Improving UAV Magnetic Surveys with a Theory-Guided Empirical Model for Locating and Characterizing Undocumented Orphaned Oil and Gas Wells

Undocumented orphaned oil and gas wells can pose risks through unintended releases of substances, yet they remain difficult to locate because records are incomplete and surface indicators are often absent. Unmanned aerial vehicle (UAV) magnetometry is increasingly used to identify steel-cased wells, but surveys commonly stop at target detection and provide limited guidance on how sensor height affects anomaly strength, burial-depth estimates, or confidence in non-detection. Here, we develop a physics-informed, calibrated empirical model between peak magnetic-anomaly amplitude and distance from the magnetometer to the top of steel casing. Using anomaly amplitude measured at known sensor height, the model provides three practical outputs: estimated casing-top burial depth where casing is not visible, maximum sensor height at which casing at a specified depth remains detectable, and correction of variable-height anomalies to a common reference height. We calibrate the relationship using multi-altitude UAV surveys at Wildcat Canyon Regional Park, California, and Osage Ranch, Oklahoma, and apply it at Hillman State Park, Pennsylvania, identifying one undocumented-well candidate supported by ground magnetometry and estimating burial depths for three documented wells consistent with independent depth constraints.