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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 Alarcón 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 (τ), scarp height (u0), and goodness of fit of the model on the scarp profiles and cuestas (ε). The LDA transforms the parametric space τ, u0, ε 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 ∼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.
Plain Language Summary
Geologists often have to investigate large amounts of data to identify new ideas about the processes that sculpt the Earth’s surface. The data are usually not sufficiently classified, making structure identification a time‐consuming task. The effort is especially challenging in submarine environments, given their inaccessibility and difficulty in collecting direct observations. We present a semi‐automated method for detecting faults in high‐resolution gridded bathymetry data collected by an autonomous underwater vehicle. We use a machine‐learning technique to classify fault‐line scarps based on key geomorphological attributes measured from the scarp’s erosion. The detection technique uses a brute‐force approach that systematically scans all the bathymetry data and searches for fault‐line scarps. The results of the proposed method detect fault‐scarps of different sizes and stages of degradation. Moreover, the method is robust to moderate noise (i.e., random topography and data collection artifacts) and correctly handles different fault dip angles. Tests show that both isolated and linkage fault configurations are detected and tracked reliably. The method can also get relative timing information of the faulting episodes. Getting all this information is valuable to understand the processes that shape submarine geomorphology.
Key Points
Feature extraction using the solution of the diffusion equation for modeling fault‐scarp degradation by erosion
Linear discriminant analysis technique is used for fault‐line scarp classification plus a windows search approach for detection
The method provide information of spatial distribution, slip, timing and mode of growth of fault‐line scarps