The neighborhood edge distance dmax → 0 as ζ → 0. As time marches on, the neighborhood edge shrinks to zero and continued processing steps of SOM are similar to K-means clustering (Bishop, 2007). Additional details of SOM learning are found in Appendix A on SOM analysis operation.
Rather than apply the SOM learning process to a large time or depth window spanning an entire 3D survey, we sample a subset of the full complement of multi-attribute samples in a process called harvesting. This is first introduced by Taner et al. (2009) and is described in more detail by Smith and Taner (2010).
First, a representative set of harvest patches from the 3D survey is selected, and then on each of these patches, we conduct independent SOM training. Each harvest patch is one or more lines, and each SOM analysis yields a set of winning neurons. We then apply a harvest rule to select the set of winning neurons that best represent the full set of data samples of interest.
A variety of harvest rules has been investigated. We often choose a harvest rule based on best learning. Best learning selects the winning neuron set for the SOM training, in which there has been the largest proportional reduction of error between initial and final epochs on the data that were presented. The error is measured by summing distances as a measure of how near the winning neurons are to their respective data samples. The largest reduction in error is the indicator of best learning. Additional details on harvest sampling and harvest rules are found in Appendix A on SOM analysis operation.
Self-organizing-map classification and probabilities
Once natural clusters have been identified, it is a simple task to classify samples in survey space as members of a particular cluster. That is, once the learning process has completed, the winning neuron set is used to classify each selected multi-attribute sample in the survey. Each neuron in the winning neuron set (j = 1 to J) is tested with equation 9 against each selected sample in the survey (i = 1 to I). Each selected sample then has assigned to it a neuron that is nearest to that sample in Euclidean distance. The winning neuron index is assigned to that sample in the survey.
Every sample in the survey has associated with it a winning neuron separated by a Euclidean distance that is the square root of equation 7. After classification, we study the Euclidean distances to see how well the neurons fit. Although there are perhaps many millions of survey samples, there are far fewer neurons, so for each neuron, we collect its distribution of survey sample distances. Some samples near the neuron are a good fit, and some samples far from the neuron are a poor fit. We quantify the goodness-of-fit by distance variance as described in Appendix A. Certainly, the probability of a correct classification of a neuron to a data sample is higher when the distance is smaller than when it is larger. So, in addition to assigning a winning neuron index to a sample, we also assign a classification probability. The classification probability ranges from one to zero corresponding to distance separations of zero to infinity. Those areas in the survey where the classification probability is low correspond to areas where no neuron fits the data very well. In other words, anomalous regions in the survey are noted by low probability. Additional comments are found in Appendicx A.
Case Studies – Offshore Gulf of Mexico
This case study is located offshore Louisiana in the Gulf of Mexico in a water depth of 143 m (470 ft). This shallow field (approximately 1188 m [3900 ft]) has two producing wells that were drilled on the upthrown side of an east–west-trending normal fault and into an amplitude anomaly identified on the available 3D seismic data. The normally pressured reservoir is approximately 30 m (100 ft) thick and located in a typical “bright-spot” setting, i.e., a Class 3 AVO geologic setting (Rutherford and Williams, 1989). The goal of the multi-attribute analysis is to more clearly identify possible DHI characteristics such as flat spots (hydrocarbon contacts) and attenuation effects to better understand the existing reservoir and provide important approaches to decrease risk for future exploration in the area.
Table 2. Instantaneous seismic attributes used in the PCA evaluation for the Gulf of Mexico case study.
