This webinar features a 45-minute presentation by Dr. Bob Hardage (CV below), a researcher and proponent of the application of Direct-P and Converted-P data since its inception in 2011. The technique is receiving renewed interest with the use of machine learning. An interactive Q&A with Dr. Hardage will follow his presentation.
Title: Unsupervised Machine Learning Applied to Direct-P and Converted-P Data | Presenter: Dr. Bob Hardage | Date: Wednesday/Thursday, 17/18 February 2021
What you will learn in this webinar:
Joint interpretation of direct-P and converted-P images of stacked turbidites.
Value provided by a long-ignored seismic mode generated by P sources and recorded by vertical geophones – the SV-P (or converted-P) mode.
Comparisons between principal components of P-P, P-SV, and SV-P data.
Comparisons of self-organized maps (SOMs) of direct-P and converted-P data.
SOM examples of damaging data-acquisition footprints.
Why direct-P data and converted-P data often do not detect the same rock boundaries.
Examples of turbidite attribute fabric defined by specific direct-P and converted-P winning neurons.
First, there are several types of machine learning so the qualifier “Unsupervised” machine learning is important to inform people as to what type of machine learning will be discussed.
Second, during the past 10 years, I have found frequently that any reference to “S” data turns off many people who do not want to jump into the arena of S-wave reflection seismology. In contrast, the term “converted-P” (which is what SV-P data are) usually attracts people. In fact, the most common reaction is that people are interested because they have never heard the term, converted-P, and are curious as to the nature of the data. So, I now use the term “converted-P” more frequently than “SV-P”.
As a side note, here is an analogy that may help us all understand how SV-P (or converted-P) data and P-SV (or converted-S) data are related. In my younger years, the most famous dancing team in the world was Fred Astaire and Ginger Rogers. Fred Astaire could do beautiful dance steps and was the more famous of the pair. However, Ginger Rogers did the same steps, but did them backwards and in high heels, so it is arguable as to who was the more talented.
Today, P-SV data are popular and respected. SV-P data are the mirror image of P-SV data, but do not have the esteem that P-SV data do. Thus, P-SV data are Fred Astaire, and SV-P data are Ginger Rogers. Whatever people have done to demonstrate the value of P-SV data can also be done with SV-P data. We just have to do everything backwards when processing SV-P data compared to the methodology that is used to process P-SV data. At any rock boundary, an SV-P reflectivity curve exactly follows the P-SV reflectivity curve for that same boundary, except that the magnitudes of the SV-P reflection coefficients are usually about 10 or 15 percent smaller than the magnitude of the P-SV curve. The result is that whatever P-SV data (Fred Astaire) can do, SV-P data (Ginger Rogers) can do the same thing by reversing the ray paths.
Any well log data to confirm the seismic interpretation?
There were 8 or 10 wells inside the image space, but there was a limited amount of log data at the depths of the Wolfberry turbidites. The seismic data used in this study were acquired 20 years ago before there was interest in fracking tight turbidites. Thus, log data acquisition focused on deeper intervals, below the Wolfberry turbidites, that were the drilling targets two decades ago.
How do you interpret by seeing only single SOM slices?
In order to interpret geology, you absolutely must view SOM results in 3D space and not rely on just a few slices through a SOM volume. I used single SOM slices because I was attempting to teach how winning neurons reveal clusters of attributes that look like the three key, large-scale, features of turbidites that I wanted people to focus on; i.e., (1) map views of linear shearing in the direction that a turbidite system slides into the basin, (2) map views of features oriented orthogonal to the direction of sediment movement that appear to be front edges of prograding debris flows, and (3) section views of folding units inside the turbidite system. Recognizing these 3 key features is essential to defining the basic internal architecture of debris flows that stacked to vertical thickness of 2000 to 5000 ft. in the Midland Basin.
Nice image. Clay K and μ moduli may vary too much. Which actual values did you use?
