Inverting Debris Flow Basal Impact Forces from Seismic Waveforms via Deep Learning

Debris flows usually generate large basal impact forces because of their gravity-driven nature and moving mass, posing catastrophic threats to mountain communities. This basal impact force is a key parameter for understanding debris-flow dynamics and offers insights for hazard mitigation. However, developing cost-effective and easy-to-maintain approaches to measure or estimate this force remains challenging. While theoretical models have been developed to invert basal impact force from seismic signals, data-driven deep learning approaches offer greater flexibility and scalability, yet their performance for this task remains underexplored. Here, we train a Long Short-Term Memory (LSTM) model and an eXtended LSTM (xLSTM) model to invert basal impact force from debris-flow seismic signals. Formulating the inversion as a regression task, we used 2019 seismic and impact-force data from seven debris-flow events at Illgraben (Switzerland) for training and validation. The 2020-2023 dataset, comprising 21 events, was used to evaluate the trained models and empirical relationships between basal impact force and physical properties. The xLSTM performs similarly to the baseline LSTM across metrics, including root mean squared error and peak inverted basal impact force. Peak-force estimates achieve a mean absolute percentage error of ≤ 5%, equivalent to ≤10 kN. Using xLSTM, we further find a strong correlation (Pearson's r = 0.867) between observed debris-flow volume and cumulative inverted impact force, supporting volume estimation without direct flow measurements. This work provides insights into using seismic signals to estimate debris-flow physical properties, supporting seismic-based early-warning systems that extend beyond event detection to characterize event magnitude and impacts.