Initially, 18 instantaneous seismic attributes were generated from the 3D data in this area (see Table 2). These seismic attributes were put into a PCA evaluation to determine which produced the largest variation in the data and the most meaningful attributes for SOM analysis. The PCA was computed in a window 20 ms above and 150 ms below the mapped top of the reservoir over the entire survey, which encompassed approximately 26 km2 (10 mi2). Figure 3a displays a chart with each bar representing the highest eigenvalue on its associated inline over the displayed portion of the survey. The bars in red in Figure 3a specifically denote the inlines that cover the areal extent of the amplitude feature and the average of their eigenvalue results are displayed in Figure 3b and 3c. Figure 3b displays the principal components from the selected inlines over the anomalous feature with the highest eigenvalue (first principal component) indicating the percentage of seismic attributes contributing to this largest variation in the data. In this first principal component, the top seismic attributes include the envelope, envelope modulated phase, envelope second derivative, sweetness, and average energy, all of which account for more than 63% of the variance of all the instantaneous attributes in this PCA evaluation. Figure 3c displays the PCA results, but this time the second highest eigenvalue was selected and produced a different set of seismic attributes. The top seismic attributes from the second principal component include instantaneous frequency, thin bed indicator, acceleration of phase, and dominant frequency, which total almost 70% of the variance of the 18 instantaneous seismic attributes analyzed. These results suggest that when applied to an SOM analysis, perhaps the two sets of seismic attributes for the first and second principal components will help to define two different types of anomalous features or different characteristics of the same feature.
Results from PCA using 18 instantaneous seismic attributes: (a) bar chart with each bar denoting the highest eigenvalue for its associated inline over the displayed portion of the seismic 3D volume. The red bars specifically represent the highest eigenvalues on the inlines over the field, (b) average of eigenvalues over the field (red) with the first principal component in orange and associated seismic attribute contributions to the right, and (c) second principal component over the field with the seismic attribute contributions to the right. The top five attributes in panel (b) were run in SOM A, and the top four attributes in panel (c) were run in SOM B.
The first SOM analysis (SOM A) incorporates the seismic attributes defined by the PCA with the highest variation in the data, i.e., the five highest percentage contributing attributes in Figure 3b. Several neuron counts for SOM analyses were run on the data with lower count matrices revealing broad, discrete features and the higher counts displaying more detail and less variation. The SOM results from a 5 × 5 matrix of neurons (25) were selected for this paper. The north–south line through the field in Figures 4 and 5 shows the original stacked amplitude data and classification results from the SOM analyses. In Figure 4b, the color map associated with the SOM classification results indicates all 25 neurons are displayed, and Figure 4c shows results with four interpreted neurons highlighted. Based on the location of the hydrocarbons determined from well control, it is interpreted from the SOM results that attenuation in the reservoir is very pronounced with this evaluation. As Figure 4b and 4c reveal, there is apparent absorption banding in the reservoir above the known hydrocarbon contacts defined by the wells in the field. This makes sense because the seismic attributes used are sensitive to relatively low-frequency broad variations in the seismic signal often associated with attenuation effects. This combination of seismic attributes used in the SOM analysis generates a more pronounced and clearer picture of attenuation in the reservoir than any one of the seismic attributes or the original amplitude volume individually. Downdip of the field is another undrilled anomaly that also reveals apparent attenuation effects.
Figure 4. SOM A results on the north–south inline through the field: (a) original stacked amplitude, (b) SOM results with associated 5 × 5 color map displaying all 25 neurons, and (c) SOM results with four neurons selected that isolate interpreted attenuation effects.
Figure 5. SOM B results on the same inline as Figure 4: (a) original stacked amplitude, (b) SOM results with associated 5 × 5 color map, and (c) SOM results with color map showing two neurons that highlight flat spots in the data. The hydrocarbon contacts (flat spots) in the field were confirmed by well control.
The second SOM evaluation (SOM B) includes the seismic attributes with the highest percentages from the second principal component based on the PCA (see Figure 3). It is important to note that these attributes are different than the attributes determined from the first principal component. With a 5 × 5 neuron matrix, Figure 5 shows the classification results from this SOM evaluation on the same north–south line as Figure 4, and it clearly identifies several hydrocarbon contacts in the form of flat spots. These hydrocarbon contacts in the field are confirmed by the well control. Figure 5b defines three apparent flat spots, which are further isolated in Figure 5c that displays these features with two neurons. The gas/oil contact in the field was very difficult to see on the original seismic data, but it is well defined and mappable from this SOM analysis. The oil/water contact in the field is represented by a flat spot that defines the overall base of the hydrocarbon reservoir. Hints of this oil/water contact were interpreted from the original amplitude data, but the second SOM classification provides important information to clearly define the areal extent of reservoir. Downdip of the field is another apparent flat spot event that is undrilled and is similar to the flat spots identified in the field. Based on SOM evaluations A and B in the field that reveal similar known attenuation and flat spot results, respectively, there is a high probability this undrilled feature contains hydrocarbons.
