Multi-quadric collocation model of horizontal crustal movement

To establish the horizontal crustal movement velocity field of the Chinese mainland, a Hardy multi-quadric fitting model and collocation are usually used. However, the kernel function, nodes, and smoothing factor are difficult to determine in the Hardy function interpolation. Furthermore, the covariance function of the stochastic signal must be carefully constructed in the collocation model, which is not trivial. In this paper, a new combined estimation method for establishing the velocity field, based on collocation and multi-quadric equation interpolation, is presented. The crustal movement estimation simultaneously takes into consideration an Euler vector as the crustal movement trend and the local distortions as the stochastic signals, and a kernel function of the multi-quadric fitting model substitutes for the covariance function of collocation. The velocities of a set of 1070 reference stations were obtained from the Crustal Movement Observation Network of China, and the corresponding velocity field was established using the new combined estimation method. A total of 85 reference stations were used as checkpoints, and the precision in the north and east component was 1.25 and 0.80 mm yr−1, respectively. The result obtained by the new method corresponds with the collocation method and multi-quadric interpolation without requiring the covariance equation for the signals.

Multi-quadric collocation model of horizontal crustal movement

To establish the horizontal crustal movement velocity field of the Chinese mainland, a Hardy multi-quadric fitting model and collocation are usually used, but the kernel function, nodes, and smoothing factor are difficult to determine in the Hardy function interpolation, and in the collocation model the covariance function of the stochastic signal must be carefully constructed. In this paper, a new combined estimation method for establishing the velocity field, based on collocation and multi-quadric equation interpolation, is presented. The crustal movement estimation simultaneously takes into consideration an Euler vector as the crustal movement trend and the local distortions as the stochastic signals, and a kernel function of the multi-quadric fitting model substitutes for the covariance function of collocation. The velocities of a set of 1070 reference stations were obtained from the Crustal Movement Observation Network of China (CMONOC), and the corresponding velocity field established using the new combined estimation method. A total of 85 reference stations were used as check points, and the precision in the north and east directions was 1.25 and 0.80 mm yr−1, respectively. The result obtained by the new method corresponds with the collocation method and multi-quadric interpolation without requiring the covariance equation for the signals.

An Attempt to Evaluate Horizontal Crustal Movement by Geodetic and Geological Approach in the Horonobe Area, Northern Hokkaido, Japan

In this study, we present the preliminary results for the estimation of a horizontal crustal movement by using geodetic and geological approach in the Horonobe area, northern Hokkaido, Japan. The estimations have been carried out by using a GPS data and a geological cross section obtained by applying balanced-section method. As results of this study, both of the shortening rates estimated by GPS data and balanced-section method indicate several millimeters per year. Namely, there is no contradiction between geodetic and geological data, and it is considered that Horonobe area is still situated similar tendency and magnitude of a crustal movement. It is seemingly considered that geodetic data is unhelpful for estimating the long-term crustal movement, because period of geodetic observations is a very short. However, the result of this study indicates that geodetic data provide valuable information for estimating the long-term crustal movement in the area, and it is considered that geodetic approach play an important role in improvement of the credibility of evaluation for prediction of long-term stability.