I assume you are referring to slides 24 and 25. The dots on slide 24 show the mineralogy counts made from SEM scans of approximately 150 thin sections cut from cores taken at various depths in the Wolfberry turbidite interval. The thickness of the Wolfberry stacked turbidites vary from 700-m to 1600-m across the basin. These cores were also acquired at widely spaced wells across the 300-km X 100-km area of the Midland Basin. I use slide 24 only to illustrate that the mineralogy mixtures in Wolfberry turbidites vary widely. The 3 choices of mineral mixtures used for the matrix of a numerical turbidite in slide 25 do not represent any particular data point in slide 24. Our rock physicists made 50 or 60 arbitrary choices of possible mineral mixtures, created a synthetic rock that had stiffness coefficients that imitated a medium that had each set of those minerals evenly distributed throughout the turbidite unit. All stiffness coefficients, including K and μ, were different for each synthetic rock. The rock physicist calculated P-P and SVP reflection coefficients for each synthetic rock boundary. I picked 3 pairs of reflection coefficient results that interested me and made slide 25. I did not document what the numerical values of K and μ were for these 3 choices. I fear the analysis cannot be retrieved. It was done in 2010. The rock physicist left the university shortly after the DV-P imaging stage of this study was done in 2010-2011.
How do you depth register P-P and SV-P data?
The best option is to use VSP data acquired inside the image space that is being interpreted. VSP data are the only data that are acquired simultaneously as a function of depth and time. Thus, VSP data are the most reliable information as to: (1) the travel time when P and S reflections are created and start their upward journey to the surface, and (2) the exact depths where those upward journeys start.
The second choice, if dipole sonic log data are available to provide Vs velocities, would be to make P and S synthetic seismograms and see what they predict for the arrival times of P and S reflections from a target depth. This method forces you to estimate the average Vp and Vs velocities from the surface to the depth where dipole sonic-log data begin, which can be challenging. In contrast, the P and S travel times from the surface to the top receiver in a VSP receiver array is captured precisely in VSP data.
There were no VSP data or any extensive dipole sonic-log data available inside the image space at the site that I discuss. We thus implemented a practice that was often used during the 18 years that my research group at UT interpreted multicomponent seismic data. This practice was that 2 or 3 of the best interpreters in our group used their knowledge and experience to agree that 2 or 3 P-P reflections were the same rock boundary defined by 2 or 3 reflections in the S-mode data that we were utilizing. Each interpreter presented their arguments, a collective decision was made, and then the S data were dynamically time-warped so that the 2 or 3 key S reflections were time-matched with their interpreted P-P equivalents. This procedure is simply guesswork by experienced interpreters, but we had a string of successes using this method. If you are a lone interpreter, my advice would be that you have a session with 2 or 3 interpreters that you respect, present your arguments as to what are depth-equivalent P and S reflections, and then let your colleagues present counter arguments. I predict you will, as a group, come to an acceptable conclusion. The real answer for all of us is provided by the “rotary lie detector” test, which is the drill bit.
Why didn’t you run a single SOM on P-P and SV-P?
That would have been an interesting and valuable SOM option to have implemented. I walked away from this data set after getting to the point that I discussed in the Webinar so that I could apply unsupervised machine learning to other seismic data. The field of applications for unsupervised ML in reflection seismology spans analysis of pre-stack data, comparisons of fast-S and slow-S images, vertical seismic profile data, field data acquired with source A and then with source B, and on and on. When you gain access to ML software like Geophysical Insights provides, you become a kid in a candy store and run from opportunity to opportunity. Researchers like me can change from study A to study B at a whim. Interpreters who are charged with drilling a specific geographic area do not have this flexibility and have to try every logical way to implement a variety of SOM analyses that focus on a specific reservoir within a specific area. Your suggested option should be on the list of SOM procedures that should be done.
Isn’t it inconsistent that curve 3 is flat in PP (incidence) = null gradient = decrease of Vp/Vs while it is zero for SV-P?