Shallow Yegua trend in Gulf Coast of Texas
This case study is located in Lavaca County, Texas, and targets the Yegua Formation at approximately 1828 m (6000 ft). The initial well was drilled just downthrown on a small southwest–northeast regional fault, with a subsequent well being drilled on the upthrown side. There were small stacked data amplitude anomalies on the available 3D seismic data at both well locations. The Yegua in the wells is approximately 5 m (18 ft) thick and is composed of thinly laminated sands. Porosities range from 24% to 30% and are normally pressured. Because of the thin laminations and often lower porosities, these anomalies exhibit a class 2 AVO response, with near-zero amplitudes on the near offsets and an increase in negative amplitude with offset (Rutherford and Williams, 1989). The goal of the multi-attribute analysis was to determine the full extent of the reservoir because both wells were performing much better than the size of the amplitude anomaly indicated from the stacked seismic data (Figure 6a and 6b). The first well drilled downthrown had a stacked data amplitude anomaly of approximately 70 acres, whereas the second well upthrown had an anomaly of about 34 acres.
Figure 6. Stacked data amplitude maps at the Yegua level denote: (a) interpreted outline of hydrocarbon distribution based on upthrown amplitude anomaly and (b) interpreted outline of hydrocarbons based on downthrown amplitude anomaly.
Table 3. The AVO seismic attributes computed and used for the SOM evaluation in the Yegua case study.
Figure 7. The SOM classification at the Yegua level denoting a larger area around the wells associated with gas drainage than indicated from the stacked amplitude response as seen in Figure 6. Also shown is the location of the arbitrary line displayed in Figure 8. The 1D color bar has been designed to highlight neurons 1 through 9 interpreted to indicate those neuron patterns which represent sand/reservoir extents.
The gathers that came with the seismic data had been conditioned and were used in creating very specific AVO volumes conducive to the identification of class 2 AVO anomalies in this geologic setting. In this case, the AVO attributes selected were based on the interpreter’s experience in this geologic setting.
Table 3 lists the AVO attributes and the attributes generated from the AVO attributes used in this SOM evaluation. The intercept and gradient volumes were created using the Shuey three-term approximation of the Zoeppritz equation (Shuey, 1985). The near-offset volume was produced from the
0°–15° offsets and the far-offset volume from the 31°–45° offsets. The attenuation, envelope bands on the envelope breaks, and envelope bands on the phase breaks seismic attributes were all calculated from the far-offset volume. For this SOM evaluation, an 8 × 8 matrix (64 neurons) was used.
Figure 7 displays the areal distribution of the SOM classification at the Yegua interval. The interpretation of this SOM classification is that the two areas outlined represent the hydrocarbon producing portion of the reservoir and all the connectivity of the sand feeding into the well bores. On the downthrown side of the fault, the drainage area has increased to approximately 280 acres, which supports the engineering and pressure data. The areal extent of the drainage area on the upthrown reservoir has increased to approximately 95 acres, and again agreeing with the production data. It is apparent that the upthrown well is in the feeder channel, which deposited sand across the then-active fault and splays along the fault scarp.
In addition to the SOM classification, the anomalous character of these sands can be easily seen in the probability results from the SOM analysis (Figure 8). The probability is a measure of how far the neuron is from its identified cluster (see Appendix A). The low-probability zones denote the most anomalous areas determined from the SOM evaluation. The most anomalous areas typically will have the lowest probability, whereas the events that are present over most of the data, such as horizons, interfaces, etc., will have higher probabilities. Because the seismic attributes that went into this SOM analysis are AVO-related attributes that enhance DHI features, these low-probability zones are interpreted to be associated with the Yegua hydrocarbonbearing sands.
