DDSync: Denoising and outlier removal in differential travel-time observations using graph synchronization

Differential travel-time observations from waveform cross-correlation are among the most precise measurements in observational seismology and underpin high-resolution relative relocation. In large modern catalogs, however, HypoDD-style pair files (dt.cc) often contain outliers, cycle skipping, and internally inconsistent links that can bias downstream workflows, particularly cluster-based relocation pipelines. We present DDSync, a lightweight preprocessing method that treats the differential-time measurements for each station–phase as a weighted event graph and solves a graph synchronization problem to recover a self-consistent set of relative arrival-time proxies (one scalar per event and station–phase). The baseline estimator is a sparse weighted least-squares solution of a graph Laplacian system, which implicitly averages over redundant constraints in dense graphs and yields stable long-baseline differentials without enumerating paths.

DDSync adds two robustness layers. First, it computes an edgewise inconsistency diagnostic from the global fit (a loop-closure-style residual) and prunes grossly inconsistent links using a MAD-based threshold, with automatic re-identification of connected components. Second, it refines the solution using iteratively reweighted least squares, with a Huber loss to downweight remaining heavy tails while preserving connectivity. Beyond producing cleaned and synchronized dt.cc files, DDSync estimates uncertainty in the synchronized results by approximating per-event variance of the inferred potentials using a stochastic diagonal estimator of the inverse reduced Laplacian, and propagating these to conservative pairwise σ estimates and weights for downstream inversions.

We evaluate DDSync on the Ridgecrest synthetic benchmark of Yu et al. (2025), where differential times are perturbed with Laplacian-distributed errors and outliers added, and show near complete removal of gross outliers and strong tightening of residual distributions relative to ground truth, reducing error by about a factor of 5. The inferred uncertainty on the denoised observations capture station–phase and event-specific constraint quality and provide a practical, uncertainty-aware weighting scheme for relocation and related inverse problems. We also highlight a subglacial volcanic example with distinct event family types (icequake and VT events) where pruning preferentially removes inconsistent links that bridge otherwise separated event families, improving interpretability and robustness for analysis of dense catalogs.