Video: Leveraging Deep Learning in Extracting Features of Interest from Seismic Data

Video: Leveraging Deep Learning in Extracting Features of Interest from Seismic Data

 

Abstract:

 

Mapping and extracting features of interest is one of the most important objectives in seismic data interpretation. Due to the complexity of seismic data, geologic features identified by interpreters on seismic data using visualization techniques are often challenging to extract. With the rapid development in GPU computing power and the success obtained in computer vision, deep learning techniques, represented by convolutional neural networks (CNN), start to entice seismic interpreters in various applications. The main advantages of CNN over other supervised machine learning methods are its spatial awareness and automatic attribute extraction. The high flexibility in CNN architecture enables researchers to design different CNN models to identify different features of interest. In this webinar, using several seismic surveys acquired from different regions, I will discuss three CNN applications in seismic interpretation: seismic facies classification, fault detection, and channel extraction. Seismic facies classification aims at classifying seismic data into several user-defined, distinct facies of interest. Conventional machine learning methods often produce a highly fragmented facies classification result, which requires a considerable amount of post-editing before it can be used as geobodies. In the first application, I will demonstrate that a properly built CNN model can generate seismic facies with higher purity and continuity. In the second application, compared with traditional seismic attributes, I deploy a CNN model built for fault detection which provides smooth fault images and robust noise degradation. The third application demonstrates the effectiveness of extracting large scale channels using CNN. These examples demonstrate that CNN models are capable of capturing the complex reflection patterns in seismic data, providing clean images of geologic features of interest, while also carrying a low computational cost.

To view this webinar in Chinese, please click here.

Tao Zhao

Research Geophysicist | Geophysical Insights

TAO ZHAO joined Geophysical Insights in 2017. As a Research Geophysicist, Dr. Zhao develops and applies shallow and deep machine learning techniques on seismic and well log data, and advances multiattribute seismic interpretation workflows. He received a B.S. in Exploration Geophysics from the China University of Petroleum in 2011, an M.S. in Geophysics from the University of Tulsa in 2013, and a Ph.D. in geophysics from the University of Oklahoma in 2017. During his Ph.D. work at the University of Oklahoma, Dr. Zhao was an active member of the Attribute-Assisted Seismic Processing and Interpretation (AASPI) Consortium developing pattern recognition and seismic attribute algorithms.

Machine Learning Essentials for Seismic Interpretation: an e-Course by Dr. Tom Smith

Machine Learning Essentials for Seismic Interpretation: an e-Course by Dr. Tom Smith

Machine learning is foundational to the digital transformation of the oil & gas industry and will have a dramatic impact on the exploration and production of hydrocarbons.  Dr. Tom Smith, the founder and CEO of Geophysical Insights, conducts a comprehensive survey of machine learning technology and its applications in this 24-part series.  The course will benefit geoscientists, engineers, and data analysts at all experience levels, from data analysts who want to better understand applications of machine learning to geoscience, to senior geophysicists with deep experience in the field.

Aspects of supervised learning, unsupervised learning, classification and reclassification are introduced to illustrate how they work on seismic data.  Machine learning is presented, not as an end-all-be-all, but as a new set of tools which enables interpretation on seismic data on a new, higher level that of abstraction  that promises to reduce risks and identify features that which might otherwise be missed.

The following major topics are covered:

  • Operation  – supervised and unsupervised learning; buzzwords; examples
  • Foundation  – seismic processing for ML; attribute selection list objectives; principal component analysis
  • Practice  – geobodies; below-tuning; fluid contacts; making predictions
  • Prediction – the best well; the best seismic processing; over-fitting; cross-validation; who makes the best predictions?

This course can be taken for certification, or for informational purposes only (without certification). 

Enroll today for this valuable e-course from Geophysical Insights!

Seismic Facies Classification Using Deep Convolutional Neural Networks

Seismic Facies Classification Using Deep Convolutional Neural Networks

By Tao Zhao
Published with permission: SEG International Exposition and 88th Annual Meeting
October 2018

Summary

Convolutional neural networks (CNNs) is a type of supervised learning technique that can be directly applied to amplitude data for seismic data classification. The high flexibility in CNN architecture enables researchers to design different models for specific problems. In this study, I introduce an encoder-decoder CNN model for seismic facies classification, which classifies all samples in a seismic line simultaneously and provides superior seismic facies quality comparing to the traditional patch-based CNN methods. I compare the encoder-decoder model with a traditional patch- based model to conclude the usability of both CNN architectures.

