Modelling quasi-periodic signals in geodetic time-series using Gaussian processes
Modelling quasi-periodic signals in geodetic time-series using Gaussian processes
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DOI：
10.1093/gji/ggab168
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发表时间：
2021-05
影响因子：
2.8
通讯作者：
A. Koulali;P. Clarke
中科院分区：
文献类型：
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作者：
A. Koulali;P. Clarke
大地测量时间序列中的季节信号长期以来被认为与环境现象有关，如极移、大气负荷、地下水负荷和其他水文过程。对这些周期性信号进行建模对于这些时间序列的地球物理解释至关重要。最常见的方法用于解决季节性（年度和半年）信号是他们的近似正弦函数具有恒定的振幅。然而，由于它们的环境源，季节信号可能是准周期性的。在这项研究中，我们研究了高斯过程（GP）来模拟大地时间序列中的准周期信号，这是一种灵活的方法，可以使用协方差函数捕获数据中的变异性结构。我们使用马尔可夫链蒙特卡罗方法来评估后验概率密度函数。为了测试其有效性，我们将此方法应用于存在时间相关噪声的合成时间序列。我们发现，GP模型提供了一个更好的拟合的时间序列，导致时间序列残差较少的系统性影响。我们使用GP模型来估计长期的速度从南极洲和阿拉斯加州，以及重力恢复和气候实验时间序列的一个例子选择的GPS站点。GP模型的贝叶斯方面允许推断在真实解附近的线速度集合，同时考虑到时间序列中的准周期系统学。
Seasonal signals in geodetic time-series have long been recognized to be associated with environmental phenomena such as polar motion, atmospheric loading, groundwater loading and other hydrological processes. Modelling these periodic signals is crucial for the geophysical interpretation of these time-series. The most common approach used for resolving seasonal (annual and semi-annual) signals is their approximation by sinusoidal functions with constant amplitudes. However, because of their environmental source, seasonal signals are likely to be quasi-periodic. In this study, we investigate a Gaussian process (GP) to model quasi-periodic signals in geodetic time-series, a flexible method that allows capturing the variability structure in the data using covariance functions. We use the Markov Chain Monte Carlo method to evaluate the posterior probability density function. To test its effectiveness, we apply this method to a synthetic time-series in the presence of time-correlated noise. We find that the GP model provides a better fit to the time-series, resulting in time-series residuals with fewer systematic effects. We use the GP model to estimate the secular velocity of selected GPS sites from Antarctica and Alaska, as well as an example of Gravity Recovery and Climate Experiment time-series. The Bayesian aspect of the GP model allows inferring the linear velocity ensemble in the vicinity of the true solution while taking into account the quasi-periodic systematics in the time-series.