Two-Step Infrasound Source Localization Method Integrating Spherical-Coordinate Ray Tracing

Infrasound waves attenuate weakly in the atmosphere and can propagate over regional, teleseismic, and global distances, which makes them valuable for monitoring artificial explosions, volcanic eruptions, earthquakes, and nuclear test-related events. Conventional infrasound localization based on the intersection of array back azimuths are computationally efficient, but it often approximates propagation paths as straight geometric rays and therefore cannot fully represent wind fields, temperature gradients, atmospheric waveguides, or Earth curvature. To address this limitation, this paper presents a two-step localization method that couples geometric preliminary localization with local travel-time residual optimization constrained by spherical-coordinate ray tracing. First, multi-station arrival azimuths are intersected, and k-means clustering with least-squares estimation is used to obtain a robust initial source position. Second, a local grid is constructed around the initial solution; for each candidate source, theoretical travel times to the recording stations are calculated using a ray-tracing model for a moving, inhomogeneous atmosphere in spherical coordinates. The final source location is selected by minimizing multi-station travel-time residuals. The method is tested using three representative events: the 2018 Ingolstadt refinery explosion, the 2019 Stromboli eruption, and the 2022 Hunga eruption. The final localization errors are 13.23 km, 5.93 km, and 6.98 km, respectively, corresponding to accuracy improvements of more than 84% relative to conventional geometric localization. The results show that incorporating atmospheric propagation constraints and local residual optimization can substantially reduce systematic bias while maintaining computational efficiency.