When I saw this result and made slide 25, I had no concerns. I have seen so many instances where a P-P reflection occurs at a rock boundary, but its companion S-mode creates no reflection that now I never get too concerned when I see contrasting P-mode and S-mode behaviors at a target boundary. As you do joint interpretations of P and S data, you will commonly find reflectivity behaviors that correspond to strong-P but weak-S, strong-S but weak-P, positive-P but negative-S, positive-S but negative-P, zero-P, yet some S, and zero-S yet some P. People who do joint interpretations of P and S data need a talented rock physicist by their side. Only when I did this, did I begin to fully understand what I saw in P and S images across the same geology, and the rock-physics answers as to why reflection differences occurred in P-P and S-mode images that I was examining.
On slide 29, the color of neuron 9 between 1 and 17. Is it arbitrary or a property of SOM mapping? How do you determine the periodicity of 9?
The color of any winning neuron is arbitrary. SOM is concerned only about the “number” that is assigned to each winning neuron, not the “color” that is assigned to that neuron. SOM migrates all neurons through multi-dimensional attribute space until they each locate all of the natural clusters of attributes where there are unique mixtures of certain amounts of certain attributes. All neurons usually complete this “search and find” activity after 60 or so epochs of searching through the entirety of attribute space. When searching ends, each neuron then is a “winning” neuron. At this point, SOM knows the X-Y-Z coordinates where each numbered neuron is located. SOM does not know or care what the color of a winning neuron is. The color is controlled by the software user. You use a color of your choice, not SOM’s choice, to see where each winning neuron found the natural clusters that it sought and what shape and appearance each natural cluster has.
I am not sure what you mean by “periodicity,” so I will not guess.
In extracting SV-P, how do you minimize cross-feed/leakage from P-P data?
SV-P reflections are not hidden in vertical-geophone data. In contrast, they are prominent, and every data processor has seen them for years. I had seen SV-P reflections for decades and assumed that they were interbedding multiples, just like data processors still do. Because SV-P stacking velocities are slower than P-P stacking velocities, SV-P reflections have greater curvature than do P-P reflections. Whatever procedure that data processors use to isolate large-curvature reflections from small-curvature reflections can be used to isolate P-P reflections and SV-P reflections into separate data-processing streams. These concepts are covered by four U.S. Patents that are owned by the Board of Regents of The University of Texas. The University has created a company named VertiShear to commercialize the technology. VertiShear can provide no-cost licenses to interested data-processing companies. Yes, I wrote this statement correctly – the cost for a data-processing company to offer these patented SV-P data-processing services to their clients is zero.
Any recommendations/tips on processing the converted-P data. Especially for someone new to utilizing these data?
Locating a proper seismic data-processing company in the U.S. is an increasing problem today (year 2021) because of the widespread collapse of our seismic reflection seismology profession. Data-processing companies are closing their doors everywhere for lack of business. Any data-processing company that is still operating can implement proper SV-P data-processing procedures by working with VertiShear, the company that was founded by The University of Texas to provide SV-P technology to the public.
Please contact Vertishear at www.vertishear.com for advice and recommendations. Several SV-P technical reports and SV-P image examples are available at this site in the Whitepapers section. These papers provide valuable information and education. I just went to the site and realized that several recently published SV-P studies had not been inserted into this Whitepapers section. I will correct that lapse of due diligence. Meanwhile, do a search of papers that appear in the Interpretation journal (which is jointly published by SEG and AAPG) for any publication that shows “Hardage” as the first author. This search will provide the SV-P papers that have not yet been added to the Vertishear Website.
I am surprised that the attributes that dominate the information in the direct-P, converted-P, and converted-S data are identical. Any comments about why that occurs?
I, too was surprised. I anticipated that any mode that traveled as an S-wave on either its down path or on its up path, would have a different attribute structure than a mode that was a pure P-wave on both its down path and its up path. This initial assumption was based on the fact that a displacement vector of a P mode probes a rock system in a direction that is perpendicular to the direction that an S-mode displacement vector probes that same rock. My simple assumption was that 2 orthogonal probes would be affected by different rock stiffness coefficients and thus would “probably” react to different rock attributes.