Introduction

With the rapid development in GPU computing and success obtained in computer vision domain, deep learning techniques, represented by convolutional neural networks (CNNs), start to entice seismic interpreters in the application of supervised seismic facies classification. A comprehensive review of deep learning techniques is provided in LeCun et al. (2015). Although still in its infancy, CNN-based seismic classification is successfully applied on both prestack (Araya-Polo et al., 2017) and poststack (Waldeland and Solberg, 2017; Huang et al., 2017; Lewis and Vigh, 2017) data for fault and salt interpretation, identifying different wave characteristics (Serfaty et al., 2017), as well as estimating velocity models (Araya-Polo et al., 2018).

The main advantages of CNN over other supervised classification methods are its spatial awareness and automatic feature extraction. For image classification problems, other than using the intensity values at each pixel individually, CNN analyzes the patterns among pixels in an image, and automatically generates features (in seismic data, attributes) suitable for classification. Because seismic data are 3D tomographic images, we would expect CNN to be naturally adaptable to seismic data classification. However, there are some distinct characteristics in seismic classification that makes it more challenging than other image classification problems. Firstly, classical image classification aims at distinguishing different images, while seismic classification aims at distinguishing different geological objects within the same image. Therefore, from an image processing point of view, instead of classification, seismic classification is indeed a segmentation problem (partitioning an image into blocky pixel shapes with a coarser set of colors). Secondly, training data availability for seismic classification is much sparser comparing to classical

image classification problems, for which massive data are publicly available. Thirdly, in seismic data, all features are represented by different patterns of reflectors, and the boundaries between different features are rarely explicitly defined. In contrast, features in an image from computer artwork or photography are usually well-defined. Finally, because of the uncertainty in seismic data, and the nature of manual interpretation, the training data in seismic classification is always contaminated by noise.

To address the first challenge, until today, most, if not all, published studies on CNN-based seismic facies classification perform classification on small patches of data to infer the class label of the seismic sample at the patch center. In this fashion, seismic facies classification is done by traversing through patches centered at every sample in a seismic volume. An alternative approach, although less discussed, is to use CNN models designed for image segmentation tasks (Long et al., 2015; Badrinarayanan et al., 2017; Chen et al., 2018) to obtain sample-level labels in a 2D profile (e.g. an inline) simultaneously, then traversing through all 2D profiles in a volume.

In this study, I use an encoder-decoder CNN model as an implementation of the aforementioned second approach. I apply both the encoder-decoder model and patch-based model to seismic facies classification using data from the North Sea, with the objective of demonstrating the strengths and weaknesses of the two CNN models. I conclude that the encoder-decoder model provides much better classification quality, whereas the patch-based model is more flexible on training data, possibly making it easier to use in production.

The Two Convolutional Neural Networks (CNN) Models

Patch-based model

A basic patch-based model consists of several convolutional layers, pooling (downsampling) layers, and fully-connected layers. For an input image (for seismic data, amplitudes in a small 3D window), a CNN model first automatically extracts several high-level abstractions of the image (similar to seismic attributes) using the convolutional and pooling layers, then classifies the extracted attributes using the fully- connected layers, which are similar to traditional multilayer perceptron networks. The output from the network is a single value representing the facies label of the seismic sample at the center of the input patch. An example of patch-based model architecture is provided in Figure 1a. In this example, the network is employed to classify salt versus non-salt from seismic amplitude in the SEAM synthetic data (Fehler and Larner, 2008). One input instance is a small patch of data bounded by the red box, and the corresponding output is a class label for this whole patch, which is then assigned to the sample at the patch center. The sample marked as the red dot is classified as non-salt.

