Successful leveraging of image processing and machine learning in

Successful leveraging of image processing and machine learning in seismic structural interpretation: A review Zhen Wang1, Haibin Di1, Muhammad Amir Shafiq1, Yazeed Alaudah1, and Ghassan AlRegib1 Downloaded 06/13/18 to 163.185.148.245. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/

https://doi.org/10.1190/tle37060451.1.

Abstract

As a process that identifies geologic structures of interest such as faults, salt domes, or elements of petroleum systems in general, seismic structural interpretation depends heavily on the domain knowledge and experience of interpreters as well as visual cues of geologic structures, such as texture and geometry. With the dramatic increase in size of seismic data acquired for hydrocarbon exploration, structural interpretation has become more time consuming and labor intensive. By treating seismic data as images rather than signal traces, researchers have been able to utilize advanced image-processing and machine-learning techniques to assist interpretation directly. In this paper, we mainly focus on the interpretation of two important geologic structures, faults and salt domes, and summarize interpretation workflows based on typical or advanced imageprocessing and machine-learning algorithms. In recent years, increasing computational power and the massive amount of available data have led to the rise of deep learning. Deep-learning models that simulate the human brain’s biological neural networks can achieve state-of-the-art accuracy and even exceed human-level performance on numerous applications. The convolutional neural network — a form of deep-learning model that is effective in analyzing visual imagery — has been applied in fault and salt dome interpretation. At the end of this review, we provide insight and discussion on the future of structural interpretation.

Introduction

In general, seismic interpretation acquires subsurface information from seismic data and reveals geologic meanings. As a main category of interpretation workflows, structural interpretation aims to identify important geologic structures in hydrocarbon exploration. Interpretation that depends only on domain experts is becoming increasingly time consuming and labor intensive because seismic surveys have grown over the years in size and complexity. Data sizes have increased from hundreds of megabytes for the first 3D seismic survey collected in the 1970s to hundreds of gigabytes or even terabytes today. In addition, seismic data generated by advanced acquisition systems have a higher resolution and reveal more complicated details of geologic structures in the subsurface, which makes manual interpretation more difficult. To tackle these challenges, researchers have investigated image-processing and machine-learning algorithms and utilized them to implement automated or semiautomated interpretation workflows. For years, image-processing theories and algorithms have been employed to assist structural interpretation and have made essential contributions to the field. Structural interpretation commonly involves two main steps — attribute extraction and structure identification. Attributes that capture the key

components of seismic data are implicitly or explicitly defined based on signal and image-processing techniques. For example, instantaneous attributes (Taner et al., 1979) are derived from the Hilbert transform, and spectral attributes (Sinha et al., 2005) are the results of multiresolution analysis. Since edge, texture, and shape information are important to both images from nature and seismic images, edge detectors (Amin and Deriche, 2015), texture descriptors (Shafiq et al., 2017), and the Hough transform (Wang and AlRegib, 2017), although initially designed for use with natural images, have shown strong capability in identifying geologic structures in seismic images. From another perspective, interpretation as a complex and subjective task can be conducted based on the human visual system. Recently, algorithms involving the human visual system model, such as saliency detection (Shafiq et al., 2018) and color space analysis (Wang et al., 2014), have been proposed to mimic the interpretation process by extracting the most perceptually representative attributes of seismic data. The richness and rapid progress in image processing and computer vision have taken the automation of structural interpretation to a higher level. We believe that seismic interpretation as a challenging problem will continue to impact the advancement of image processing in the future. Although a deep understanding of and training in geophysics have been considered prerequisites for developing effective interpretation workflows, recent progress in machine learning has shed new light on its role in this domain-specific problem (Zhao et al., 2015; Huang et al., 2017; AlRegib et al., 2018). Machine-learning models trained on input data can produce repeatable, reliable results for seismic interpretation and alleviate two significant issues that interpreters may encounter — interpreting large volumes of data and understanding the relationship of various types of data simultaneously. Machine-learning-based interpretation methods have two main schemes. One extracts multiple seismic attributes based on interpreters’ domain knowledge and experience and trains them on conventional supervised or unsupervised machine-learning models such as the self-organizing map (Strecker and Uden, 2002), the multilayer perceptron (Aminzadeh, 2013; Zheng et al., 2014), and K-means clustering (Di and AlRegib, 2017). The other utilizes deep-learning models, especially the convolutional neural network (CNN). In recent years, with the dramatic growth of computational power and available data, deep learning that simulates the brain’s structures and functions has achieved remarkable success in various artificial intelligence applications. The CNN motivated by the visual cortex in the brain, as one form of deep-learning models, consists of one or more convolutional layers. 2D kernels in convolutional layers are trained to capture spatial and structural features from input images, which makes the CNN better suited for visual

