Method for accurately estimating post-earthquake relaxation time in colored noise

Abstract

The invention discloses a method for accurately estimating post-earthquake relaxation time in colored noise, which comprises the following steps of: selecting a combination of white noise and flicker noise, estimating a pre-earthquake GNSS (Global Navigation Satellite System) time sequence by using a maximum likelihood technology, and acquiring a pre-earthquake signal; pre-earthquake signals in the GNSS time sequence after the earthquake are deleted; and constructing a random model of the post-earthquake GNSS time sequence. Setting a damping factor lambda according to actual needs; calculating the amplitude Al, Ae and x2 (X) of post-earthquake deformation by using a linear least square method; calculating normal matrixes N and L, and calculating Al, Ae and x2 (X + delta X) by using a linear least square method; and when the number of iterations of x2 (X + delta X) is reduced to the negligible degree of lambda, iteration is stopped. According to the method, the accuracy of the initial value is not required, the interference of colored noise can be solved, the adaptability of the algorithm is remarkably improved, the result of estimating the relaxation time is basically not influenced by the initial value, and a large number of errors carried by signal extraction are effectively avoided.

Description

technical field [0001] The invention belongs to the field of crustal movement analysis, in particular to a method for accurately estimating relaxation time after an earthquake in colored noise. Background technique [0002] The relaxation time parameter in the post-earthquake deformation model is nonlinearly related to the observations, so it cannot be estimated by linear least squares. The result of the conventional nonlinear least squares estimation depends on the initial value, and the simple nonlinear least squares method cannot solve the relaxation time problem. On the other hand, there is a large amount of colored noise in the continuous GNSS time series, which will bring great difficulties to the calculation of relaxation time. [0003] Usually colored noise in GNSS time series is modeled as a combination of white noise and flicker noise (Zhang et al. 1997; Mao et al. 1995; Williams 2004; Langbein 2008; Andrei et al. 2018; Li et al. 2019; He et al. 2019). The ratio ...

AI Technical Summary

Problems solved by technology

[0002] The relaxation time parameter in the post-earthquake deformation model is nonlinearly related to the observations, and linear least squares estimation cannot be used

The result of the conventional nonlinear least squares estimation depends on the initial value, and the simple nonlinear least squares method cannot solve the relaxation time problem

On the other hand, there is a large amount of colored noise in the continuous GNSS time series, which will bring great difficulties to the calculation of relaxation time

Images