CNN architecture patch-based model

Figure 1. Sketches for CNN architecture of a) 2D patch-based model and b) encoder-decoder model. In the 2D patch-based model, each input data instance is a small 2D patch of seismic amplitude centered at the sample to be classified. The corresponding output is then a class label for the whole 2D patch (in this case, non-salt), which is usually assigned to the sample at the center. In the encoder-decoder model, each input data instance is a whole inline (or crossline/time slice) of seismic amplitude. The corresponding output is a whole line of class labels, so that each sample is assigned a label (in this case, some samples are salt and others are non-salt). Different types of layers are denoted in different colors, with layer types marked at their first appearance in the network. The size of the cuboids approximately represents the output size of each layer.

Encoder-decoder model

Encoder-decoder is a popular network structure for tackling image segmentation tasks. Encoder-decoder models share a similar idea, which is first extracting high level abstractions of input images using convolutional layers, then recovering sample-level class labels by “deconvolution” operations. Chen et al. (2018) introduce a current state-of-the-art encoder-decoder model while concisely reviewed some popular predecessors. An example of encoder-decoder model architecture is provided in Figure 1b. Similar to the patch-based example, this encoder-decoder network is employed to classify salt versus non-salt from seismic amplitude in the SEAM synthetic data. Unlike the patch- based network, in the encoder-decoder network, one input instance is a whole line of seismic amplitude, and the corresponding output is a whole line of class labels, which has the same dimension as the input data. In this case, all samples in the middle of the line are classified as salt (marked in red), and other samples are classified as non-salt (marked in white), with minimum error.

Application of the Two CNN Models

For demonstration purpose, I use the F3 seismic survey acquired in the North Sea, offshore Netherlands, which is freely accessible by the geoscience research community. In this study, I am interested to automatically extract seismic facies that have specific seismic amplitude patterns. To remove the potential disagreement on the geological meaning of the facies to extract, I name the facies purely based on their reflection characteristics. Table 1 provides a list of extracted facies. There are eight seismic facies with distinct amplitude patterns, another facies (“everything else”) is used for samples not belonging to the eight target facies.

Facies numberFacies name
1Varies amplitude steeply dipping
2Random
3Low coherence
4Low amplitude deformed
5Low amplitude dipping
6High amplitude deformed
7Moderate amplitude continuous
8Chaotic
0Everything else

To generate training data for the seismic facies listed above, different picking scenarios are employed to compensate for the different input data format required in the two CNN models (small 3D patches versus whole 2D lines). For the patch-based model, 3D patches of seismic amplitude data are extracted around seed points within some user-defined polygons. There are approximately 400,000 3D patches of size 65×65×65 generated for the patch-based model, which is a reasonable amount for seismic data of this size. Figure 2a shows an example line on which seed point locations are defined in the co-rendered polygons.

The encoder-decoder model requires much more effort for generating labeled data. I manually interpret the target facies on 40 inlines across the seismic survey and use these for building the network. Although the total number of seismic samples in 40 lines are enormous, the encoder-decoder model only considers them as 40 input instances, which in fact are of very small size for a CNN network. Figure 2b shows an interpreted line which is used in training the network

In both tests, I randomly use 90% of the generated training data to train the network and use the remaining 10% for testing. On an Nvidia Quadro M5000 GPU with 8GB memory, the patch-based model takes about 30 minutes to converge, whereas the encoder-decoder model needs about 500 minutes. Besides the faster training, the patch-based model also has a higher test accuracy at almost 100% (99.9988%, to be exact) versus 94.1% from the encoder- decoder model. However, this accuracy measurement is sometimes a bit misleading. For a patch-based model, when picking the training and testing data, interpreters usually pick the most representative samples of each facies for which they have the most confidence, resulting in high quality training (and testing) data that are less noisy, and most of the ambiguous samples which are challenging for the classifier are excluded from testing. In contrast, to use an encoder-decoder model, interpreters have to interpret all the target facies in a training line. For example, if the target is faults, one needs to pick all faults in a training line, otherwise unlabeled faults will be considered as “non-fault” and confuse the classifier. Therefore, interpreters have to make some not-so-confident interpretation when generating training and testing data. Figure 2c and 2d show seismic facies predicted from the two CNN models on the same line shown in Figure 2a and 2b. We observe better defined facies from the encoder-decoder model compared to the patch- based model.

