Rapid and Consistent Identification of Stratigraphic Boundaries and Stacking Patterns in Well-logs - An Automated Process Utilizing Wavelet Transforms and Beta Distributions
Authors: Ye Shin-Ju , Wellner Robert W. , Dunn Paul A. 
Published: October 2017

Abstract
Historically, well log response and pattern matching have been used to define surface-based stratal frameworks, identify depositional facies, and distribute rock properties within subsurface geologic models. Framework surfaces are typically defined by relatively abrupt changes in lithologic trends and/or log curve shape. However, the significance, types, and locations of surfaces defined using this subjective technique can be highly variable and can result in significantly different interpretations. The semi-automated, well log pattern recognition methodology proposed here mitigates many of these inconsistencies and can yield more accurate frameworks by detecting and highlighting patterns in suites of logs that may otherwise have been missed by an interpreter.
This innovative method is capable of identifying, with little or no user input, the stratal stacking pattern expressed in a typical oil-field well log suite. Furthermore, this method generates a hierarchy of surface bounded, rock packages that can used to build a consistent, repeatable stratigraphic framework for a field or basin, by removing interpreter-specific biases. This new method can detect subtle, but stratigraphically important breaks in deposition or erosion, which if ignored will result in stratal architectures with little or no predictive capability.
A typical one-dimensional well log signal can be transformed into a joint, two-dimensional wavelet-scale and log-depth representation using a continuous wavelet transform (CWT). The resulting multi-scale CWT phase image of a well log exhibits (after mirroring) oval-shaped patterns that correspond surface-bounded depositional packages. The nesting and encapsulation of smaller ovals by larger ovals reveals multi-scale hierarchical patterns carried within the well log signal that is not readily apparent upon visual inspection. In order to extract the boundary information from CWT phase images, a significance-of-cone (SOC) method has been developed to quantify the significance of the smoothed cones located at the tops and bases of the CWT mirrored ovals. Ranked, hierarchical boundaries are then derived from the integration of SOC curves from all available logs each weighted according to interpreter wishes. In summary, individual CWT-derived ovals represent discrete depositional packages, while the SOC-derived surfaces may reflect the extent to which individual sedimentary packages are genetically linked or separated by discontinuities.
The utility and accuracy of this automated method was tested on a suite of logs from the Mannville Group, lower Cretaceous of Alberta, Canada. Here, we compared CWT results to a subset of wells (~40 wells) from a larger dataset of &gt;200 wells in regional cross sections that were analyzed over many months and used to define a sequence stratigraphic framework for a portion of the Mannville Group. Of the 1400+ surfaces (tops) identified using the classic, but time consuming sequence stratigraphic approach, we were able to rapidly identify and replicate 75% of the manually identified tops, generally to within ±1 meter of significant boundaries picked by the program. Furthermore, we argue that the surfaces that comprise the missing 25% may not be significant, framework building surfaces and could be ignored with little effect on the understanding of the Mannville Group stratigraphy.
A spectrum of simple and common curve shapes, such as coarsening-upward, fining-upward, bell, funnel and cylindrical shapes can be described by two shape parameters, which are referred to as α and β, within a Beta distribution. A numerical method has been developed to fit a Beta distribution to diagnostic shapes observed on well log curves. Each Beta-distribution curve shape can be represented by a point on an α-β cross plot, which allows visualization of curve shape related interpretations in absolute parametric space. Well log curve shapes within and among stratigraphic units can be visualized using appropriate color coding and interactivity between a 3D or map view and the α-β cross plot. This method provides an efficient and consistent foundation for well log lithofacies distributions within stratigraphic units or zones and provides a solid foundation for interpretation of depositional facies and 3-D modeling of rock properties.