Data-Driven Tool Uses Amplitude-Based Statistics To Identify Seismic Fractures
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Data-analysis tools for extracting information about critical subsurface features such as fractures are still evolving. Traditional methods rely on time-consuming iterative work flows, which involve computing seismic attributes, denoising, and expert interpretation. Additionally, the increasingly widespread acquisition of time-lapse seismic surveys has led to heightened demand for reliable automated work flows to assist in deriving feature interpretation from seismic data. The authors present a novel data-driven tool for fast fracture identification in post-stack seismic data sets.
The paper develops an automated work flow for fast and robust fracture identification that directly uses seismic amplitude data as input. Adapted from real-time face-detection methods, the proposed algorithm computes spatiotemporal amplitude statistics using Haar-like bases to characterize the seismic amplitude properties that correspond to fracture occurrence in a unit window. In this approach, the amplitude data are decomposed into a lower-dimensional collection of simple-to-calculate miniattributes, which contain gradient and curvature characteristics at varying locations and scales. These features serve as inputs to a cascade of boosted classification trees, which select and combine the most-discriminative features to develop a probabilistic binary classification model. This approach helps to eliminate the computationally intensive and subjective use of seismic attributes in existing approaches.
The proposed methodology uses a supervised learning approach. This involves specifying examples of seismic amplitude regions that either contain or do not contain fractures and subsequently presenting these examples to a binary classification scheme that develops a set of rules to distinguish between both fracture and nonfracture windows. Finally, using this trained classification model, any arbitrary amplitude section or volume can be scanned to determine the location of fractures on the basis of the rules defined within the specified window.
Training-Window Selection. Careful consideration is required in defining the dimensions of the unit window. In 2D, this unit window is a rectangular region parallel to time and space axes. In 3D, the unit window refers to a cuboidal region with one time and two space axes. The dimensions of the window in the vertical (time) direction are influenced by the time-sampling interval and the source wavelet frequency. In the lateral directions, window dimensions are influenced by the spatial sampling interval, which is a result of the survey acquisition geometry. Overall, smaller unit windows lead to higher resolution in identifying fracture presence. This, however, is achieved at the expense of fewer amplitude features to characterize the window, as well as slower scan speeds, because more regions must be visited to make predictions.
Once a seismic amplitude data set with known fracture locations and a unit window with specified dimensions has been established, multiple locations within the data set may be visited and amplitude samples extracted from both fractured and nonfractured regions.
Seismic Amplitude Characterization. Given a set of training windows containing seismic amplitudes from both fracture and nonfracture regions, the next step is to establish a set of numerical criteria for distinguishing between both cases. Using a method adapted from real-time face detection, this is achieved by computing a set of amplitude-derived Haar-like features with respect to all fracture and nonfracture training instances.
Each Haar-like feature consists of adjacent voxels of equal dimensions with symmetry along one or more axes. The feature geometries with two voxels serve to evaluate the net gradient of seismic amplitude within the unit window with respect to time and inline and crossline directions. The three-voxel features are analogous to numerical approximations of second-order gradients in orthogonal directions at multiple locations and scales. The four-voxel features capture amplitude gradients in two directions at a time, while the eight-voxel features consider amplitude gradients in all three directions simultaneously.
Thus, by representing the seismic amplitude information in fracture and nonfracture windows using Haar-like features, the data are decomposed into a rich set of miniattributes that carry both gradient and curvature information at multiple locations and scales within the unit window.
Classifier Training Framework. The next step is to define the statistical framework for distinguishing fracture and nonfracture windows within the training data set. A cascade of boosted classification tree models is used for probabilistic binary classification.
Adaptive boosting is an ensemble machine-learning framework under which the predictions made by a set of weakly discriminative models are combined (i.e., boosted) in a manner similar to a committee vote in order to yield a more-accurate prediction. One important advantage of the sequential fitting procedure is that it acts as a natural feature-selection process such that each iteration is focused on selecting the most-useful features in distinguishing between fracture and nonfracture windows; the contributions of these selected features to the final prediction are weighted relative to their individual performance.
Classifier Scanning. The output from the previous steps is a unit window within which a set of numerical rules for distinguishing between fracture and nonfracture windows has been defined by considering the most discriminative Haar-like features or miniattributes within the unit window. Using these rules, the final step in the proposed work flow is, then, to translate this template in both space and time within an arbitrary post-stack amplitude data set, each time predicting the absence or presence of fractures within the region encompassed by the window, along with the estimated fracture probability.
Results and Discussion
In order to generate synthetic data, the authors have simulated a 2D seismic survey using an interior-penalty discontinuous Galerkin elastic wave-propagation model, a process described in detail in the complete paper. Once the seismic amplitude sections have been determined, the next step is to define the dimensions of the unit window and criteria for fracture occurrence used in training-data selection. In the horizontal direction, in order to maximize resolution, the span of the unit window has been limited to three common-midpoint (CMP) samples, corresponding to 100 m in width on the basis of the survey-acquisition geometry. The fracture orientation is also worth considering when defining the spatial extent of the window, with steeply dipping fractures calling for fewer CMP samples and vice versa. In the time domain, the extent of the unit window has been limited to 2 milliseconds, which represents the period corresponding to dominant frequency of the source wavelet. The unit window and criteria for fracture occurrence are depicted in Fig. 1.
In this figure, the black rectangle represents the unit window with the specified dimensions. When this window is translated within a stack section to select training data or scan the trained model, the authors predict that the window will contain a fracture only when the fracture intersects either the top and bottom edge or the left and right edge of the unit window and is symmetrically located approximately at the center of the window, subject to a tolerance in the vertical direction.
The next step is to characterize the amplitude information by decomposition into a set of numerical features. This is achieved by computing multiple combinations of Haar-like features at various scales and locations within the unit window.
Given a pool of training windows extracted from the training windows and their associated Haar-like feature scores, the final step is to implement the cascaded classifier training framework. The final trained classifier contains a total of 1,202 weak classifiers in eight cascade stages, with a maximum of 428 weak classifiers in any stage. The overall classification accuracy with respect to a randomly selected test set is 90.1%. Next, the performance of the trained classification model has been evaluated by translating the unit window throughout the stack section and predicting fracture probability at each location.
The regions of high fracture probability are in agreement with the fracture locations indicated in the training amplitude sections. Overall, these results demonstrate the viability of the proposed approach in identifying fractures using only amplitude-based statistics.
Having established the viability of the proposed methodology for a synthetic case, the next step is to demonstrate the applicability of the work flow to identifying fractures in a 3D field data set. With this objective in mind, the authors consider the 3D post-stack seismic data from the Teapot Dome field in Wyoming, once federally owned, and for which, therefore, there is available literature on geological and geophysical studies to validate the results of the fracture-identification study. Using solely amplitude information in traces adjacent to fractured intervals, a probabilistic classification model is developed to identify subsurface fractures at multiple scales, which reproduce existing knowledge of fracture spatial distribution in the field under study. The results of the field case are described in detail in the complete paper.
Under the proposed methodology, the amplitude information is decomposed within a unit window using Haar-like features, which carry information about gradient and curvature characteristics at multiple scales and locations within the window. With the aid of a probabilistic binary classification approach, the distribution of these features within example fracture and nonfracture windows is used to develop a set of numerical criteria for identifying fractures in seismic data.
The authors present the viability of the proposed approach using both synthetic and field data for fracture identification at both macro- and subseismic scales. In the field case, the proposed approach has been validated by showing agreement between the predicted spatial fracture distribution and those reported within existing geological studies.
Data-Driven Tool Uses Amplitude-Based Statistics To Identify Seismic Fractures
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