Interpolation strategy based on Dynamic Time Warping

Abstract

In oil industry, it is essential to have the knowledge of the stratified rocks’ lithology and, as consequence, where are placed the oil and the natural gases reserves, in order to efficiently drill the soil, without a major expense. In this context, the analysis of seismological data is highly relevant for the extraction of such hydrocarbons, producing predictions of profiles through reflection of mechanical waves in the soil. The image of the seismic mapping produced by wave refraction and reflection into the soil can be analysed to find geological formations of interest. In 1978, H. Sakoe et al. defined a model called Dynamic Time Warping (DTW)[23] for the local detection of similarity between two time series. We apply the Dynamic Time Warping Interpolation (DTWI) strategy to interpolate and simulate a seismic landscape formed by 129 depth-dependent sequences of length 201 using different values of known sequences m, where m = 2, 3, 5, 9, 17, 33, 65. For comparison, we done the same operation of interpolation using a Standard Linear Interpolation (SLI). Results show that the DTWI strategy works better than the SLI when m = 3, 5, 9, 17, or rather when distance between the known series has the same order size of the soil layers.