Magma sloshing in a three dimensional crater and its constraint on lava lake viscosity during the 2018 Kilauea Volcano eruption

Magma viscosity is a crucial physical parameter that controls the eruptive behavior of active volcanoes, yet methods for constraining it in the in-situ condition remain limited. Lava lakes, such as that on Kilauea Volcano, are frequently perturbed by observable degassing and rockfalls, producing very long period (VLP) magma sloshing motion recorded by near-field broadband seismometers. Particularly, the decaying characteristic of VLP seismic signal reveals the rate of energy dissipation during magma sloshing and can be used to constrain the in-situ magma viscosity. However, previous models either assume zero viscosity or simplistic crater geometries (2D wedge or 3D cylinder) that prevent the full exploitation of the seismic data. In this work, we present the first computational model that captures the sloshing of viscous magma in a realistic 3D crater geometry and apply it to interpret the VLP sloshing signals at Kilauea Volcano during its 2018 eruption. By assimilating the accurate 3D geometry of the Halemaumau crater and lava lake level data, we successfully match the periods of multiple lake sloshing modes in the 10-20 s band of the seismic data with minimal parameter tuning. We then focus on modeling the decaying rates of the longest sloshing mode by adjusting the kinematic viscosity of the lava lake. As the lava lake level drops, an increasing kinematic viscosity matches the increasing periods and decreasing quality factor (from 80 to 16). Due to strong viscous damping and weak coupling efficiency at a reduced fluid density, the sloshing modes ceased to be observable from the seismograms after a certain moment between May 5 and May 6th. The notable reduction of magma density is confirmed by a drop in the period of fundamental mode caused by resonance of the underlying conduit and reservoir system. Our work demonstrates that integrating numerical simulation of lava lake dynamics and geophysical observations provides critical constraints on magma physical properties, such as viscosity and density, which gives further insight into the evolution of the underlying volcanic processes. The numerical framework is also applicable to many other cases with liquid sloshing.