the adjusted heights of the partial nets. The covariance matrices of the partial nets give the stochastic model for the general system. The first stage of calculating the general system is to adopt a static velocity model for the bench marks. A highly sensitive global test will reject the model if it is not justified by the observation precision. The strict form of a deformation analysis will filter out all bench marks which indeed are stable. The next stage will be to adopt a linear velocity model for the unstable points. Again, a deformation analysis will give those points which move linearily. The third stage will give all points which move accordingly to a quadratic velocity model. All moving parameters are given with their covariance matrix. The remaining bench marks have to be taken as disturbed in their height. The local distribution of the disturbed bench marks will indicate possible boundaries of tectonic plates. Within one plate a tilt should be recognizable.