1 Georgia Institute of Technology, Center for Energy and Geo Processing, Atlanta, Georgia, USA. E-mail: [email protected]; haibin.di@ece. gatech.edu; [email protected]; [email protected]; [email protected].

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tasks. In the CNN, the first convolutional layer extracts the lowlevel features of images such as edges, lines, and corners. In contrast, higher convolutional layers extract more abstract high-level features such as shapes and patterns. Unlike conventional machine-learning models that depend on predefined features, the CNN has 2D amplitude images as the input, builds the mapping relationships between poststack amplitude and structure spaces, and extracts features automatically in the training process. Without intervention by interpreters, the CNN-based workflow relies only on the appearance of geologic structures in the data set and mimics the behavior of interpreters to a certain extent. All interpretation methods introduced in the preceding paragraph seek to identify geologic structures in poststack seismic data. However, poststack seismic data are commonly of low quality because of seismic imaging algorithms and velocity models, and this limits the performance of interpretation methods. To alleviate such a limitation, in recent years, researchers have proposed conducting interpretation tasks on prestack seismic data, which are the input of time or depth migration and have less noise than migrated ones. Zhang et al. (2014) introduce kernel-regularized least-squares fitting to identify and localize faults in prestacked seismic data at the initial stage of velocity model building. Similarly, Lin et al. (2017) employ the Nyström method for dimensionality reduction and apply the kernel ridge regression model to extract faults from prestack seismic measurements. Araya-Polo et al. (2017) propose training a deep neural network to learn the mapping relationship between prestack data and fault spaces using the Wasserstein loss function. Experimental results show that fault identification on prestack seismic data, which has high computational efficiency and achieves comparable performance with that of poststack seismic data, provides a new and promising direction for structural interpretation. In this paper, we focus mainly on the interpretation of two geologic structures — faults and salt domes — on poststack seismic data. As the least controversial structures in interpretation, they are closely related to the formation of hydrocarbon reservoirs. We first investigate the detection methods of faults and salt domes and then introduce structure-tracking algorithms. Finally, we state our conclusion and provide insights on the future direction of seismic interpretation.

Fault detection

A fault is defined as a lineament or planar surface across which apparent relative displacement occurs in rocks layers. The movement of impermeable rocks and sediments along the fault surface creates membranes that hinder the migration of hydrocarbons from source rocks and create structural hydrocarbon traps. Such deformation determines two distinct features of faults that can be characterized by image-processing techniques: one is the geologic feature, which is the discontinuity along horizons; the other is the geometric feature, i.e., line-like or curved shapes in 2D seismic sections, which appear as curved surfaces in 3D seismic volumes. Fault-detection methods are commonly developed based on these two features. The discontinuity of faults can be characterized by several seismic attributes such as coherence (Bahorich and Farmer, 1995), curvature (Roberts, 2001), similarity (Tingdahl and de Rooij, 2005), entropy (Cohen et al., 2006), and flexure

