2022 年 75 巻 p. 1-12
Present day crustal displacement rates are accurately observed by global navigation satellite system (GNSS). In estimating continuous displacement fields from spatially discrete GNSS data, the method of basis function expansion is a powerful tool. As basis functions, the boxcar function is the easiest to be implemented, while the cubic B-spline function has good nature in estimating continuous and smooth fields. In this study, we quantitatively compare the performance of the boxcars with that of the cubic B-splines, changing the basis-function interval L in estimating velocity fields from observed GNSS data in Japan. The result shows that the performance of the cubic B-splines with L＝50, 60, and 80 km is nearly the same or better than that of the boxcars with L＝20, 25, and 30 km, respectively. In other words, to achieve similar performance, at least about 2.52＝6.25 times as many boxcars as cubic B-splines are needed. In the method of basis function expansion, the computation of inverse matrices is the most time-consuming process. Because its computational cost is usually proportional to the cube of the matrix size (the number of basis functions), computing inverse matrices for the boxcars takes about 250 times as much time as that for the cubic B-splines, although the difference of actual computational costs in this study was about 100 times or more. In addition, strain rates can be easily obtained by analytically differentiating the velocity field when we use the cubic B-splines. On the other hand, a main disadvantage in using the cubic B-splines is complicated computation to obtain the explicit expression of the smoothness constraint for the inversion analysis. To mitigate this problem, we show the computation results in Appendix.