Pattern of recent vertical crustal movements in Canada

We used the method of smooth piecewise algebraic approximation to automatically compute a smooth approximation of large functional scattered re-levelling data and historical tide gauge records given over Canada and northern US to thereby compile a unified map of vertical crustal movements (VCM). The area of study is divided into pieces and piecewise algebraic surfaces are fitted to the tide gauge trends and to the height difference differences, computed from monthly mean sea-level and re-levelling segments, respectively. When the surfaces are fitted to the data, a set of continuity and smoothness constraints is imposed in such a way that rather than the surfaces being fitted sequentially, they are fitted simultaneously, using the constraints as a set-conditions which the parameters of the surfaces must also satisfy.The VCM model obtained in this research gives enough details of the movements. It highlights the long wavelength spatial and temporal variations of the crust in Canada, mainly due to postglacial rebound (PGR). In Eastern Canada, the PGR hinge line appears from Gulf of St. Lawrence in the map of VCM. It follows the Atlantic coast line to the south of the country. In the Great Lakes, the relative movements or the tilt varies slightly between 0.5 and 1.5 mm/year per hundred kilometers) along northeast–southeast direction, which is toward the maximum ice center in Hudson Bay. The computed tilt is in a relatively good agreement with the tilt obtained from the glacial isostatic adjustment (GIA) model of ICE-3G (VM2) in this region (∼1 mm/year per hundred kilometers). The predicted rate of tilt in eastern prairies in Manitoba from VCM is in the range of 1.5–2 mm/year per hundred kilometers toward Hudson Bay. This solution is in good agreement with the results of previous studies for subsidence in southern Lake Athabaska in Saskatchewan and for uplift in southern prairies. However, GIA models do not agree with such findings. The zero line in the map of VCM nearly follows the Pacific coastal line, which is consistent with the PGR zero line in the prairies.