Extending Long-Period Ambient Noise Surface-Wave Imaging in Small-Aperture Dense Arrays With Beamforming-Assisted Eikonal Tomography

Extracting reliable long-period surface waves from ambient noise cross correlation functions (CCFs) remains challenging for small-aperture dense arrays, where the interstation distances are commonly shorter than the target wavelengths. This geometric limitation leads to unstable phase-delay estimates and labor-intensive, manual dispersion analysis. Here we present a beamforming-enabled Eikonal tomography framework that integrates array beamforming with interferometric surface-wave fields to stabilize and automate phase-velocity estimation at both short and long periods. Beamforming is first applied to the CCF wavefield at each period to estimate its dominant propagation direction and associated slowness, and the individual CCFs are subsequently aligned using the estimated slowness. Relative arrival-time fields derived from these aligned CCFs are then used as input for Eikonal tomography to recover spatially continuous phase-velocity maps across the array. This approach effectively extends the measurable period range beyond the conventional aperture-limited regime while preserving computational efficiency and minimizing subjective dispersion picking. Application to a ~96-station dense seismic network in Taiwan demonstrates the retrieval of coherent long-period phase-delay wavefields and substantially improved phase-velocity maps that more clearly delineate crustal and seismogenic structures compared with conventional ambient noise tomography. Our results indicate coupling beamforming with automated Eikonal tomography provides a transferable and robust pathway for long-period imaging using existing dense arrays, yielding better constraints on deep crustal structures that are essential for tectonic interpretation and regional seismic hazard assessment in complex geological settings.