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(Di and Gao, 2017a). Among them, coherence is the best known for highlighting faults. Similarly, Marfurt et al. (1998) calculate semblance by comparing the dissimilarity of local regions on the two sides of a fault. Later, Gersztenkorn and Marfurt (1999) propose the eigenstructure-based coherence, referred to as C3 coherence, which analyzes the eigenstructure of covariance matrices of windowed seismic traces. Instead of calculating the eigenvalues of the covariance matrix, Yang et al. (2015) propose a computationally efficient coherence algorithm on the basis of a normalized information divergence criterion. In addition, Li and Lu (2014) combine spectral decomposition and complex coherence computation to map discontinuities at different scales. To avoid false low-coherence values in steeply dipping structures, Sui et al. (2015) propose a coherence algorithm that analyses the eigenstructure of the spectral amplitudes of seismic traces. More recently, Alaudah and AlRegib (2016) propose a generalizedtensor-based coherence (GTC) attribute that derives covariance matrices from the unfolding matrices of a seismic analysis tensor along different modes corresponding to time, inline, and crossline directions, respectively. Figures 1a–1c illustrate the time section at 1600 ms in the Netherlands offshore F3 block (https://www.opendtect.org/osr/ Main/NetherlandsOffshoreF3BlockComplete4GB) and the corresponding C3 coherence and GTC attributes. In contrast to C3 coherence, GTC enhances the details of discontinuity in seismic data. On the basis of GTC, Alaudah and AlRegib (2017) implement directional selectivity using a directional Gaussian preprocessing kernel, which can be rotated to arbitrary angles by 3D rotational matrices. Figures 1d and 1e illustrate directional GTC attributes with different rotation angles. Black arrows indicate that the boundaries of a channel formation, which are not visible in either C3 coherence or GTC attributes, appear in the directional GTC attributes. In some cases, relying on one seismic attribute does not produce accurate fault delineation. Therefore, enhancement operations such as nonlinear mapping and structure-oriented filtering (Fehmers and Höcker, 2003) may be applied to increase the contrast between faults and surrounding structures. In the attribute space, the most likely fault regions are commonly specified using a hard threshold or are selected from local maxima. Since 2000, researchers have utilized various imageprocessing techniques to interactively delineate fault surfaces in seismic volumes or faults in 2D seismic sections. Specifically, fault interpretation using 3D image-processing techniques that simultaneously involve information in all three directions have become a main direction. By assuming that a fault is continuous and barely curved, Pederson et al. (2002) propose utilizing an ant tracking or ant colony optimization algorithm to delineate fault surfaces. In the work of Cohen et al. (2006), the proposed directional filters enhance the contrast of normalized differential entropy, and the skeletonization process (Pavlidis, 1980) extracts one-pixel-width fault surfaces from likely fault regions. Gibson et al. (2005) design a multistage approach that first highlights fault points in modified semblance cubes, generates local planar patches from grouped fault points, and finally merges small patches into large fault surfaces. In the work of Hale (2013), fault points with the largest fault likelihoods are selected and connected to construct meshes of quadrilaterals, which are further used to form fault surfaces.