Figure 3 shows prediction results from the two networks on a line away from the training lines, and Figure 4 shows prediction results from the two networks on a crossline. Similar to the prediction results on the training line, comparing to the patch-based model, the encoder-decoder model provides facies as cleaner geobodies that require much less post-editing for regional stratigraphic classification (Figure 5). This can be attributed to an encoder-decoder model that is able to capture the large scale spatial arrangement of facies, whereas the patch-based model only senses patterns in small 3D windows. To form such windows, the patch-based model also needs to pad or simply skip samples close to the edge of a 3D seismic volume. Moreover, although the training is much faster in a patch-based model, the prediction stage is very computationally intensive, because it processes data size N×N×N times of the original seismic volume (N is the patch size along each dimension). In this study, the patch-based method takes about 400 seconds to predict a line, comparing to less than 1 second required in the encoder-decoder model.

Conclusion

In this study, I compared two types of CNN models in the application of seismic facies classification. The more commonly used patch-based model requires much less effort in generating labeled data, but the classification result is suboptimal comparing to the encoder-decoder model, and the prediction stage can be very time consuming. The encoder-decoder model generates superior classification result at near real-time speed, at the expense of more tedious labeled data picking and longer training time.

Acknowledgements

The author thanks Geophysical Insights for the permission to publish this work. Thank dGB Earth Sciences for providing the F3 North Sea seismic data to the public, and ConocoPhillips for sharing the MalenoV project for public use, which was referenced when generating the training data. The CNN models discussed in this study are implemented in TensorFlow, an open source library from Google.

Figure 2. Example of seismic amplitude co-rendered with training data picked on inline 340 used for a) patch-based model and b) encoder-decoder model. The prediction result from c) patch-based model, and d) from the encoder-decoder model. Target facies are colored in colder to warmer colors in the order shown in Table 1. Compare Facies 5, 6 and 8.

Figure 3. Prediction results from the two networks on a line away from the training lines. a) Predicted facies from the patch-based model. b) Predicted facies from the encoder-decoder based model. Target facies are colored in colder to warmer colors in the order shown in Table 1. The yellow dotted line marks the location of the crossline shown in Figure 4. Compare Facies 1, 5 and 8.

Figure 4. Prediction results from the two networks on a crossline. a) Predicted facies from the patch-based model. b) Predicted facies from the encoder-decoder model. Target facies are colored in colder to warmer colors in the order shown in Table 1. The yellow dotted lines mark the location of the inlines shown in Figure 2 and 3. Compare Facies 5 and 8.

Figure 5. Volumetric display of the predicted facies from the encoder-decoder model. The facies volume is visually cropped for display purpose. An inline and a crossline of seismic amplitude co-rendered with predicted facies are also displayed to show a broader distribution of the facies. Target facies are colored in colder to warmer colors in the order shown in Table 1.

References

Araya-Polo, M., T. Dahlke, C. Frogner, C. Zhang, T. Poggio, and D. Hohl, 2017, Automated fault detection without seismic processing: The Leading Edge, 36, 208–214.

Araya-Polo, M., J. Jennings, A. Adler, and T. Dahlke, 2018, Deep-learning tomography: The Leading Edge, 37, 58–66.

Badrinarayanan, V., A. Kendall, and R. Cipolla, 2017, SegNet: A deep convolutional encoder-decoder architecture for image segmentation: IEEE Transactions on Pattern Analysis and Machine Intelligence, 39, 2481–2495.

Chen, L. C., G. Papandreou, I. Kokkinos, K. Murphy, and A. L. Yuille, 2018, DeepLab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected CRFs: IEEE Transactions on Pattern Analysis and Machine Intelligence, 40, 834–848.

Chen, L. C., Y. Zhu, G. Papandreou, F. Schroff, and H. Adam, 2018, Encoder-decoder with atrous separable convolution for semantic image segmentation: arXiv preprint, arXiv:1802.02611v2.

Fehler, M., and K. Larner, 2008, SEG advanced modeling (SEAM): Phase I first year update: The Leading Edge, 27, 1006–1007.

Huang, L., X. Dong, and T. E. Clee, 2017, A scalable deep learning platform for identifying geologic features from seismic attributes: The Leading Edge, 36, 249–256.

LeCun, Y., Y. Bengio, and G. Hinton, 2015, Deep learning: Nature, 521, 436–444.