Figure 8. Arbitrary line (location in Figure 7) showing low probability in the Yegua at each well location, indicative of anomalous results from the SOM evaluation. The colors represent probabilities with the wiggle trace in the background from the original stacked amplitude data.
Figure 9. The SOM classification results at a time slice show the base of the upthrown reservoir and the upper portion of the downthrown reservoir and denote: (a) full classification results defined by the associated 2D color map and (b) isolation of upthrown and downthrown reservoirs by specific neurons represented by the associated 2D color map
Figure 9 displays the SOM classification results with a time slice located at the base of the upthrown reservoir and the upper portion of the downthrown reservoir. There is a slight dip component in the figure. Figure 9a reveals the total SOM classification results with all 64 neurons as indicated by the associated 2D color map. Figure 9b is the same time slice slightly rotated to the west with very specific neurons highlighted in the 2D color map defining the upthrown and downthrown fields. The advantage of SOM classification analyses is the ability to isolate specific neurons that highlight desired geologic features. In this case, the SOM classification of the AVO-related attributes was able to define the reservoirs drilled by each of the wells and provide a more accurate picture of their areal distributions than the stacked data amplitude information.
Eagle Ford Shale
This study is conducted using 3D seismic data from the Eagle Ford Shale resource play of south Texas. Understanding the existing fault and fracture patterns in the Eagle Ford Shale is critical to optimizing well locations, well plans, and fracture treatment design. To identify fracture trends, the industry routinely uses various seismic techniques, such as processing of seismic attributes, especially geometric attributes, to derive the maximum structural information from the data.
Geometric seismic attributes describe the spatial and temporal relationship of all other attributes (Taner, 2003). The two main categories of these multitrace attributes are coherency/similarity and curvature. The objective of coherency/similarity attributes is to enhance the visibility of the geometric characteristics of seismic data such as dip, azimuth, and continuity. Curvature is a measure of how bent or deformed a surface is at a particular point with the more deformed the surface the more the curvature. These characteristics measure the lateral relationships in the data and emphasize the continuity of events such as faults, fractures, and folds.
Figure 10. Three geometric attributes at the top of the Eagle Ford Shale computed from (left) the full-frequency data and (right) the 24.2-Hz spectral decomposition volume with results from the (a) dip of maximum similarity, (b) curvature most positive, and (c) curvature minimum. The 1D color bar is common for each pair of outputs.
Table 4 Geometric attributes used in the Eagle Ford Shale SOM analysis.
Figure 11. SOM results from the top of the Eagle Ford Shale with associated 2D color map.
The goal of this case study is to more accurately define the fault and fracture patterns (regional stress fields) than what had already been revealed in running geometric attributes over the existing stacked seismic data. Initially, 18 instantaneous attributes, 14 coherency/similarity attributes, 10 curvature attributes, and 40 frequency subband volumes of spectral decomposition were generated. In the evaluation of these seismic attributes, it was determined in the Eagle Ford interval that the highest energy resided in the 22- to 26-Hz range. Therefore, a comparison was made with geometric attributes computed from a spectral decomposition volume with a center frequency of 24.2 Hz with the same geometric attributes computed from the original fullfrequency volume. At the Eagle Ford interval, Figure 10 compares three geometric attributes generated from the original seismic volume with the same geometric attributes generated from the 24.2-Hz spectral decomposition volume. It is evident from each of these geometric attributes that there is an improvement in the image delineation of fault/fracture trends with the spectral decomposition volumes. Based on the results of the geometric attributes produced from the 24.2-Hz volume and trends in the associated PCA interpretation, Table 4 lists the attributes used in the SOM analysis over the Eagle Ford interval. This SOM analysis incorporated an 8 × 8 matrix (64 neurons). Figure 11 displays the results at the top of the Eagle Ford Shale of the SOM analysis using the nine geometric attributes computed from the 24.2-Hz spectral decomposition volume. The associated 2D color map in Figure 11 provides the correlation of colors to neurons. There are very clear northeast–southwest trends of relatively large fault and fracture systems, which are typical for the Eagle Ford Shale (primarily in dark blue). What is also evident is an orthogonal set of events running southeast–northwest and east–west (red).