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midpoints of fault features and illustrates the rough position of fault. Therefore, features with larger distances to the fitted fault are treated as outliers and discarded. In contrast, features in a neighboring group are merged into one fault feature, since they represent the same local region. After false feature removal, the remaining features connected by blue lines roughly label the fault. Finally, geologic constraints are involved to improve delineation accuracy. The same concept of the Hough transform has also been applied to extract fault planes from discontinuity volumes (Wang and AlRegib, 2014). All fault-detection methods introduced in the preceding text were proposed based on typical image-processing techniques, which commonly involve some necessary parameters. The selection of parameters determines interpretation performance. Because of the limitation of models and the existence of parameters, it is difficult for these algorithms to simultaneously achieve both high recall and high precision when extracting faults. The common result is either an aggressive case with higher recall (most or all faults are extracted) but lower precision (many artifacts are involved), or a conservative Figure 1. Coherence attributes of the time section at 1600 ms in the Netherlands North Sea F3 block: (a) seismic amplitude, (b) C3 coherence attribute, (c) GTC attribute, (d) GTC attribute with 40°, (e) GTC attribute with 75°, and one with higher precision (few artifacts (f) GTC attribute with 150°. are involved) but lower recall (few faults are extracted) (Di and Gao, 2017b). To However, depending only on attribute maps, fault regions alleviate this trade-off and increase robustness and generality, detected by these methods are not often able to accurately reveal machine-learning techniques have been involved in fault-detection the details of faults because of the inevitable presence of noisy methods (Meldahl et al., 2001) and have become more popular structures. To solve this problem, interpreters utilize the geometric in recent years (Zheng et al., 2014; Huang et al., 2017). features of faults. The Hough transform, a mapping procedure Di et al. (2017a) present an innovative workflow based on a between the image and parameter spaces, has been used widely support vector machine (SVM) (Cortes and Vapnik, 1995) to to detect lines, circles, planes, and other parametric shapes. For detect faults. First, three groups of seismic attributes are calculated example, Jacquemin and Mallet (2005) propose using the cascaded from the amplitude volume. These attributes, including edge-based, Hough transform to roughly detect fault surfaces in seismic geometric, and texture attributes, can highlight faults moderately volumes. To improve the local accuracy of detected faults, Wang well. Second, the samples of faults and nonfaulting zones are and AlRegib (2017) propose delineating faults using line-like picked manually from the amplitude volume. Third, training the features extracted by the Hough transform. Figure 2 illustrates SVM model on the attribute vectors of selected samples leads to the diagram of the proposed method, in which authors first an optimal binary classifier for volumetric processing. Finally, highlight likely fault points by applying a hard threshold on the applying the trained SVM model on the entire seismic volume discontinuity map and then extract line-like fault features (yellow generates a binary volume, in which the presence of a fault is line segments) using the Hough transform. Because of the Hough labeled as one. transform’s limitation, detected results inevitably contain some The accuracy of the multiattribute-based classification workflow false features that violate certain geologic constraints. The steps depends highly on the selection of seismic attributes, which should of false feature removal are shown in Figure 2. False features are be capable of distinguishing faults and other geologic structures classified into two types based on their appearance: outliers, which (Zhao et al., 2015). Because of the complexities of subsurface geology are isolated from the rest, and neighboring groups, which contain and the presence of seismic noise, most seismic attributes fail to similar features located nearby. The red line is fitted from all have robust performance in highlighting faults. Without manually

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choosing seismic attributes, the CNN provides a way to learn certain seismic attributes that can capture the spatial and structural features of faults only from the appearance of faults in seismic data. Huang et al. (2017) develop a cloud-based seismic analytics platform that facilitates the interpretation of large-scale seismic data using deeplearning techniques, especially the CNN. In the example of fault interpretation, first, nine attributes that provide the independent representations of faults are extracted. To capture the local features of faults, every voxel in a seismic volume corresponds to nine local attribute cubes. Second, cubes extracted from the same attribute volume are fed into a CNN, which is trained to learn fault features and has an output of a 1D feature. Because nine attribute volumes are calculated, nine CNNs need to be trained in parallel for efficiency. Third, the outputs of all CNNs are concatenated and fed into the classifier based on the SVM or logistic regression to construct the final fault identification model. This CNN-based fault interpretation method has three main drawbacks. The first is the mismatch between the 3D input of the CNN and the 2D kernels in convolutional layers, which leads to the failure of capturing spatial information between neighboring sections. Second is the redundancy of the feature-extraction step, since the CNN has proved its ability to automatically extract representative features from amplitude data. The third drawback is computational inefficiency since nine CNNs are required to be trained. To overcome these drawbacks, Di et al. (2018b) propose a new method for attribute-free fault detection using the CNN. Instead of using attributes as the input, the CNN-based method defines the input as local seismic reflection patches, which have been labeled as fault or nonfaulting zones, respectively, according to the location of the central point. Training the predefined CNN on local patches builds the mapping relationship between seismic signals and fault structures. Figure 3a illustrates the proposed CNN architecture that is constructed by only one convolutional and one fully connected layer. The fault volume and extracted fault

surfaces are shown in Figures 3b and 3c, respectively. To avoid overfitting, the proposed network structure contains only two layers. Although the network structure is simple, experimental results show that it is capable of identifying faults in seismic volumes. For faults with complicated structures, extra convolutional layers may need to be added to improve interpretation performance. We notice that the CNN-based method can detect faults with high precision and recall, which not only verifies the capability of the CNN in assisting fault interpretation but also indicates greater potentials of more advanced networks (e.g., fully convolutional networks [Long et al., 2015]) on structure interpretation. In addition, except for the labeling of training data, this whole scheme does not require the intervention of interpreters and is applicable to vast data sets without repeated efforts in attribute selection.

