Least squares prediction of the spatial distribution of the rates of vertical crustal movements in the Tokai district, Central Japan, was performed with the aid of an empirically deduced local covariance function referring to data obtained during the period from 1979 to 1985, and the results are illustrated with contour lines.
Although least squares prediction which is related to least squares collocation was originally developed to obtain the distribution of gravity anomalies, it had not been widely applied in the study of crustal deformation. This was partially due to some difficulties in obtaining an empirical covariance function of crustal deformation. In order to apply least squares collocation for the study of vertical crustal movements in the Tokai district, we tried first to deduce a covariance function of Gaussian type. From the rates of vertical crustal movements at 67 stations in the Tokai district obtained during the period from 1979 to 1985, we estimated C_s(0)=8.0[(mm/a)²], k=0.035, C_r(0)=3.0[(mm/a)²] in the Gaussian function of the form C(d)=C_s(0)exp(-k²d²), where d is the distance between two stations and C_r(0) is the variance of observational errors at d=0. We applied this function to estimate the distribution of the rates of vertical crustal movements. Predicted contour lines of the rates of vertical crustal movements derived from 197 data signals showed almost the same pattern as those from 67 signals in the case of an area of approximately 200×350 km² in the Tokai district. Uncertainty in the parameter k had certainly some influence on the contour lines, but this effect is not so definitive. On the contrary, prediction without filtering sometimes produced results distinguished from the those obtained with filtering. Generally we recommend to perform prediction with filtering. As for the tectonic implication from the present results, we emphasize that a paired motion of subsidence at Omaezaki and uplift at Akaishi is more clearly concluded to exist than the one by the other methods.