Lewis, W., and D. Vigh, 2017, Deep learning prior models from seismic images for full-waveform inversion: 87th Annual International Meeting, SEG, Expanded Abstracts, 1512–1517.

Long, J., E. Shelhamer, and T. Darrell, 2015, Fully convolutional networks for semantic segmentation: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 3431–3440.

Serfaty, Y., L. Itan, D. Chase, and Z. Koren, 2017, Wavefield separation via principle component analysis and deep learning in the local angle domain: 87th Annual International Meeting, SEG, Expanded Abstracts, 991–995.

Waldeland, A. U., and A. H. S. S. Solberg, 2017, Salt classification using deep learning: 79th Annual International Conference and Exhibition, EAGE, Extended Abstracts, Tu-B4-12.

Geobody Interpretation Through Multi-Attribute Surveys, Natural Clusters and Machine Learning

By Thomas A. Smith 
June 2017

Geobody interpretation through multi-attribute surveys, natural clusters and machine learning

Summary

Multi-attribute seismic samples (even as entire attribute surveys), Principal Component Analysis (PCA), attribute selection lists, and natural clusters in attribute space are candidate inputs to machine learning engines that can operate on these data to train neural network topologies and generate autopicked geobodies. This paper sets out a unified mathematical framework for the process from seismic samples to geobodies.  SOM is discussed in the context of inversion as a dimensionality-reducing classifier to deliver a winning neuron set.  PCA is a means to more clearly illuminate features of a particular class of geologic geobodies.  These principles are demonstrated with geobody autopicking below conventional thin bed resolution on a standard wedge model.

Introduction

Seismic attributes are now an integral component of nearly every 3D seismic interpretation.  Early development in seismic attributes is traced to Taner and Sheriff (1977).  Attributes have a variety of purposes for both general exploration and reservoir characterization, as laid out clearly by Chopra and Marfurt (2007).  Taner (2003) summarizes attribute mathematics with a discussion of usage.

Self-Organizing Maps (SOM) are a type of unsupervised neural networks that self-train in the sense that they obtain information directly from the data.  The SOM neural network is completely self-taught, which is in contrast to the perceptron and its various cousins undergo supervised training.  The winning neuron set that results from training then classifies the training samples to test itself by finding the nearest neuron to each training sample (winning neuron).  In addition, other data may be classified as well.  First discovered by Kohonen (1984), then advanced and expanded by its success in a number of areas (Kohonen, 2001; Laaksonen, 2011), SOM has become a part of several established neural network textbooks, namely Haykin (2009) and Dutta, Hart and Stork (2001).  Although the style of SOM discussed here has been used commercially for several years, only recently have results on conventional DHI plays been published (Roden, Smith and Sacrey, 2015).

Three Spaces

The concept of framing seismic attributes as multi-attribute seismic samples for SOM training and classification was presented by Taner, Treitel, and Smith (2009) in an SEG Workshop.  In that presentation, survey data and their computed attributes reside in survey space.  The neural network resides in neuron topology space.  These two meet in attribute space where neurons hunt for natural clusters and learn their characteristics.

Results were shown for 3D surveys over the venerable Stratton Field and a Gulf of Mexico salt dome.  The Stratton Field SOM results clearly demonstrated that there are continuous geobody events in the weak reflectivity zone between C38 and F11 events, some of which are well below seismic tuning thickness, that could be tied to conventional reflections and which correlated with wireline logs at the wells.  Studies of SOM machine learning of seismic models were presented by Smith and Taner (2010).  They showed how winning neurons distribute themselves in attribute space in proportion to the density of multi-attribute samples.  Finally, interpretation of SOM salt dome results found a low probability zone where multi-attribute samples of poor fit correlated with an apparent salt seal and DHI down-dip conformance (Smith and Treitel, 2010).

Survey Space to Attribute Space:

Ordinary seismic samples of amplitude traces in a 3D survey may be described as an ordered  set .  A multi-attribute survey is a “Super 3D Survey” constructed by combining a number of attribute surveys with the amplitude survey.  This adds another dimension to the set and another subscript, so the new set of samples including the additional attributes is .  These data may be thought of as separate surveys or equivalently separate samples within one survey.  Within a single survey, each sample is a multi-attribute vector.  This reduces the subscript by one count so the set of multi-attribute vectors  .

