Towards an Analytical Model for the Seismic Signal Generated by Debris Flows

Debris flows are a major natural hazard in steep areas but due to their unpredictability, direct observations are rare. The seismic signals generated by these events can provide information about debris-flow location and dynamics. However, the relationship between the macroscopic parameters of debris flows and the characteristics of the associated seismic signals is still unclear. Here, we propose a simple analytical model for the high-frequency (> 1 Hz) signal generated by the multiple impacts of particles with the underlying bed over which the debris flow travels. We assume that the flow has a constant speed, thickness and density along a constant slope. The speed and rate of particle impact at the flow base are estimated using a simple kinetic theory for granular gases on a slope. From this theory, we deduce the basal force per unit surface applied by particle impacts. This force is then convolved with a Green's function that describes seismic wave propagation for a surface source. We thus obtain an expression for the seismic ground motion at a given distance from the debris flow as a function of the flow and bed parameters. We also investigate how strongly the highly agitated flow front consisting of relatively larger particles contributes to the seismic signal in comparison to the steady and uniform part of the flow. We test the analytical model using data from six experiments conducted in June 2016 at the USGS debris flow flume. The dynamics of the debris flows generated in the flume are well constrained by instrumentation. Five "smart rocks" were also introduced in some of the experimental flows to measure three component acceleration of large clasts and obtain data on the rate of particle impact and force amplitude within the flow. In parallel, the seismic signal generated by the flows was recorded by multiple seismic stations. The preliminary results allow us to quantify how much the seismic power radiated by debris flows increases when flows contains larger particles or involve a larger volume. However, we find that the frequency content is independent of particle size and flow volume and is between 1 Hz and 300 Hz. This is also observed in the theory. In addition, we observe an increase in seismic amplitude with decreasing distance to a station, but maximum seismic amplitude does not correlate with maximum debris-flow speed.