The automatic detection and structural characterization of deep karst features, such as vertical sinkholes and cave shafts, represent a significant challenge in remote sensing due to off-nadir satellite viewing angles, obstruction caused by dense forest canopies, and the high computational cost associated with large-scale raster data processing. This paper presents an efficient localized framework, implemented within a native web environment (BigPit_Lok software), for the identification and classification of massive vertical sinkholes in steep karst terrains. The proposed methodology employs a dual-threshold luminance binarization technique to detect shadows and adjacent illuminated limestone walls, correcting satellite image obliquity through a spatial proximity fusion algorithm validated using Ramanujan’s first approximation of the elliptical perimeter. Once the structure is confirmed, a localized 64 × 64-pixel submatrix centered on the feature centroid is subjected to a two-dimensional Fast Fourier Transform (2D FFT) using the Cooley-Tukey Radix-2 algorithm. By extracting the logarithmic magnitude spectral envelope from the central frequency row, we derive an isotropic profile that serves as a diagnostic structural signature. This profile successfully differentiates the characteristics of deep Tiangkeng-type sinkholes (such as Sótano de las Golondrinas, Sótano del Barro, and Sótano Koalitlametzin, among others), including their overall morphology, the degree of obstruction produced by surrounding vegetation, and the physical particularities of the terrain. The results demonstrate that localized frequency-domain analysis provides an efficient and low-cost alternative to airborne LiDAR and InSAR techniques for preliminary speleological prospecting and geological hazard assessment.
The Sótano de las Golondrinas is characterized by a massive, direct free-fall shaft. Its upper limestone walls descend almost vertically and, as the cave widens into a bell-shaped chamber, overhead or slightly inclined sunlight produces an extensive, clean, and highly homogeneous zone of absolute shadow within the pit. Because there are no intermediate ledges, terraces, or rock steps disrupting this shadow during the first several hundred meters of descent, the Fourier spectrum responds with a radical and clean energy decay (a very steep slope), confirming the presence of a geometrically colossal void free from major structural obstructions.
In the Fourier domain, such an extreme and abrupt gradient produces a mathematical oscillation effect (similar to the Gibbs phenomenon). The depression below the axis represents a region of “spectral silence” generated by the shadow cast by the overhanging wall into the shaft interior, which completely suppresses any medium-frequency light scattering. The spectral signature displayed by Sótano Koalitlametzin in the image (Figure 11) is particularly interesting because it reveals a morphology entirely opposite to the clean and colossal structure of Sótano de las Golondrinas.
Unlike Golondrinas, the left side of the wave corresponding to Sótano Koalitlametzin does not exhibit a clean or abrupt decay. Instead, it remains at a relatively high energy level with continuous small horizontal oscillations. This indicates the absence of a massive void or a large region of homogeneous shadow in the initial section of the cave. Rather, the terrain transitions gradually. Such behavior suggests that the cave is probably not a purely vertical free-fall shaft, but instead possesses a narrow entrance, an inclined descent ramp, or a sequence of rock terraces and ledges that partially reflect incoming light. Consequently, the internal shadow is fragmented and does not occupy a large area of uniformly dark pixels.
In the case of Sótano del Barro, the spectral signature forms an elevated horizontal “plateau” that is relatively free from noise. Because the entrance of Sótano del Barro is exceptionally large and exhibits an elongated oval geometry, the area of absolute shadow projected onto the satellite image is both extensive and highly uniform. In the Fourier domain, such a large and continuous dark region is translated into a solid block of energy concentrated within the low-frequency range. Immediately after passing the central peak toward the right, the waveform undergoes a stepped decline and stabilizes at a lower level than that observed on the left side, exhibiting only small low-amplitude oscillations (Figure 11). This behavior reveals important information about both the surrounding environment and the structure of the sinkhole rim. Unlike Sótano Koalitlametzin, which is saturated with forest-generated spectral noise, Sótano del Barro is situated within a more open environment consisting of oak woodland and semi-warm karst shrubland. Its exposed vertical limestone walls prevent vegetation from extensively colonizing or obscuring the shaft. The decay of the waveform toward the right demonstrates that high-frequency components lose energy rapidly, indicating that the algorithm does not detect excessive biological noise (leaves, branches, or dense undergrowth) interfering with the entrance of the sinkhole.