Statistical Segmentation of Geophysical Log Data
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Statistical Segmentation of Geophysical Log Data Danilo R. Velis
Received: 2 June 2006 / Accepted: 18 December 2006 / Published online: 14 August 2007 © International Association for Mathematical Geology 2007
Abstract Stationary segments in well log sequences can be automatically detected by searching for change points in the data. These change points, which correspond to abrupt changes in the statistical nature of the underlying process, can be identified by analysing the probability density functions of two adjacent sub-samples as they move along the data sequence. A statistical test is used to set a significance level of the probability that the two distributions are the same, thus providing a means to decide how many segments comprise the data by keeping those change points that yield low probabilities. Data from the Ocean Drilling Program were analysed, where a high correlation between the available core-log lithology interpretation and the statistical segmentation was observed. Results show that the proposed algorithm can be used as an auxiliary tool in the analysis and interpretation of geophysical log data for the identification of lithology units and sequences. Keywords Data mining · Segmentation · Zonation · Change point · Probability density function
Introduction Segmentation is an important data mining process. One important application is the identification of locally stationary intervals or, equivalently, the location of change points. In this context, segmentation (also known as zonation) is the dividing of a sequence into relatively homogeneous and stationary intervals such that each segment D.R. Velis () Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, La Plata, Argentina e-mail: [email protected] D.R. Velis CONICET, Paseo del Bosque s/n, B1900FWA La Plata, Argentina
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Math Geol (2007) 39: 409–417
is distinctive from the adjacent ones. Well logs can be subdivided into relatively uniform segments that represent zones of similar lithologic character (stratigraphic units and formations). Segment boundaries correspond to abrupt changes in the layering and conform the limits of relatively stable periods or geologically meaningful zones. These elementary units of similar properties can then be used as the basis for inferring correlations between wells. A different approach consists of blocking or filtering the data to get a simpler approximation (e.g. piecewise constant segments). This segmentation problem will not be considered here, and the reader is referred to, for example, Kaaresen and Taxt (1998) and the references therein for details. In this work, the focus is on the identification of statistically distinct intervals in the log sequences. There are various strategies for addressing this segmentation problem. Classical approaches include the detection of abrupt changes in the mean (Webster 1973) or in the variance (Gill 1970; Hawkins and Merriam 1973). A general description of these techniques is given in Davis (1986). Recent studies include zonation
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