Lineament analysis is commonly undertaken by interpreting a wide range of geoscientific data to delineate geologic structures. These structures include faults, fractures, dykes, and lithological contacts, which provide information for geologic mapping and mineral and energy exploration. We offer a simple automatic lineament analysis method that combines the principles of peak-identification algorithms typically used in geophysical data interpretation and a GIS drainage “network-extraction” algorithm commonly applied to a topographic surface. We apply this network-extraction process to a magnetic surface (grid) rather than a topographic one. The GIS approach calculates the curvature of a surface to determine whether a specific coordinate is at a minimum (trough). A simple quadratic surface is computed for a moving 3 × 3 window to determine if the local surface has the form of a dipping plane (or a trough). Continuity of troughs between adjacent kernels defines lineaments that typically correspond to streamflow pathways when analysis is carried out on a topographic surface. On a magnetic anomaly map surface, network extraction identifies magnetic lows that may represent faults that have undergone magnetite (depletion) alteration, or dykes with predominantly reversed polarity remanence. As network extraction is designed to locate troughs, it is possible to isolate normally magnetized dykes by inverting the values of a magnetic data set by to produce ridges. This modified ridge analysis method is successfully applied to three synthetic data sets, showing that network extraction offers the principal benefits of continuity in solutions to produce polylines (over isolated ridge solutions), automation for consistency and reliability, and optional amplitude thresholding.