Salt dome detection

A salt dome is defined as a dome-shaped structure formed by the evaporation of a large mass of salt in sedimentary rocks. Salt domes are impermeable structures that prevent the migration of hydrocarbons and provide entrapment for oil and gas reservoirs. Compared with the surrounding strata, salt domes often exhibit chaotic reflections in the form of a distinct texture. Therefore, salt dome interpretation can be treated as a structure segmentation problem in digital image processing. However, the boundaries of salt domes are not easily identified in most geologic scenarios because of the underlying physics as well as noisy and low-resolution data. In addition to typical seismic attributes introduced in the previous section, researchers have proposed various novel seismic attributes in recent years to characterize the boundaries of salt domes. Shafiq et al. (2018) propose a seismic attribute, referred to as SalSi, which highlights the salient areas of a seismic image by comparing local spectral features based on the 3D fast Fourier transform. Chopra and Marfurt (2016) propose a seismic disorder attribute assessing randomness and the signal-to-noise ratio of data to delineate seismic

Figure 2. Diagram of the fault-detection method proposed by Wang and AlRegib (2017), which utilizes the Hough transform to extract fault features and remove false ones using geologic constraints.

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Special Section: Advancements in image processing

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Figure 3. The proposed CNN on fault detection. (a) The proposed CNN. (b) 3D view of the generated fault volume; black regions represent faults. (c) Fault surfaces automatically extracted from (b).

structures such as faults and salt domes. Wu (2016) proposes a method that computes salt likelihoods highlighting salt boundaries, extracts oriented salt samples on the ridges of salt likelihoods, and constructs salt boundaries with salt samples by solving a screened Poisson surface reconstruction problem. By defining salt dome detection as a segmentation task, some automated workflows have been proposed to involve image-processing techniques such as graph cuts, edge detection, and texture analysis. Lomask et al. (2004) define seismic sections as weighted undirected graphs in which nodes are pixels while edges are the connections of all node pairs. The weight of an edge is determined by the spatial distance of two corresponding nodes and the similarity of their attribute intensity. Based on the normalized cut image segmentation (NCIS) criterion (Shi and Malik, 2000), the delineation of salt dome boundaries can be globally optimized. As an extension, Lomask et al. (2007) add the local dip difference to the weight function and involve bound constraints to remove boundary artifacts. Similarly, Halpert et al. (2009) apply the NCIS on multiple seismic attributes such as instantaneous amplitude, dip, and

Special Section: Advancements in image processing

instantaneous frequency and combine corresponding segmentation results using adaptive weights. Although these NCIS-based methods can be implemented in parallel, the high computational cost limits their future application on high-resolution or 3D seismic data. To improve the efficiency of global segmentation, Halpert et al. (2010) modify the pairwise region comparison algorithm (Felzenszwalb and Huttenlocher, 2004) using the refined graph structure and the weight function. In contrast to NCIS-based methods with the time complexity of O(n2), the method based on pairwise region comparison involves the minimum spanning tree and reduces time complexity to O(nlogn), where n is the number of pixels. Different from graph cuts, edge-detection techniques are simple and have high computational efficiency. In recent years, methods based on edge detectors have been proposed to delineate the boundaries of salt domes. Jing et al. (2007) apply the 2D Sobel filter, a form of derivatives with weighted masks, on poststack time sections to highlight salt dome boundaries. Without amplitude normalization, the scheme works well only when seismic data exhibits small amplitude variations in two directions. To