The PCA results shown in this webinar indicate that my anticipation was unfounded because they show that the attributes that dominate the information content of P-P, P-SV, and SV-P are identical. I have been studying this PCA behavior by applying ML analyses to VSP data. In these studies, I create (1) SOMs of down-going illuminating P and S VSP wavefields that are produced by a single vertical-vibrator, (2) SOMs of the P and S reflection wavefields that each of these 2 illuminating VSP wavefields create, and (3) SOMs of the interbed multiples that these up-going P and S reflections then create as they travel upward to surface receivers. These SOMs show that when any illuminating wavefield, be it a P wavefield or a S wavefield, creates a reflection (be that reflection either a P or a S reflection), the attribute structure of the illuminating wavefield transfers intact to each reflection that it generates. Similarly, these up-going reflections (be they either P or S) transfer their attributes (which are the same attributes in the illuminating wavefield) perfectly intact to interbed multiples.
The process is much like the DNA of a multi-generational family. The first generation (the illuminating wavefields) transfer their DNA to the second generation (the up-going reflections), and these up-going reflections transfer the DNA to the third generation (the interbed multiples). When we accept this DNA-type principle, then the issue of “why do P-P, P-SV, and SV-P modes have the same attributes” boils down to one question, which is “why do the down-going P and S wavefields produced by a vertical vibrator (the first-generation wavelets) have identical attribute structures.”
I offer my opinion, which is – “illuminating P and S wavefields produced by a vertical vibrator have the same attribute structure because both wavefields are created simultaneously, by the same vibrator sweep, experience the same baseplate-to-earth coupling and exactly the same ground-stiffness environment during their creation, and are born at exactly the same clock time and at exactly the same location on the earth surface”.
How can I test this hypothesis? One obvious way is to apply PCA and SOM analyses to revert to the old way of collecting P and S VSP data in which you use a vertical vibrator to generate the down-going P wavefield but a horizontal vibrator to generate the down-going S wavefield. In this original VSP practice, the down-going P and S illuminating wavefields are produced by different sources, with different baseplate-to-earth couplings, different frequency sweeps, at slightly different baseplate locations, in slightly different stiffness environments, and at different clock times.
My first assumption is that in such a test, P-P and P-SV data will have the same attribute structure because both modes are produced by the same illuminating P wave. My second assumption is that the attribute structure of SV-P data will be different because the SV-P mode was generated by a different source with a different baseplate coupling, different sweep rate, etc. If I am able to do such a ML investigation, we may have to have another Webinar sometime.
Why did an acquisition footprint appear in the P-SV data but not in the SV-P data?
The data were acquired 9 years before we implemented this first-ever effort to make a SV-P image from vertical-geophone data. Our research lab at UT was not involved in the acquisition design. The evidence that an acquisition footprint would be encountered in the P-SV data should have been shown by examining appropriate stacking-fold maps that survey designers always make. I have no explanation why the problem was not revealed during the acquisition design. In 2001, when the data were acquired, no one even thought of acquiring SV-P data, so no one made a stacking-fold map to show the fold behavior of SV-P illumination.
A large 200-mi2 vertical-geophone survey was implemented by company A, the data owner. Company A had never worked with 3C data, so they decided to lay out a (2-mi2) X (2-mi.2) grid of 3C geophones in the interior of the large vertical-geophone survey. They then recorded 3C data using a (3-mi2) X (3-mi2) grid of source stations from the large survey that was centered on the (2-mi2) X (2-mi2) grid of 3C geophones.
Here now is an important insight into P-SV and SV-P imaging. The P-SV image point between a source and a receiver is closer to the receiver than to the source. This principle means that all P-SV reflection points in this instance were concentrated around the small (2-mi2) X (2-mi2) receiver area. In contrast, the SV-P image point between a source and a receiver is closer to the source than to the receiver. This fact means that all SV-P reflection points in this instance tried to expand to fill the large (3-mi2) X (3-mi2) source area. The same number of source-receiver pairs were used to make both the P-SV image and the SV-P image. The concentration of N reflection points into a small image area produced a footprint. The expansion of these N reflection points into a large image area avoided a footprint.
The seismic data must have some characteristics in sample rate or process?
