Disclaimer: these examples are mostly taken from my pre-Eikomagos career
After a hole is drilled into the ground and the core is removed, the borehole is imaged with a resistivity measurement tool consisting of four pads. The result is visualised in figure 1. Note that the pads do not cover the entire wall. Regular striata (bedding) can be observed as well as fracture planes. One is highlighted. These planes are of particular interest.
Figure 2 shows the 2D wall image of another sample. Here it may be observed that planar intersections with the borehole manifest themselves as sinusoids. Detecting these is complicated due to:
A standard approach to extract the sinusoids would be: edge detection+Radon transform. Here, we replaced the edge detection step by an orientation space. The image I(φ,z) is transformed into a 3D volume O(z,ψ,φ) which registers the amount of evidence for a line/edge under orientation φ at (z,ψ): orientation selective edge/line detection. Fractures and bedding are separated in orientation space (fig 3). The elongated filters that are used to compute O(z,ψ,φ) also suppress noise.
The (generalised) Radon transform R(A,ψ0,d) computes the amount of evidence for a sinusoid with amplitude A, phase ψ0 at depth d taking the orientation space O as its input. Peaks in R(A,ψ0,d) correspond to potential fractures.
Some measurements are performed on the candidate fractures to weed out poor detections; for details we refer to the paper. Figure 4 shows how well the algorithm fares against a trained geologist.