Modeling periodic phenomena with accuracy is a key aspect to detect abnormal behavior in time series for the context of Structural Health Monitoring. Modeling complex non-harmonic periodic pattern currently requires sophisticated techniques and significant computational resources. To overcome these limitations, this paper proposes a novel approach that combines the existing Bayesian Dynamic Linear Models with a kernel-based method for handling periodic patterns in time series. The approach is applied to model the traffic load on the Tamar Bridge and the piezometric pressure under a dam. The results show that the proposed method succeeds in modeling the stationary and non-stationary periodic patterns for both case studies. Also, it is computationally efficient, versatile, self-adaptive to changing conditions, and capable of handling observations collected at irregular time intervals.

In order to detect possible signal redundancies in the ambient seismic wavefield, we develop a new method based on pairwise comparisons among a set of synchronous time-series. This approach is based on instantaneous phase coherence statistics. The first and second moments of the pairwise phase coherence distribution are used to characterize the phase randomness. For perfect phase randomness, the theoretical values of the mean and variance are equal to 0 and $\sqrt{1-2/\pi }$, respectively. As a consequence, any deviation from these values indicates the presence of a redundant phase in the raw continuous signal. A previously detected microseismic source in the Gulf of Guinea is used to illustrate one of the possible ways of handling phase coherence statistics. The proposed approach allows us to properly localize this persistent source, and to quantify its contribution to the overall seismic ambient wavefield. The strength of the phase coherence statistics relies in its ability to quantify the redundancy of a given phase among a set of time-series with various useful applications in seismic noise-based studies (tomography and/or source characterization).

Summary The quantification of uncertainty associated with the model parameters and the hidden state variables is a key missing aspect for the existing Bayesian dynamic linear models. This paper proposes two methods for carrying out the uncertainty quantification task: (a) the maximum a posteriori with the Laplace approximation procedure (LAP‐P) and (b) the Hamiltonian Monte Carlo procedure (HMC‐P). A comparative study of LAP‐P with HMC‐P is conducted on simulated data as well as real data collected on a dam in Canada. The results show that the LAP‐P is capable to provide a reasonable estimation without requiring a high computation cost, yet it is prone to be trapped in local maxima. The HMC‐P yields a more reliable estimation than LAP‐P, but it is computationally demanding. The estimation results obtained from both LAP‐P and HMC‐P tend to the same values as the size of the training data increases. Therefore, a deployment of both LAP‐P and HMC‐P is suggested for ensuring an efficient and reliable estimation. LAP‐P should first be employed for the model development and HMC‐P should then be used to verify the estimation obtained using LAP‐P.

Summary Due to a too sparse permanent seismic coverage during the last decades, the crustal structure of western France and the surrounding regions is poorly known. In this study, we present a 3-D seismic tomographic model of this area obtained from the analysis of 2-year continuous data recorded from 55 broad-band seismometers. An unconventional approach is used to convert Rayleigh wave dispersion diagrams obtained from ambient noise cross-correlations into posterior distributions of 1-D VS models integrated along each station pair. It allows to avoid the group velocity map construction step (which means dispersion curve extraction) while providing meaningful VS posterior uncertainties. VS models are described by a self-adapting and parsimonious parameterization using cubic Bézier splines. 1268 separately inverted 1-D VS profiles are combined together using a regionalization scheme, to build the 3-D VS model with a lateral resolution of 75 km over western France. The shallower part of the model (horizontal cross-section at 4 km depth) correlates well with the known main geological features. The crystalline Variscan basement is clearly associated with positive VS perturbations while negative heterogeneities match the Mesocenozoic sedimentary basins. At greater depths, the Bay of Biscay exhibits positive VS perturbations,which eastern and southern boundaries can be interpreted as the ocean-continent transition. The overall crustal structure below the Armorican Massif appears to be heterogenous at the subregional scale, and tends to support that both the South-Armorican Shear Zone and the Paris Basin Magnetic Anomaly are major crustal discontinuities that separate distinct domains.