An Iterative Least Squares Method Based on the F-J Inversion for Linear-Non-Linear Models

ZHANG Yandong; XU Caijun; WANG Jianjun

doi:10.13203/j.whugis20180117

Volume 44 Issue 12

Dec. 2019

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Geomatics and Information Science of Wuhan University > 2019 > 44(12): 1816-1822. > DOI: 10.13203/j.whugis20180117

ZHANG Yandong, XU Caijun, WANG Jianjun. An Iterative Least Squares Method Based on the F-J Inversion for Linear-Non-Linear Models[J]. Geomatics and Information Science of Wuhan University, 2019, 44(12): 1816-1822. DOI: 10.13203/j.whugis20180117

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An Iterative Least Squares Method Based on the F-J Inversion for Linear-Non-Linear Models

ZHANG Yandong^1,,
XU Caijun^{1, 2, 3},
WANG Jianjun^{1, 2, 3, ,}

1.
School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China
2.
Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University, Wuhan 430079, China
3.
Collaborative Innovation Center of Geospatial Technology, Wuhan 430079, China

Funds:

The National Key Research and Development Program of China 2018YFC1503605

the National Natural Science Foundation of China 41431069

the National Natural Science Foundation of China 41574002

the National Natural Science Foundation of China 41774011

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Author Bio:
ZHANG Yandong, master, majors in inversion algorithms for geophysical and geodetic data. E-mail:ydzhang@whu.edu.cn
Corresponding author:
WANG Jianjun, PhD, associate professor, specializes in earthquake stress triggering.E-mail:jjwang@sgg.whu.edu.cn
Received Date: December 24, 2018
Published Date: December 04, 2019

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Abstract

Abstract

Fukuda and Johnson (2010) proposed an inversion method associated with the Bayesian theory (hereinafter termed the F-J method) for linear-non-linear geophysical/geodetic problems. Since then this method has been widely applied to estimating globally optimal parameters and their precisions for linearnon-linear geophysical/geodetic models. Yet for the application of the F-J method the choice of Markov chain Monte Carlo (MCMC) sampling parameters somewhat affects the invered results. Additionally, searching the most appropriate sampling parameters is time-consuming. On the other hand, an iterative least squares method can also be applied to the inversion for linear-non-linear models if their non-linear parameters are linearized beforehand. However, this method depends on optimum initial values. To make full use of the advantages of the both methods, here we propose a hybrid method termed as the iterative least squares with initial values constrained by using the F-J method. The proposed method refers to the calculation of linear-nonlinear parameters using the F-J method just one time and to refining those parameters using the iterative least squares method a few times. Thus, it reduces the computation time relevant to the F-J method on the one hand and gains a global solution after a few times of employing the iterative least squares method on the other hand. To verify the efficacy of the hybrid method, we make comparisons using synthetic and real data sets. We employ the F-J method, iterative least squares method with random initial values and iterative least squares method with initial values provided by the F-J method, respectively. Our results show that:(1) the choice of sampling parameters indeed affects the results by using the F-J method; (2) based on the iterative least squares method with random initial values, inverted results generally diverge and sometimes converge to wrong results for some synthetic tests, and (3) using the iterative least squares method with initial values provided by the F-J method produces converged results without the dependence on MCMC sampling parameters and initial values, as expected thanks to absorbing the merits of the global optimality of the F-J method and efficiency of the iterative least squares method.
- linear-non-linear models,
- Bayesian theory,
- MCMC,
- iterative least squares,
- interseismic deformation model,
- Mogi model

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