A reverse-time source-point gather framework for evaluating 3-D crustal velocity models using ambient-noise surface waves

Reliable evaluation of three-dimensional seismic velocity models is critical for wave-propagation simulations and seismic hazard assessment, yet remains challenging in tectonically complex regions where source-related uncertainties and strong lateral heterogeneity limit conventional validation approaches. Here we present a propagation-centered framework for velocity-model evaluation based on reverse-time source-point gathers constructed from ambient-noise–derived surface waves.

Empirical Green’s functions are retrieved from ambient-noise cross correlations and reverse-time propagated under candidate velocity models to virtual source locations. If a velocity model adequately captures the kinematic characteristics of wave propagation, back-propagated wavefields from different azimuths and offsets refocus coherently near the zero-time reference. Systematic time shifts in the reverse-time source-point gathers indicate kinematic inconsistencies and reveal velocity biases. We quantify this behavior using the arrival-time deviation, Δt, and analyze its dependence on period, offset, and azimuth.

We apply this framework to evaluate four recently developed three-dimensional S-wave velocity models in the Sichuan–Yunnan region, southwest China. The results reveal clear model-dependent patterns in back-propagated arrivals across multiple period bands. At short periods (5–10 s), the back-propagated arrivals are more scattered in time and exhibit stronger directional variability, indicating that the tested velocity models still have limited accuracy in representing shallow structures and local-scale heterogeneity. In contrast, at longer-period waves (15–45 s), the back-propagated wavefields refocus more coherently at the virtual source, with arrival times clustering closer to zero, suggesting that the models are able to reproduce the large-scale characteristics of wave propagation more consistently. Consistent trends observed across multiple virtual source locations highlight both regional-scale performance differences and azimuth-dependent kinematic biases among the tested models.

The proposed reverse-time source-point gather approach offers a source-robust and physically intuitive perspective for velocity-model evaluation. By emphasizing kinematic self-consistency of wave propagation rather than detailed waveform matching, this framework complements existing evaluation methods and provides a flexible tool for diagnosing the strengths and limitations of three-dimensional velocity models in structurally complex regions.