A SCR method for uncertainty estimation in geodesy non-linear error propagation: Comparisons and applications

Abstract

We review three derivative-free methods developed for uncertainty estimation of non-linear error propagation, namely, MC (Monte Carlo), SUT (scaled unscented transformation), and SI (sterling interpolation). In order to avoid preset parameters like as these three methods need, we introduce a new method to uncertainty estimation for the first time, namely, SCR (spherical cubature rule), which is no need for setting parameters. By theoretical derivation, we prove that the precision of uncertainty obtained by SCR can reach second-order. We conduct four synthetic experiments, for the first two experiments, the results obtained by SCR are consistent with the other three methods with optimal setting parameters, but SCR is easier to operate than other three methods, which verifies the superiority of SCR in calculating the uncertainty. For the third experiment, real-time calculation is required, so the MC is hardly feasible. For the forth experiment, the SCR is applied to the inversion of seismic fault parameter which is a common problem in geophysics, and we study the sensitivity of surface displacements to fault parameters with errors. Our results show that the uncertainty of the surface displacements is the magnitude of ±10 mm when the fault length contains a variance of 0.01 km2.