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Figure 4. Illustration of the 3D-GoT and the corresponding salt dome detection results. (a) Computing GoT along the crossline, i.e., x-direction. (b) Salt dome boundary detected by various delineation algorithms. Magenta (Aqrawi et al., 2011), black (Amin and Deriche, 2015), blue (Shafiq et al., 2017), green (reference salt dome boundary). (c) A 3D salt body detected from the F3 block in the North Sea using 3D-GoT (Shafiq et al., 2017).

enhance salt dome boundaries in different directions, Aqrawi et al. (2011) propose a salt body detection algorithm based on the 3D Sobel detector, which involves both amplitude normalization and dimension weighting. In a more recent work, Amin and Deriche (2015) propose an approach that highlights small variations in seismic data by detecting edges along not only the x, y, and z directions but also directions slanted at 45° and −45° using 3D Sobel filters. The 3D Sobel filter along a direction of 45° is shown as follows: ⎡ −2 −1 0 ⎤ ⎢ ⎥ S 45! (:,:,−1) = ⎢ −1 0 1 ⎥, ⎢ 0 1 2 ⎥ ⎣ ⎦

⎡ −2 −1 0 ⎤ ⎢ ⎥ 0 1 ⎥, ! (:,:,−1) = ⎢ −1 ⎢ 0 1 2 ⎥ ⎣ ⎦

⎡ −4 −2 0 ⎤ ⎢ ⎥ S 45! (:,:,0) = ⎢ −2 0 2 ⎥, ⎢ 0 2 4 ⎥ ⎣ ⎦

⎡ −4 −2 0 ⎤ ⎢ ⎥ (:,:,0) = ⎢ −2 0 2 ⎥, 45! ⎢ 0 2 4 ⎥ ⎣ ⎦

⎡ −2 −1 0 ⎤ ⎢ ⎥. S 45! (:,:,1) = ⎢ −1 0 1 ⎥ ⎢ 0 1 2 ⎥ ⎣ ⎦

seismic images in which the green dashed vertical line separates two textured regions depicted in dotted and striped lines, respectively, and evaluates the GoT in the x direction (i.e., the crossline direction). As the center point and its two neighboring cubes move along the blue line, texture dissimilarity function d(•) yields a GoT profile shown at the bottom of Figure 4a. Theoretically, the highest GoT value corresponds to the highest dissimilarity and is obtained when the center point falls exactly on the texture boundary. Similarly, GoT is also calculated along t (time or depth) and y (inline) directions. To improve the delineation efficiency and robustness, the calculation 3D-GoT attribute employs ⎡ −4 −2 ⎡ −2 −1of the 0 ⎤ 0 ⎤ ⎢ ⎥ ⎢ ⎥ a multiscale gradient expressed as follows:

S 45! (:,:,0) = ⎢ −2 ⎢ 0 ⎣

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2 4

⎥, ⎥ ⎦

S 45! (:,:,1) = ⎢ −1 0 1 ⎥ ⎢ 0 1 2 ⎥ 1 ⎣ ⎛ ⎦ 2 ⎞2 ⎞ ⎛N G [t,x, y ] = ⎜ ∑ ⎜∑ωn ⋅ d ( Wi−n , Wi+n ) ⎟ ⎟ , ⎜ ⎠ ⎟⎠ ⎝ i∈{t ,x , y} ⎝ n=1

(2)

⎡ −2 −1 0 ⎤ ⎢ ⎥ S 45! (:,:,1) = ⎢ −1 0 1 ⎥ n ⎢ 0 1 2 ⎥ n ⎣ where ⎦Wi- and Wi+ denote the neighboring cubes, n represents the

(1)

With most of the above algorithms, the underlying assumption is that a salt dome body can be recognized by the different appearance of the salt body and its surrounding structures. Therefore, comparing the textures inside and outside the salt body has been an effective methodology to delineate salt dome bodies. On the basis of the work of Wang et al. (2015), Shafiq et al. (2017) propose a seismic attribute, 3D gradient of textures (3D-GoT), which describes the texture dissimilarity between neighboring cubes around each voxel in a seismic volume across time (or depth), crossline, and inline directions. Figure 4a illustrates synthetic

