Spectral Analysis of Topography as Proxy for Lineament Analysis

Abstract

Spectral analysis (SA) for image processing, utilizing the Fast Fourier Transform (FFT), computes the 2D power spectrum to capture the amplitude of each frequency component of an image. Recent studies have applied SA on digital elevation models (DEMs) to characterize repetitive and spatially homogeneous landforms in terms of their orientation, frequency, and amplitude. Here, we advance the application of SA by introducing a new preprocessing step and an appropriate windowing function, tailored to analyze heterogenous and complex topographies and derive lineament spatial distributions. The validation of our approach involved two phases: (a) testing on synthetic images, and (b) application to a case study. The synthetic image validation illustrated the length-weighted characteristics of SA-derived rose diagrams and the robustness of the method, evidenced by a 99% similarity across 1,000 synthetically generated lineament networks. The case study consisted of three areas characterized by different topographic patterns within the Oslo region of Norway. The SA-derived results were compared to lineaments automatically extracted using a conventional peak-and-valley seeking algorithm that mimics manual tracing of lineaments inside a 3D map domain. The comparison showed similarity better than 90%. Lastly, we addressed a key pitfall of SA by locating signatures observed in the power spectrum on the map through cross-correlation (CC) of profiles. Although CC results are not consistently perfect, they provide a promising avenue for further development.