Real-Time Reconstruction of Ground Motion During Small Magnitude Earthquakes: A Pilot Study

TL;DR

This work addresses real-time reconstruction of ground motion for small magnitude earthquakes, modeled as $M<4.5$, using sparse sensor data and the Gappy Auto-Encoder (Gappy AE) to bypass expensive source characterization and full-wave simulations. The method learns a nonlinear latent manifold via a shallow, sparse encoder–decoder and reconstructs full-field data by solving a Gauss-Newton optimization over latent coordinates using sparse measurements, with sampling strategies including DEIM to select informative points. Numerical experiments on SW4 simulations show reconstruction errors in the low-to-mid single digits for MGV/MMI and online step times on the order of a few milliseconds (e.g., ~6.63 ms per step with 61 DEIM samples), indicating practical real-time capability. Field-data tests on the 2018 Berkeley Mw ~4.37 event demonstrate potential applicability but also reveal limitations due to domain mismatch between training data and real subsurface structure, motivating future work on noise robustness and regional-scale extension for improved reliability.

Abstract

This study presents a pilot investigation into a novel method for reconstructing real-time ground motion during small magnitude earthquakes (M < 4.5), removing the need for computationally expensive source characterization and simulation processes to assess ground shaking. Small magnitude earthquakes, which occur frequently and can be modeled as point sources, provide ideal conditions for evaluating real-time reconstruction methods. Utilizing sparse observation data, the method applies the Gappy Auto-Encoder (Gappy AE) algorithm for efficient field data reconstruction. This is the first study to apply the Gappy AE algorithm to earthquake ground motion reconstruction. Numerical experiments conducted with SW4 simulations demonstrate the method's accuracy and speed across varying seismic scenarios. The reconstruction performance is further validated using real seismic data from the Berkeley area in California, USA, demonstrating the potential for practical application of real-time earthquake data reconstruction using Gappy AE. As a pilot investigation, it lays the groundwork for future applications to larger and more complex seismic events.

Figures (16)

• Figure 1: Simulation domain in the Berkeley area, outlined by the black rectangular box. Point-source earthquakes are positioned along the thick white line.
• Figure 2: Autoencoder MSE Loss
• Figure 3: Gappy AE Projection Error (The data index is used to indicate each parameter combination.)
• Figure 4: Sampling Points
• Figure 5: Gappy AE Reconstruction Error