A New Method for Fault-Scarp Detection Using Linear Discriminant Analysis in High-Resolution Bathymetry Data From the Alarcon Rise and Pescadero Basin

The linear discriminant analysis (LDA) is a common technique used in machine learning and pattern recognition for dimensionality reduction problems. Here, the LDA is applied to detect faults-scarps in high-resolution bathymetric profiles in the Southern Pescadero Basin (SPB) in the Gulf of California. The LDA uses fault scarps and cuestas (sloping topography) identified by a geomorphologist in the neighboring Alarcon Rise (AR). These geometric representations are transformed into a parametric space by an idealized fault-scarp degradation model. Through inversion, we extracted the product of the mass diffusion coefficient with time (tau), scarp height (u(0)), and goodness of fit of the model on the scarp profiles and cuestas (epsilon). The LDA transforms the parametric space tau, u(0), epsilon by the Fisher's criterion into a 1D dimensional space that maximizes separability of classes. Then, the classification is performed by Bayes decision rule using the probability density functions (PDF) built from the 1D projected data for each class (fault-scarps and cuestas). The implementation results in cross-sectional profiles across the SPB show the ability to detect faults in the deepest part of the basin where the flat basin floor is interrupted by morphologically young fault-scarp arrays. The LDA interpretation outperforms manual identification, particularly in faults scarps that are longer than similar to 3 km, whereas shorter faults are challenging to discern from other linear features like channels. The model can extract information about the state of degradation of the scarps. This application allows the identification of fault generation episodes and resolves kinematic interactions between faults.