Geometric phase sensing using seismic waves for comprehensive volcano monitoring at Kı̄lauea Hawaii.

Monitoring volcanic activity requires sensitive tools capable of detecting subtle subsurface changes across eruptive cycles. While seismic methods are widely used to study volcanic unrest, few provide continuous tracking throughout eruptive stages with clearly interpretable signals. We present a geometric phase sensing approach, rooted in topological acoustics, that encodes the intrinsic geometry of the seismic wavefield. By integrating signals across a station array, the geometric phase change (Δη) captures wavepath-integrated medium perturbations, providing a stable measure of evolving subsurface conditions distinct from conventional waveform coherence metrics. Applied to Kı̄lauea volcano, Δη closely tracks precursory magmatic pressurization and co-eruptive caldera collapse during the 2018 eruption, identifies two major intrusion events and post-eruptive recovery spanning five eruptions from 2020 to 2024. Δη exhibits systematic and interpretable signatures of eruptive transitions, even under strongly perturbed ambient noise conditions. Numerical simulations corroborate these observations, indicating a sensitivity of  ~15.0% per MPa to subsurface pressure changes. By leveraging geometric phase approach, we establish a monitoring framework applicable to volcanic and other dynamic Earth systems.