Next, a two-way mapping function may be defined that references the location of any sample in the 3D survey by single and triplet indices  Now the three survey coordinates may be gathered into a single index so the multi-attribute vector samples are also an unordered set in attribute space  The index map is a way to find a sample a sample in attribute space from survey space and vice versa.

Multi-attribute sample and set in attribute space: 

A multi-attribute seismic sample is a column vector in an ordered set of three subscripts c,d,e representing sample index, trace index, and line index. Survey bins refer to indices d and e.  These samples may also be organized into an unordered set with subscript i.  They are members of an -dimensional real space.  The attribute data are normalized so in fact multi-attribute samples reside in scaled attribute space.

Natural clusters in attribute space: 

Just as there are reflecting horizons in survey space, there must be clusters of coherent energy in attribute space.  Random samples, which carry no information, are uniformly distributed in attribute space just as in survey space.  The set  of natural clusters in attribute space is unordered and contains m  members.  Here, the brackets [1, M]  indicate an index range.  The natural clusters may reside anywhere in attribute space, but attribute space is filled with multi-attribute samples, only some of which are meaningful natural clusters.  Natural clusters may be big or small, tightly packed or diffuse.  The rest of the samples are scattered throughout F-space.  Natural clusters are discovered in attribute space with learning machines imbued with simple training rules and aided by properties of their neural networks.

A single natural cluster: 

A natural cluster may have elements in it.  Every natural cluster is expected to have a different number of multi-attribute samples associated with it.  Each element is taken from the pool of the set of all multi-attribute samples   Every natural cluster may have a different number of multi-attribute samples associated with it so for any natural cluster,  then N(m).  Every natural cluster has its own unique properties described by the subset of samples  that are associated with it.  Some sample subsets associated with a winning neuron are small (“not so popular”) and some subsets are large (“very popular”).  The distribution of Euclidean distances may be tight (“packed”) or loose (“diffuse”).

Geobody sample and geobody set in survey space: 

For this presentation, a geobody G_b is defined as a contiguous region in survey space composed of elements which are identified by members g.  The members of a geobody are an ordered set  which registers with those coordinates of members of the multi-attribute seismic survey .

A geobody member is just an identification number (id), an integer .  Although the 3D seismic survey is a fully populated “brick” with members ,  the geobody members  register at certain contiguous locations, but not all of them.  The geobody  is an amorphous, but contiguous, “blob” within the “brick” of the 3D survey.  The coordinates of the geobody blob in the earth are  where  By this, all the multi-attribute samples in the geobody may be found, given the id and three survey coordinates of a seed point.

A single geobody in survey space

Each geobody  is a set of  N geobody  members with the same id.  That is, there are N members in , so N(b).  The geobody members for this geobody are taken from the pool of all geobody samples, the set  Some geobodies are small and others large.  Some are tabular, some lenticular, some channels, faults, columns, etc.  So how are geobodies and natural clusters related?

A geobody is not a natural cluster

This expression is short but sweet.  It says a lot.  On the left is the set of all B geobodies.  On the right is the set of M natural clusters.  The expression says that these two sets aren’t the same.  On the left, the geobody members are id numbers  These are in survey space.  On the right, the natural clusters  These are in attribute space.  What this means is that geobodies are not directly revealed by natural clusters.  So, what is missing?

Interpretation is conducted in survey space.  Machine learning is conducted in attribute space.  Someone has to pick the list of attributes.  The attributes must be tailored to the geological question at hand.  And a good geological question is always the best starting point for any interpretation.

A natural cluster is an imaged geobody

Here, a natural cluster C_m is defined as an unorganized set of two kinds of objects: a function I of a set of geobodies G_i and random noise N.  The number of geobodies is I and unspecified.  The function  is an illumination function which places the geobodies in  The illumination function is defined by the choice of attributes.  This is the attribute selection list.  The number of geobodies in a natural cluster C_m is zero or more, 0<i<I.  The geobodies are distributed throughout the 3D survey.

The natural cluster concentrates geobodies of similar illumination properties.  If there are no geobodies or there is no illumination with a particular attribute selection list,  , so the set is only noise.  The attribute selection list is a critically import part of multi-attribute seismic interpretation.  The wrong attribute list may not illuminate any geobodies at all.

