and where k N include the samples drawn from k for that winning neuron. Some winning neurons in equation (9) have a small collection of x samples while others will have a larger collection.
In the set x for a winning neuron wk, for each of the f attributes [1 to F] we can determine a histogram. If there is a peak in the histogram we have found a higher magnitude in the probability distribution in that particular dimension and so score this attribute as a success. We count all attributes in this way (1 for success or 0 for failure) and divide the result by the number of attributes. Curvature measures density and lies in the range [0,1]. Each neuron and each attribute has a curvature measure.
Harvesting and consistency
A harvesting process consists of three steps. First, unsupervised neural network analyses are run on independent sets of data that have been drawn from a 2D or
3D survey. A rule is then used to decide which candidate is the best solution. Finally, the set of neurons of the best solution are used to classify the entire survey.
We have conducted a series of SOM analysis and classification steps for the Stratton Field 3D Seismic Survey (provided to us by courtesy of the Bureau of Economic Geology and the University of Texas). A time window of 1.2 to 1.8s was selected for SOM analysis with an 8 x 8 hexagonal network and 100 learning epochs. We measured performance by standard deviation of error between data samples and their winning neurons. Standard deviation error reduction was typically 35%. A separate SOM analysis was conducted on each of the 100 lines in order to assess consistency of results. The SOM results were highly consistent with a variation of final standard deviation of error of only 1.5% of the mean. The rule used here is to select the SOM solution for the line which best fits its data through smallest error of fit.
Figure 5: SOM classification of Line 53. Timing lines at 1.3 and 1.6s are marked by arrows.
Figure 6: Hexagonal colorbar for Figure 5.
The SOM results form a new attribute volume of winning neuron classifications. Every sample in this new volume is the index of the winning neuron number for a given data sample. The SOM analysis was derived from 50 attributes which included basic trace attributes, geometric attributes and spectral decompositions. A solution line is shown in Figure 5.
First observe that the SOM results more or less track geology as shown by flat reflections near 1.3s. At the well are shown SP and GR well log curves with lithologic shading, formation top picks as well as a synthetic seismogram (white WTVA trace along the borehole). A second reflector above 1.6s is a second key marker. Also notice the green patches near 1.5s. These were identified as patches with lateral consistency. We have no geologic interpretation at this time. In Figure 6 we show the colorbar patterned to the neuron topology and colored to assist in identification of regions of neuron clusters.
Figure 7:Vertical section through a 3D survey of a Gulf of Mexico
Figure 8: SOM classification with p > .1 corresponding to the same
slice as Figure 7.
Figure 9: Time slice for Figure 8.
Curvature measure (CM) of the neurons fell in the range .72 to .9 except for one neuron which had a curvature measure of .26. It was found that this winning neuron resulted from only 8 samples while others had 17 to 139.
We have investigated the CM attribute measure and found that there were 3 poor performing attributes (CM < .2); 4 attributes which we consider questionable (CM ≈ .5) and 43 strong attributes (CM > .8).
Automatic anomaly identification
Equation 9 is the basis on which we classify the quality of classification samples. For any winning neuron, we select samples with probability p which exceed threshold pmin
based on the distance between the winning neuron and its samples, shown here as equation 10. Those samples that are near their winning neuron have higher probability.
From Figure 7, the classification of Figure 8 results from a SOM analysis with an 8 x 8 neuron network, designed on the basis of F=13 attributes and 100 epochs. Those samples whose probabilities lie below pmin are anomalous and assigned a white color. The rest of the classification uses the colorbar of Figure 6.
The red lines of Figures 8 and 9 register their views so the white area anomaly on the right side of the salt in Figure 8 has an areal extent that appears to be bounded by the salt in Figure 9. We are not suggesting that all anomalies are of geologic interest. However, those of sufficient size are worthy of investigation for geologic merit.
This presentation investigates the areas within a 3D survey where multiple attributes are of unusual character. Self-organizing maps assist with an automatic identification process. While these results are encouraging, it is readily apparent that additional investigations must be made into appropriate learning controls. Various structural and stratigraphic questions which might be posed to SOM analysis will require careful selection of appropriate attributes. It is also clear that calibration of SOM analyses with borehole information offers an attractive area of investigation.
Tury Taner was our inspiration and pioneer in this area.
THOMAS A. SMITH received BS and MS degrees in Geology from Iowa State University. In 1971, he joined Chevron Geophysical as a processing geophysicist. In 1980 he left to pursue doctoral studies in Geophysics at the University of Houston. Dr. Smith founded Seismic Micro-Technology in 1984 and there led the development of the KINGDOM software suite for seismic interpretation. In 2007, he sold the majority position in the company but retained a position on the Board of DIrectors. SMT is in the process of being acquired by IHS. On completion, the SMT Board will be dissolved. IN 2008, he founded Geophysical Insights where he and several other geophysicists are developing advanced technologies for fundamental geophysical problems.
The SEG awarded Tom the SEG Enterprise Award in 2000, and in 2010, GSH awarded him the Honorary Membership Award. Iowa State University awarded him Distinguished Alumnus Lecturer Aware in 1996 and Citation of Merit for National and International Recognition in 2002. Seismic Micro-Technology received a GSH Corporate Star Award in 2005. In 2008, he founded Geophysical Insights to develop advanced technologies to address fundamental geophysical problems. Dr. Smith has been a member of the SEG since 1967 and is also a member of the HGS, EAGE, SIPES, AAPG, GSH, Sigma XI, SSA, and AGU.