Statistical methods of fracture characterization using acoustic borehole televiewer log interpretation

Abstract

Acoustic borehole televiewer (BHTV) logs provide measurements of fracture attributes (orientations, thickness, and spacing) at depth. Orientation, censoring, and truncation sampling biases similar to those described for one‐dimensional outcrop scanlines, and other logging or drilling artifacts specific to BHTV logs, can affect the interpretation of fracture attributes from BHTV logs. K‐means, fuzzy K‐means, and agglomerative clustering methods provide transparent means of separating fracture groups on the basis of their orientation. Fracture spacing is calculated for each of these fracture sets. Maximum likelihood estimation using truncated distributions permits the fitting of several probability distributions to the fracture attribute data sets within truncation limits, which can then be extrapolated over the entire range where they naturally occur. Akaike Information Criterion (AIC) and Schwartz Bayesian Criterion (SBC) statistical information criteria rank the distributions by how well they fit the data. We demonstrate these attribute analysis methods with a data set derived from three BHTV logs acquired from the high‐temperature Rotokawa geothermal field, New Zealand. Varying BHTV log quality reduces the number of input data points, but careful selection of the quality levels where fractures are deemed fully sampled increases the reliability of the analysis. Spacing data analysis comprising up to 300 data points and spanning three orders of magnitude can be approximated similarly well (similar AIC rankings) with several distributions. Several clustering configurations and probability distributions can often characterize the data at similar levels of statistical criteria. Thus, several scenarios should be considered when using BHTV log data to constrain numerical fracture models.

Evidence for tectonic, lithologic, and thermal controls on fracture system geometries in an andesitic high‐temperature geothermal field

“…K‐means clustering of fracture orientation identified in the BHTV logs, supported by fuzzy K‐means and agglomerative clustering, yields four fracture sets (FS1 to FS4; see detailed analysis in Massiot et al []). For each borehole and the combined data set, there are two best configurations: (1) with two fracture sets and (2) with either three or four fracture sets (Figure ).…”

“…Similarly, the separation of FS2 from FS1 in borehole RK30L1 using Fisher contours is different from the one obtained by K‐means clustering. In addition, such a configuration in borehole RK30L1 with three fracture sets made from Fisher contours is statistically less robust than with either two or four fracture sets (see discussion in Massiot et al []).…”

“…The probability distribution form and parameters of the fracture thickness and spacing are evaluated following methods described in Massiot et al [] and summarized briefly herein. Five probability distributions commonly found in geological systems, namely, negative exponential, lognormal, gamma, power law, and power exponential [ Bonnet et al , ], are fitted to the fracture thickness or spacing populations within truncation bounds, i.e., where the data are inferred to be fully sampled.…”

“…Ex: exponential; Ga: gamma; LN: lognormal; Pa: pareto. Listed distribution parameters and 95% confidence intervals are those of the highest AIC rank distribution, and displayed as according to the number of parameters of each distributions (probability distribution formulas in Stasinopoulos and Rigby [] and Massiot et al []).…”

“…To limit the sampling effects caused by variable BHTV log quality, analysis is only conducted within zones of poor to good quality (i.e., where ≥25% of the circumference of the borehole was observed) [ Massiot et al , ]. Statistical analysis performed on zones of moderate to good quality (≥50% of the circumference of the borehole was observed) provided similar spacing and thickness distribution forms and parameters to those in zones of poor to good quality, albeit less well constrained due to reduced number of data points (see analysis in the companion paper [ Massiot et al , ], which uses the same data set). A total of 1133 fractures were sampled over a cumulative borehole interval of 2074 m (measured along the length of the deviated boreholes; Table and Figure b).…”