Data-driven analysis of seismic phase using circular statistics

Recognizing seismic phase as a primary attribute in seismic processing workflows, we apply circular statistics, a robust data-driven approach for correcting phase distortions in prestack seismic data. Unlike traditional linear methods that struggle with wrapped phase and often defer phase diagnostics to the final processing stages, the proposed approach treats phase as a circular variable. We compute the circular mean, variance, and von Mises concentration parameter directly from phase ensembles in the frequency domain. These parameters provide insights into phase stability and coherence without needing phase unwrapping or wavelet assumptions. Synthetic tests using additive and multiplicative noise models confirm that phase distributions follow the von Mises distribution, an analog of the normal distribution for circular variables, with circular statistics reliably tracking the true phase even in low-signal-quality scenarios. Field examples demonstrate how this framework can map phase behavior across frequency and offset, enabling the detection of coherence bands and assessing the impact of each processing step on phase fidelity. The proposed approach can be particularly valuable in land acquisition, where prestack data often exhibit a low signal-to-noise ratio. Circular statistics allow us to evaluate phase integrity at each frequency, facilitating novel data conditioning and acquisition design strategies.