Geobody inversion from a math perspective

Multi-attribute seismic interpretation proceeds from the preceding equation in three parts.  First, as part of an inversion process, a natural cluster   is statistically estimated by a machine learning classifier such as SOM  with a neural network topology.  See Chopra, Castagna and Potniaguie (2006) for a contrasting inversion methodology.  Secondly, SOM employs a simple training rule that a neuron nearest a selected training sample is declared the winner and the winning neuron advances toward the sample a small amount.  Neurons are trained by attraction to samples.  One complete pass through the training samples is called an epoch.  Other machine learning algorithm have other training rules to adapt to data.  Finally, SOM has a dimensionality reducing feature because information contained in natural clusters is transferred (imperfectly) to the winning neuron set in the finalized neural network topology through cooperative learning.  Neurons in winning neuron neighborhood topology move along with the winning neuron in attribute space.  SOM training is also dynamic in that the size of the neighborhood decreases with each training time step so that eventually the neighborhood shrinks so that all subsequent training steps are competitive.

Because  is a statistical estimate, let it be called the statistical estimate of the “signal” part of .  The true geobody is independent of an illumination function.  The dimensionality reduction   associated with multi-attribute interpretation has a purpose of geobody recognition through identification, dimensionality reduction and classification.  In fact, in the chain of steps there is a mapping and un-mapping process with no guarantee that the geobody will be recovered: 

However, the image function   may be inappropriate to illuminate the geobody in F-space because of a poor choice of attributes.  So at best, the geobodies is illuminated by an imperfect set of attributes and detected by a classifier that is primitive.  The results often must be combined, edited and packaged into useful, interpreted geobody units, ready to be incorporated into an evolving geomodel on which the interpretation will rest.

Attribute Space Illumination

One fundamental aspect of machine learning is dimensionality reduction from attribute space because its dimensions are usually beyond our grasp.  The approach taken here is from the perspective of manifolds which are defined as spaces with the property of “mapability” where Euclidean coordinates may be safely employed within any local neighborhood (Haykin, 2009, p.437-442).

The manifold assumption is important because SOM learning is routinely conducted on multi-attribute samples in attribute space using Euclidean distances to move neurons during training.  One of the first concerns of dimensionality reduction is the potential to lose details in natural clusters.  In practice, it has been found that halving the original amplitude sample interval is advantageous, but further downsampling has not proven to be beneficial.  Infilling a natural cluster allows neurons during competitive training to adapt to subtle details that might be missed in the original data.

Curse of Dimensionality

The Curse of Dimensionality (Haykin, 2009) is, in fact, many curses.  One problem is that uniformly sampled space increases dramatically with increasing dimensionality.  This has implications when gathering training samples for a neural network.  For example, cutting a unit length bar (1-D) with a sample interval of .01 results in 100 samples.  Dividing a unit length hypercube in 10-D with a similar sample interval results in 1020 samples (1010 x 102).  If the nature of attribute space requires uniform sampling across a broad numerical range, then a large number of attributes may not be practical.  However, uniform sampling is not an issue here because the objective is to locate and detail features of natural clusters.

Also, not all attributes are important.  In the hunt for natural clusters, PCA (Haykin, 2009) is often a valuable tool to assess the relative merits of each attribute in a SOM attribute selection list.  Depending on geologic objectives, several dominant attributes may be picked from the first, second or even third principal eigenvectors or may pick all attributes from one principle eigenvector.

Geobody inversion from an interpretation perspective

Multi-attribute seismic interpretation is finding geobodies in survey space aided by machine learning tools that hunt for natural clusters in attribute space.  The interpreter’s critical role in this process is the following:

  • Choose questions that carry exploration toward meaningful conclusions.
  • Be creative with seismic attributes so as to effectively address illumination of geologic geobodies.
  • Pick attribute selection lists with the assistance of PCA.
  • Review the results of machine learning which may identify interesting geobodies  in natural clusters autopicked by SOM.
  • Look through the noise to edit and build geobodies  with a workbench of visualization displays and a variety of statistical decision-making tools.
  • Construct geomodels by combining autopicked geobodies which in turn allow predictions on where to make better drilling decisions.

