A Single-Station Localization Method (SL-MPD) to Estimate Back Azimuth and Incidence Angle, with Examples from Earth, the Moon, and Mars

Abstract Seismic event localization on planetary bodies is hampered by sparse seismographs and low signal-to-noise ratios (SNRs). Here, we develop a novel single-station localization method that extends the motion product detector (SL-MPD) to jointly estimate back azimuth and incidence angle. The SL-MPD scans rotation angles to form time-angle distributions of polarization products around P and S onsets, adaptively averages over intervals of stable polarization, and fits cosine-like angular dependencies to recover azimuth from horizontal–vertical products near P and incidence from radial–transverse products near S. The scheme explicitly compensates phase shifts across the critical angle, enabling robust operation under narrowband, strongly scattered, and noisy conditions. In synthetic heterogeneous simulations, 1000 independent tests at SNR = 1 yield a standard deviation of 5.9° for back azimuth and 3.8° for incidence angle, improving to 1.8° and 0.4° at SNR = 10, respectively. Real-data tests demonstrate cross-environment robustness: a deep earthquake recorded at 25 stations attains network-mean errors of ∼0.5° for azimuth and ∼2° for incidence after shallow-phase correction; Mars and lunar impacts produce degree-level azimuths with incidence consistent with simple models; and the A01 deep moonquake achieves small deviations at the high-SNR station S12 (azimuth within 5.4°, incidence within 0.6°). In low-SNR lunar records in which weak P limits azimuth accuracy, leveraging SP phases as supplemental constraints reduces absolute azimuth errors from 53°–68° down to 8°–40° across stations and yields consistent single-event estimates. SL-MPD operates in linear time per window, requires only narrowband segments and modest priors, and is well suited to upcoming missions (Chang’e-7, Farside Seismic Suite, Artemis III), enabling accurate, low-cost single-station localization under strong scattering and noise.