Neighborhood Width Transform: A Structural Stability Framework for Peak Selection in Noisy 1D Coherence Curves

Slowness extraction via Slowness Time Coherence (STC) serves as a fundamental technique for formation evaluation in oil and gas geophysics. Conventional amplitude-dependent peak selection methods often exhibit limitations in complex logging scenarios, including weak wave arrivals, high noise floors, and spurious local maxima. To address these challenges, this paper proposes Neighborhood Width Transform (NWT), an unsupervised data-driven mathematical framework that distinguishes genuine peaks from noise by quantifying local neighborhood structural stability rather than relying on amplitude magnitude. The core of NWT lies in a bilateral neighborhood width metric and a minimum-pooling fusion strategy, which suppresses narrow pseudo-peaks effectively. Experimental validation demonstrates that the proposed method outperforms seven representative peak-selection baseline methods (CWT Ridge Analysis, Gaussian Mixture Fitting, AMPD, SG Derivative Crossing, NMS, Random Forest, and 1D-Unet) in terms of detection reliability and accuracy on the tested challenging logging datasets. The proposed method provides an interpretable, high-throughput mathematical solution for automated geophysical signal processing.