Sparse VLF/LF Lightning Location: Propagation Correction and Accelerating-Charge-Based Peak-Field Consistency

Sparse very-low-frequency/low-frequency (VLF/LF) lightning location is a ground-based passive remote-sensing technique, but sparse station geometry and finite-conductivity propagation can shift peak arrival times, alter peak amplitudes, and produce spurious solutions. This study proposes a three-station method integrating propagation correction with accelerating charge method (ACM)-based peak-electric-field consistency. Based on the Liénard–Wiechert field, the ACM relates the radiation field to charge acceleration and assumes a common source-side peak for the same return stroke. For given ground conductivity, relative permittivity, and an ACM reference field, the range-dependent additional delay τE corrects TDOA to obtain candidate locations. After candidate coordinates are fixed, the peak-retention factor AE, candidate-to-station distances, and local response Ki recover equivalent source-side peaks, while Jamp discriminates between correct and spurious candidates. In simulations, the in-network location error decreased from 46.0 to 21.8 m and the out-of-network error from 1867.3 to 394.8 m; the ACM-based criterion selected the correct candidate in both cases. For the S7–S8–S9 rocket-triggered-lightning case, the near-candidate error decreased from 1.333 to 0.360 km, and Jamp values of 0.0419 and 0.2238 distinguished the correct and spurious solutions. The method therefore improves sparse VLF/LF lightning location accuracy through propagation-time correction and supports spurious-solution discrimination through propagation-corrected peak-field consistency.