Figure 12. SOM results from the top of the Eagle Ford Shale with (a) only neuron 31 highlighted denoting northeast–southwest trends, (b) neuron 14 highlighted denoting east–west trends, and (c) three neurons highlighted with neuron 24 displaying smoothed nonfaulted background trend.
To further evaluate the SOM results, individual clusters or patterns in the data are isolated with the highlighting of specific neurons in the 2D color map in Figure 12. Figure 12a indicates neuron 31 (blue) is defining the larger northeast–southwest fault/fracture trends in the Eagle Ford Shale. Figure 12b with neuron 14 (red) indicates orthogonal sets of events. Because the survey was acquired southeast–northwest, it could be interpreted that the similar trending events in Figure 12b are possible acquisition footprint effects, but there are very clear indications of east–west lineations also. These east–west lineations probably represent fault/fracture trends orthogonal to the major northeast–southwest trends in the region. Figure 12c displays the neurons from Figure 12a and 12b, as well as neuron 24 (dark gray). With these three neurons highlighted, it is easy to see the fault and fracture trends against a background, where neuron 24 displays a relatively smooth and nonfaulted region. The key issue in this evaluation is that the SOM analysis allows the breakout of the fault/fracture trends and allows the geoscientist to make better informed decisions in their interpretation.
Seismic attributes, which are any measurable properties of seismic data, aid interpreters in identifying geologic features, which are not clearly understood in the original data. However, the enormous amount of information generated from seismic attributes and the difficulty in understanding how these attributes when combined define geology, requires another approach in the interpretation workflow. The application of PCA can help interpreters to identify seismic attributes that show the most variance in the data for a given geologic setting. The PCA works very well in geologic settings, where anomalous features stand out from the background data, such as class 3 AVO settings that exhibit DHI characteristics. The PCA helps to determine, which attributes to use in a multi-attribute analysis using SOMs.
Applying current computing technology, visualization techniques, and understanding of appropriate parameters for SOM, enables interpreters to take multiple seismic attributes and identify the natural organizational patterns in the data. Multiple-attribute analyses are beneficial when single attributes are indistinct. These natural patterns or clusters represent geologic information embedded in the data and can help to identify geologic features, geobodies, and aspects of geology that often cannot be interpreted by any other means. The SOM evaluations have proven to be beneficial in essentially all geologic settings including unconventional resource plays, moderately compacted onshore regions, and offshore unconsolidated sediments. An important observation in the three case studies is that the seismic attributes used in each SOM analysis were different. This indicates the appropriate seismic attributes to use in any SOM evaluation should be based on the interpretation problem to be solved and the associated geologic setting. The application of PCA and SOM can not only identify geologic patterns not seen previously in the seismic data, but it also can increase or decrease confidence in already interpreted features. In other words, this multi-attribute approach provides a methodology to produce a more accurate risk assessment of a geoscientist’s interpretation and may represent the next generation of advanced interpretation.
The authors would like to thank the staff of Geophysical Insights for the research and development of the applications used in this paper. We offer sincere thanks to T. Taner (deceased) and S. Treitel, who were early visionaries to recognize the breadth and depth of neural network benefits as they apply to our industry. They planted seeds. The seismic data offshore West Africa was generously provided by B. Bernth (deceased) of SCS Corporation. The seismic data in the offshore Gulf of Mexico case study is courtesy of Petroleum Geo-Services. Thanks to T. Englehart for insight into the Gulf of Mexico case study. Thanks also to P. Santogrossi and B. Taylor for review of the paper and for the thoughtful feedback.