Seismic modelling and observations of rainfall

Abstract

Rainfall is a key driver of geomorphological processes ranging from impacting drops that lead to the small-scale dislodgement of soil particles to large-scale morphogenic floods and rainfall-induced hillslope processes. Although rainfall has been identified in seismic records, the associated power spectral density and its quantitative relation to the underlying physical processes have not yet been studied. Here, we analyze nearly 2 years of combined seismic and optical disdrometer measurements, where the latter enables the drop-based quantification of rainfall physical properties. Our measurements confirm the broadband observation of ground velocity power spectral density due to rainfall, allowing the seismic identification of rainfall at intensities as low as 1 mm/h. Seismic power, P, shows a power-law scaling with rainfall intensity, I, and kinetic energy, E: P∝I2.1 and P∝E1.6. The observed scaling relations are consistent between the three monitored sites although there are absolute differences in seismic power of about 1 order of magnitude, which are likely due to variability in landcover and subsurface seismic properties. With a physical model, we demonstrate that the observed power-law relations are set by an underlying linear relation between seismic power and rainfall impulse power, and that the associated exponent values of I and E are due to the covariance of the raindrop size distribution with the total number of drops. The largest raindrop fractions, whose relative contribution increases with rainfall intensity, dominate the seismic signal where, in our case, 90% of the seismic power is attributed to drops larger than 3 mm. Using our model, we estimate the contributing area of rainfall to seismic observations to be within a radial distance of ∼5–25 m. The spatially integrated nature of the seismic measurements and their sensitivity to large raindrops, which control the disaggregation and the mobilization of soil particles, make seismic records well-suited for the investigation of soil erosion processes. More generally, our work provides a basis for the temporally-resolved seismic quantification of rainfall that drives the dynamics of various hydro-geomorphological processes.