Denoising of Geodetic Time Series Using Spatiotemporal Graph Neural Networks: Application to Slow Slip Event Extraction

TL;DR

The paper tackles denoising multivariate GNSS time series to extract slow slip events (SSEs) from irregular sensor networks. It introduces SSEdenoiser, a multi-station model that fuses a graph-based recurrent network with a spatiotemporal Transformer and a learned adjacency matrix $A = \text{softmax}(\text{ReLU}(\mathbf{E}\mathbf{E}^T))$, enabling joint spatial-temporal denoising. Trained on synthetic data that combine realistic noise (via PCA and Fourier phase randomization) with Okada-derived SSE signals (temporal profile $\mathbf{d}_i(t) = \frac{D}{1+e^{-eta (t-t_0)}}$; $\beta = \frac{2}{T}\ln\left(\frac{1}{\gamma}-1\right)$), the model demonstrates sub-millimeter accuracy and outperforms baselines on synthetic tests. When applied to real Cascadia GNSS data (2007–2022), SSEdenoiser's denoised displacement rates correlate with tremor distributions, validating the approach and suggesting its utility for SSE detection and improved slip inversions. Overall, the method provides a robust, data-driven means to denoise geodetic time series and to leverage spatiotemporal structure for challenging, low-amplitude signal extraction.

Abstract

Geospatial data has been transformative for the monitoring of the Earth, yet, as in the case of (geo)physical monitoring, the measurements can have variable spatial and temporal sampling and may be associated with a significant level of perturbations degrading the signal quality. Denoising geospatial data is, therefore, essential, yet often challenging because the observations may comprise noise coming from different origins, including both environmental signals and instrumental artifacts, which are spatially and temporally correlated, thus hard to disentangle. This study addresses the denoising of multivariate time series acquired by irregularly distributed networks of sensors, requiring specific methods to handle the spatiotemporal correlation of the noise and the signal of interest. Specifically, our method focuses on the denoising of geodetic position time series, used to monitor ground displacement worldwide with centimeter- to-millimeter precision. Among the signals affecting GNSS data, slow slip events (SSEs) are of interest to seismologists. These are transients of deformation that are weakly emerging compared to other signals. Here, we design SSEdenoiser, a multi-station spatiotemporal graph-based attentive denoiser that learns latent characteristics of GNSS noise to reveal SSE-related displacement with sub-millimeter precision. It is based on the key combination of graph recurrent networks and spatiotemporal Transformers. The proposed method is applied to the Cascadia subduction zone, where SSEs occur along with bursts of tectonic tremors, a seismic rumbling identified from independent seismic recordings. The extracted events match the spatiotemporal evolution of tremors. This good space-time correlation of the denoised GNSS signals with the tremors validates the proposed denoising procedure.

Figures (7)

• Figure 1: Overview of the synthetic data generation. (a) Each row of the matrices represents a synthetic detrended GNSS position time series (E-W component) color-coded by the amplitude of displacement, created using the proposed synthetic data generation technique. Starting from the left: artificial noise $n(t)$, modeled SSE signals $d(t)$, synthetic GNSS time series $\xi(t)=n(t)+d(t)$. (b) The red triangles represent the location of the GNSS stations (MAGNET GNSS network) used in this study. The arrows show the static synthetic displacement modeled at each GNSS station. In this example, the SSE signal is modeled through three dislocations, shown with different colors (red, green, blue), slipping in an elastic half-space with a different slip amount, slip initiation time, and slip duration. The synthetic displacement time series associated with each dislocation are identified by rectangles in the $d(t)$ matrix in the (a) panel with the same color. The light blue contour represents the SSE area, e.g., the locations of the generated synthetic slow slip events.
• Figure 2: High-level architecture of SSEdenoiser. GNSS time series are first processed by a graph-based recurrent neural network, where temporal features are extracted and spatial relationships are inferred by learning the adjacency matrix. A spatiotemporal Transformer is then used, where temporal and spatial self-attentions attend to the learned temporal features and the spatial relationships. At the end of the pipeline, a fully connected network reprojects the Transformer's output to the input dimension to produce the denoised GNSS time series.
• Figure 3: Evaluation of the denoising power as a function of the signal-to-noise ratio for the tested deep-learning models, namely single_station_RNN, 2D_conv_u_net and SSEdenoiser. The average absolute error (see equations \ref{['eq:denoising-error']} and \ref{['eq:avg-denoising-error']}) for a given SNR bin is plotted.
• Figure 4: Evaluation of the denoising power as a function of the signal-to-noise ratio for the ablated models, namely no_transformer, spatial_attention_only and temporal_attention_only, against SSEdenoiser. The average absolute error for a given SNR bin is plotted.
• Figure 5: Graph connectivity learned by SSEdenoiser. (a) learned adjacency matrix. Nodes are sorted by latitude and color-coded by the learned edge strength. (b) Geographic representation of the strongest connections (edge strength values in the range (0.008, 0.0234) color-coded by edge strength). (c) GNSS stations used in this study, color-coded by the learned station importance, i.e., the value of the diagonal of the adjacency matrix for each node.