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0 2

edge length of cubes, and ωn represents the weight associated with each cube size. To compute dissimilarity between cubes, authors use a perceptual dissimilarity measure based on error magnitude spectrum chaos (Hegazi and AlRegib, 2014), which not only is computationally less expensive and performs better than nonperceptual dissimilarity measures, but also highlights texture variations in the most effective manner. The perceptual dissimilarity measure is calculated as follows:

(

)

d ( Wi−n , Wi+n ) = E K ⊗ K ⊗ Wi−n − Wi+n ,

i ∈ {t,x, y } , (3)

where  represents the tensor product, K is the Kronecker matrix defined as K = Dt  Dx  Dy, and Dt, Dx, and Dy are discrete

Special Section: Advancements in image processing

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Fourier transform matrices. The output of various salt dome delineation algorithms on a typical seismic inline is shown in Figure 5b. In addition, Figure 5c illustrates a salt body detected by the 3D-GoT-based method (Shafiq et al., 2017) from the F3 block in the North Sea. As we introduced earlier, automated workflows based on image-processing techniques focus on describing the appearance of geologic structures and are not robust enough for complex geologic scenarios. The inevitable parameter tuning requires extra time and limits automation efficiency. Similar to fault detection, applying machine-learning techniques on salt dome detection has become a new trend in recent years. Berthelot et al. (2013) propose a Bayesian classification model to detect salt bodies using a combination of seismic attributes such as dip, similarity, frequency-based attributes, and attributes based on the gray-level co-occurrence matrix (GLCM) (Haralick et al., 1973). A workflow proposed by Guillen et al. (2015) automatically detects salt domes from the SEG Advanced Modeling (SEAM) data set using seismic attributes and a machinelearning algorithm called the extremely randomized trees ensemble. Amin and Deriche (2016) propose a supervised codebook-based learning model for salt dome detection using texture-based attributes. Di et al. (2017b) propose an interpreter-assisted approach based on the K-means clustering of multiple seismic attributes that highlights salt dome boundaries in the F3 block. To investigate the performance of various

classification methods on salt dome detection, Di and AlRegib (2017) train six classification models — the logistic regression, the decision tree, the random forest, the SVM, the artificial neural network, and K-means clustering — on multiple attributes, including rms amplitude; GLCM-, GoT- (Wang et al., 2015), and seismic-saliency-based attributes (Shafiq et al., 2018); and Canny edge detector (Canny, 1986). Figure 5 illustrates the salt dome boundaries detected by various classification methods from the F3 block. The good match between detected salt boundaries and original seismic images indicates that with well-selected attributes all six classification models are capable of providing reliable salt detection from 3D seismic data. To avoid manual selection of seismic attributes, which requires the domain knowledge and experience of interpreters, Waldeland and Solberg (2017) design a CNN that learns to classify each voxel of the Netherlands offshore F3 block as either a salt or nonsalt sample. Using local amplitude cubes as the input, the CNN is trained to capture spatial and structural features of salt dome boundaries and construct attributes without the interventions of interpreters. Similarly, Di et al. (2018a) propose a CNN-based workflow to implement the salt dome delineation in the SEAM data set. To alleviate overfitting and reduce computational cost, the CNN designed by Di et al. (2018a) that employs local amplitude patches as the input has only two convolutional layers and one fully connected layer. The details of the network structure are shown in Figure 6. Experimental results in Figure 7 show a good match between detected salt dome boundaries and original seismic images, even for a complex intrusive in a folded Tertiary basin, which is challenging for existing salt dome interpretation tools.

Fault and salt dome tracking

Figure 5. Salt-boundary probability volumes overlaying the original seismic amplitude, which are obtained from six classification models, respectively, including (a) logistic regression, (b) decision tree, (c) random forest, (d) SVM, (e) artificial neural network, and (f) K-means clustering.

