A physical model of the high-frequency seismic signal generated by debris flows

Abstract

We propose a physical model for the high‐frequency (>1 Hz) spectral distribution of seismic power generated by debris flows. The modeled debris flow is assumed to have four regions where the impact rate and impulses are controlled by different mechanisms: the flow body, a coarser‐grained snout, a snout lip where particles fall from the snout on the bed, and a dilute front composed of saltating particles. We calculate the seismic power produced by this impact model in two end‐member scenarios, a thin‐flow and thick‐flow limit, which assume that the ratio of grain sizes to flow thicknesses are either near unity or much less than unity. The thin‐flow limit is more appropriate for boulder‐rich flows that are most likely to generate large seismic signals. As a flow passes a seismic station, the rise phase of the seismic amplitude is generated primarily by the snout while the decay phase is generated first by the snout and then the main flow body. The lip and saltating front generate a negligible seismic signal. When ground properties are known, seismic power depends most strongly on both particle diameter and average flow speed cubed, and also depends on length and width of the flow. The effective particle diameter for producing seismic power is substantially higher than the median grain size and close to the 73rd percentile for a realistic grain size distribution. We discuss how the model can be used to estimate effective particle diameter and average flow speed from an integrated measure of seismic power.