Stick-Slip at the Kilometer Scale: Estimating Rate and State Friction Parameters from Modeling Repeated Caldera Collapse Events at Kīlauea Volcano in 2018

Abstract:

Laboratory friction tests are restricted to samples centimeters to at most a few meters in size. Questions thus remain as to the applicability of derived constitutive properties to faulting in situ. This is particularly true for the characteristic slip distance, d_c ,which is observed to scale with fault roughness and is therefore challenging to extrapolate to natural conditions. This in turn hampers the utility of continuum models of faulting with rate and state friction, which are otherwise capable of explaining many features of faulting in nature.

The 2018 eruption of Kīlauea volcano, Hawaii, resulted in collapse of the summit caldera in 62 highly repeatable events in which the caldera floor dropped 2-8 meters, accompanied by M_W 5.2-5.4 long period earthquakes. Collapse events were recorded by continuous GPS receivers and tiltmeters. High-rate GPS data indicate that collapse occurred in 5-10 seconds. Stations outside the caldera record “inflationary” deformation during collapse driven largely by pressurization of the underlying magma reservoir.

We develop a lumped parameter model of a cylindrical piston collapsing into a magma reservoir. Pressure at the piston base and shear stress on its margin balance its weight. Downward motion of the piston compresses the underlying magma, which drives flow out to the eruption site. With sufficiently compressible magma the system of equations exhibit stick-slip cycles.

A Monte Carlo estimation is used to estimate system constants, including rate-state parameters, by comparing model predictions with observed inter-event period (~1.4 days), collapse duration (5-10 s), the amplitude of the pressure increase (determined by modeling GPS displacements, Segall et al, GRL in press), and the vertical displacement during collapse. We find that the nominal friction coefficient f₀ is restricted to the range 0.2-0.7, the steady-state velocity dependence b-a is 0.003 to 0.007, and d_c is constrained to be less than 0.1 meters. Furthermore, for d_c in excess of a few mm the predicted pre-collapse deformation exceeds that permitted by stacks of the GPS time series.

We conclude that d_c for kilometer scale stick-slip events in basalt cannot exceed a few millimeters. Modeling repeatable macroscopic collapse events provides important complements to laboratory scale experiments.