Singularity spectrum of intermittent seismic tremor at Kilauea Volcano, Hawaii

Fractal singularity analysis (FSA) is used to study a 22-year record of deep seismic tremor (30–60 km depth) for regions below Kilauea Volcano on the assumption that magma transport and fracture can be treated as a system of coupled nonlinear oscillators. Tremor episodes range from 1 to 100 min (cumulative duration = 1.60×10⁴ min; yearly average = 727 min yr⁻¹; mean gradient = 24.2 min yr⁻¹ km⁻¹). Partitioning of probabilities, p_i, in the phase space of normalized durations, x_i, are expressed in terms of a function f(α), where α is a variable exponent of a length scale, ℓ. Plots of f(α) vs. α are called multifractal singularity spectra. The spectrum for deep tremor durations is bounded by α values of about 0.4 and 1.9 at f = 0; f_max ≃ 1.0 for α ≃ 1. Results for tremor are similar to those found for systems transitional between complete mode locking and chaos.