A Dynamic Time Warping based covariance function for Gaussian Processes signature identification

Abstract

Modelling stratiform deposits requires a detailed knowledge of the stratigraphic boundaries. In Banded Iron Formation (BIF) hosted ores of the Hamersley Group in Western Australia these boundaries are often identified using marker shales. Both Gaussian Processes (GP) and Dynamic Time Warping (DTW) have been previously proposed as methods to automatically identify marker shales in natural gamma logs. However, each method has different advantages and disadvantages. We propose a DTW based covariance function for the GP that combines the flexibility of the DTW with the probabilistic framework of the GP. The three methods are tested and compared on their ability to identify two natural gamma signatures from a Marra Mamba type iron ore deposit. These tests show that while all three methods can identify boundaries, the GP with the DTW covariance function combines and balances the strengths and weaknesses of the individual methods. This method identifies more positive signatures than the GP with the standard covariance function, and has a higher accuracy for identified signatures than the DTW. The combined method can handle larger variations in the signature without requiring multiple libraries, has a probabilistic output and does not require manual cut-off selections.