Geodetic time series analysis in Earth sciences: Fid-Bau Portal

Geodetic time series analysis in Earth sciences

Montillet, Jean-Philippe / Bos, Machiel S.

Intro -- Foreword: Welcome to the Not-So-Spherical Cow -- Preface -- References -- Contents -- Editors and Contributors -- Abbreviations -- 1 The Art and Science of Trajectory Modelling -- 1.1 Introduction -- 1.2 Trajectory Models -- 1.3 A Gallery of Geodetic Trajectories -- 1.4 Automatic Signal Decomposition Using GrAtSiD -- 1.5 Conclusions -- References -- 2 Introduction to Geodetic Time Series Analysis -- 2.1 Gaussian Noise and the Likelihood Function -- 2.2 Linear Models -- 2.3 Models for the Covariance Matrix -- 2.4 Power Spectral Density -- 2.5 Numerical Examples -- 2.6 Discussion -- References -- 3 Markov Chain Monte Carlo and the Application to Geodetic Time Series Analysis -- 3.1 Introduction -- 3.2 Markov Chain Monte Carlo as a Parameter Estimation Method -- 3.2.1 Fundamentals -- 3.2.2 The Random-Walk Metropolis-Hasting Algorithm -- 3.2.3 The Markov Chain Monte Carlo Algorithm -- 3.3 General Considerations for Markov Chain Monte Carlo -- 3.3.1 The Equilibrium State -- 3.3.2 The Acceptance Rate -- 3.3.3 The Spectrum of the Markov Chain -- 3.4 Applications -- 3.4.1 Position Time Series -- 3.4.2 Plate Motion Models -- 3.4.3 Gravity Time Series -- 3.4.4 Mean Sea Level Time Series -- 3.5 Summary -- References -- 4 Introduction to Dynamic Linear Models for Time Series Analysis -- 4.1 Introduction to Dynamic Linear Models -- 4.2 State Space Description -- 4.2.1 Example: Spline Smoothing -- 4.3 DLM as Hierarchical Statistical Model -- 4.4 State and Parameter Estimation -- 4.5 Recursive Kalman Formulas -- 4.6 Simulation Smoother -- 4.7 Estimating the Static Structural Parameters -- 4.8 Analysing Trends -- 4.9 Examples of Different DLM Models -- 4.9.1 The Effect of Level and Trend Variance Parameters -- 4.9.2 Seasonal Component -- 4.9.3 Autoregressive Process -- 4.9.4 Regression Covariates and Proxy Variables -- 4.10 Synthetic GNSS Example.