The Geomodel

After classification, picking geobodies from their winning neurons starts by filling an empty geomodel .  Natural clusters are consolidators of geobodies with common properties in attribute space so M < B.  In fact, it is often found that M << B .  That is, geobodies “stack” in attribute space.  Seismic data is noisy.  Natural clusters are consequentially statistical.  Not every sample g classified by a winning neuron is important although SOM classifies every sample. Samples that are a poor fit are probably noise.  Construction of a sensible geomodel depends on answering well thought out geological questions and phrased by selection of appropriate attribute selection lists.

Working below classic seismic tuning thickness

Classical seismic tuning thickness is λ/4.  Combining vertical incidence layer thickness  with  λ=V/f leads to a critical layer thickness  Resolution below classical seismic tuning thickness has been demonstrated with multi-attribute seismic samples and a machine learning classifier operating on those samples in scaled attribute space (Roden, et. al., 2015). High-quality natural clusters in attribute space imply tight, dense balls (low entropy, high density).  SOM training and classification of a classical wedge model at three noise levels is shown in Figures 1 and 2 which show tracking well below tuning thickness.

Seismic Processing: Processing the survey at a fine sample interval is preferred over resampling the final survey to a fine sample interval. Highest S/N ratio is always preferred. Preprocessing: Fine sample interval of base survey is preferred to raising the density of natural clusters and then computing attributes, but do not compute attributes and then resample because some attributes are not continuous functions. Derive all attributes from a single base survey in order to avoid misties. Attribute Selection List: Prefer attributes that address the specific properties of an intended geologic geobody. Working below tuning, prefer instantaneous attributes over attributes requiring spatial sampling.  Thin bed results on 3D surveys in the Eagle Ford Shale Facies of South Texas and in the Alibel horizon of the Middle Frio Onshore Texas and Group corroborated with extensive well control to verify consistent results for more accurate mapping of facies below tuning without usual traditional frequency assumptions (Roden, Smith, Santogrossi and Sacrey, personal communication, 2017).

Conclusion

There is a firm mathematical basis for a unified treatment of multi-attribute seismic samples, natural clusters, geobodies and machine learning classifiers such as SOM.  Interpretation of multi-attribute seismic data is showing great promise, having demonstrated resolution well below conventional seismic thin bed resolution due to high-quality natural clusters in attribute space which have been detected by a robust classifier such as SOM.

Acknowledgments

I am thankful to have worked with two great geoscientists, Tury Taner and Sven Treitel during the genesis of these ideas.  I am also grateful to work with an inspired and inspiring team of coworkers who are equally committed to excellence.  In particular, Rocky Roden and Deborah Sacrey are longstanding associates with a shared curiosity to understand things and colleagues of a hunter’s spirit.

Figure 1: Wedge models for three noise levels trained and classified by SOM with attribute list of amplitude and Hilbert transform (not shown) on 8 x 8 hexagonal neuron topology. Upper displays are amplitude. Middle displays are SOM classifications with a smooth color map. Lower displays are SOM classifications with a random color map. The rightmost vertical column is an enlargement of wedge model tips at highest noise level.  Multi-attribute classification samples are clearly tracking well below tuning thickness which is left of the center in the right column displays.

Figure 2: Attribute space for three wedge models with horizontal axis of amplitude and vertical axis of Hilbert transform. Upper displays are multi-attribute samples before SOM training and lower displays after training and samples classified by winning neurons in lower left with smooth color map.  Upper right is an enlargement of tip of third noise level wedge model from Figure 1 where below-tuning bed thickness is right of the thick vertical black line.

References

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ChingWen Chen, seismic interpreterTHOMAS A. SMITH is president and chief executive officer of Geophysical Insights, which he founded in 2008 to develop machine learning processes for multiattribute seismic analysis. Smith founded Seismic Micro-Technology in 1984, focused on personal computer-based seismic interpretation. He began his career in 1971 as a processing geophysicist at Chevron Geophysical. Smith is a recipient of the Society of Exploration Geophysicists’ Enterprise Award, Iowa State University’s Distinguished Alumni Award and the University of Houston’s Distinguished Alumni Award for Natural Sciences and Mathematics. He holds a B.S. and an M.S. in geology from Iowa State, and a Ph.D. in geophysics from the University of Houston.