Special Section: Advancements in image processing

The methods introduced in the previous two sections focus mainly on the detection, or delineation, of faults and salt domes in 2D sections. To investigate the geologic structures of faults and salt domes, interpreters need to repeatedly apply these methods on each section of a seismic volume. However, for a large seismic volume, repeated detection in every section may impair interpretation efficiency. Because of the slow formation processes of subsurface structures, neighboring sections commonly have strong correlations. In recent years, fault and salt dome tracking methods have been proposed to utilize correlations between sections to improve interpretation efficiency. Borrowing the concept of motion vectors in video coding, Wang and AlRegib (2017) group seismic sections into reference and predicted sections. Faults in the predicted sections can be labeled by detection results in reference sections. Berthelot et al. (2012) propose detecting

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the salt dome boundary in one time section and tracking the boundary through adjacent sections by minimizing a defined energy function that maintains curvature and smoothness of the boundaries. Similarly, Shafiq and AlRegib (2016) take advantage of active contour to track salt dome boundaries in neighboring seismic sections. Wang et al. (2016) propose a salt dome tracking method that extracts the features of salt dome boundaries in reference sections using tensor-based subspace learning and delineates tracked boundaries by finding points in predicted sections that are the most similar to reference ones. Figure 8 illustrates salt dome tracking, in which a featureextraction process is implemented by tensor-based subspace

learning. The authors manually label the boundaries of salt domes in Nr reference sections, in which N c = ⎡⎢ N r / 2⎤⎥ is the central one. For each point in the labeled boundary of Nc , its corresponding points in neighboring (Nr – 1) reference boundaries are identified. Since every point corresponds to a patch with the size of Np × Np , stacking corresponding patches constructs third-order texture tensors from reference sections, denoted

{A

k

∈!

N p ×N p ×N r

, k = 1, 2, …, K N c , where K Nc represents the

}

number of points in the Nc -th reference boundary. Because of strong correlations between neighbors, every point in the Nc -th

Figure 6. The architecture of the CNN proposed by Di. et al. (2018a) has local amplitude patches as the input and contains only two convolutional layers and one fully connected layer.

Figure 7. 3D view of the detected salt body boundaries in synthetic SEAM data set, which is clipped to six vertical sections for performance analysis. Note that none of these sections is fed into training the CNN classifier.

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Special Section: Advancements in image processing

reference boundary corresponds to a tensor group, denoted

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G k = { A k−Ns , …, A k , …, A k+Ns } , which contains 2Ns + 1 tensors.

Using multilinear dimensionality reduction methods such as multilinear principle component analysis (De Lathauwer et al., 2000) and tensor-based linearity projection preserving (Gao et (1) (2) al., 2013), one can obtain transformation matrices Uk , Uk , and (3) Uk and map tensor group Gk to its subspace as follows: ! = A × U (1) × U ( 2) × U ( 3) , A m m 1 k 2 k 3 k

m ∈ { k − N s ,", k + N s } , (4)

where ×i, i = 1, 2, 3 denotes the i-mode product of a tensor by a ! with less dimensions in each mode contains matrix, and tensor A m the features of reference boundaries. These extracted features can help identify tracked boundary points in predicted sections. In Figure 8, the local and global comparisons between the tracked boundary in green and the manually labeled one in red imply strong similarity, which indicates the high accuracy of salt dome tracking within seismic volumes.

Conclusions

State-of-the-art image-processing and machine-learning techniques have been applied successfully in the domain of 3D seismic interpretation, especially for fault and salt dome delineation. Among image-processing techniques, the human visual system model parses seismic signals from innovative perspectives by mimicking the interpretation process of an experienced interpreter. Meanwhile, the emerging CNN provides a data-based

framework that constructs a mapping between seismic signals and subsurface structures. The CNN-based interpretation methods efficiently capture the spatial and structural features of poststack seismic data and have better performance than those based on conventional machine-learning techniques. Our initial case studies have demonstrated that such image-processing and machinelearning techniques are not only capable of identifying important structures such as faults and salt domes, but, more importantly, they also show great potential for assisting seismic interpretation and reservoir characterization such as attribute analysis, structure identification, and well-seismic ties. Corresponding author: [email protected]

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Figure 8. Diagram of salt dome tracking in which features around salt dome boundaries in reference sections are extracted by tensor-based subspace learning.

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