The seismic data used in PCA and SOM analyses can be any type of standard digital seismic data; i.e., the data can be 2D, 3D, pre-stack trace gathers, VSP, etc. Sample rate can be any standard sampling rate used in the seismic community. The data need to be in SEGY format in order to be read by the Paradise software.
How can you explain the difference between P-SV and SV-P? Can you model the differences you see?
I assume that you refer to the 3 slides that show side-by-side horizontal slices through the P-SV and SV-P SOM volumes. The differences in the spatial distributions of P-SV and SV-P winning neurons in these comparisons are strictly a matter of having an acquisition footprint and avoiding an acquisition footprint.
Yes, every seismic data-acquisition company has software that can model the pattern of the stacking fold that a particular source and receiver geometry will create. This software was originally based on analyzing only common-midpoint imaging like P-P data. In the 1990s, our profession began to focus on acquiring P-SV data, so this modeling software was modified to create stacking-fold charts of P-SV reflection points. This modification required that you provide the software the average Vp/Vs velocity ratio across the image area. Proper use of this modeling software should prevent people from implementing a source-receiver geometry that will create an acquisition footprint in P-SV image space.
Here now is a fortunate outcome in this type of modeling. We have found that you can use the standard P-SV modeling software to also calculate SV-P stacking-fold patterns if you simply invert the Vp/Vs velocity ratio that you have to input into the software in order to control where P-SV reflection points occur. In other words, if a Vp/Vs value of 2 produces accurate P-SV stacking-fold charts, then changing that parameter to 0.5 (the inverse of 2) will generate accurate SV-P stacking-fold charts.
Can you please provide a reference for SV-P processing?
To my knowledge, there is no published paper that spells out the specifics of SV-P data processing. Probably the best general description of the data-processing flow is illustrated in the U.S. patents that cover the principles of practicing full-mode S-wave reflection seismology with P sources. These patents can be provided by VertiShear if you address an inquiry to www.vertishear.com. Although these patents will be helpful, a patent has to be written in the most general language possible so that its claims will span across all specific procedures that data processors may use. People usually want specific information; patents have to be written in general language. I have presented Webinars sponsored by the Geophysical Society of Houston that address this topic. Perhaps it is time to do another of those Webinars.
I need to emphasize an important implication of the issue that is discussed here. The fact that there are no examples of SV-P images produced by P sources in any geophysical literature until 2011, nor any descriptions of how such imaging can be performed, illustrates how unique the concept of SV-P imaging with P sources is. I will attach a list of published papers immediately after the end of this string of question answering that will provide you what has been distributed publicly about SV-P technology.
What is your experience on detecting faults when using SV-P compared to using P-P waves?
The most recent investigations that I have done have focused on using SV-P data to determine the azimuth of maximum horizontal stress (SHmax). In this case, the sources were buried explosives in shot holes, and the receivers were vertical geophones. There were no faults inside this image space, but if SV-P data can indicate the azimuth of SHmax, then you also know the direction that faults should be oriented if they were present. I am always forced to work with data that become available, which may or may not be ideal data to study a specific topic.
SHmax azimuth is the same direction that fast-S shear modes are polarized, so if SV-P data allow you to determine fast-S and slow-S propagation directions, then you know SHmax azimuth. In this recent study, fast-S/slow-S analyses were done by constructing azimuth-dependent SV-P trace gathers in every stacking bin, at 3 different geological horizons, across a 24-mi2 area (98,000 stacking bins per horizon). This SV-P analysis thus totaled to almost 300,000 estimates of SHmax azimuth. The data indicated that SHmax was oriented 65 degrees clockwise from north at all 3 horizons. All local and regional SHmax information that we could find for the study area agreed with this answer.
Parallel with this SV-P effort, an amplitude-versus-azimuth (AVAZ) analysis was done using azimuth-dependent P-P trace gathers at each stacking bin. Again, this P-P effort involved almost 300,000 estimates of SHmax. The P-P AVAZ predictions agreed with the SV-P predictions at the shallowest horizon (about 2500-ft deep), had an undesirable scatter but still indicated approximately the same SHmax azimuth as did SV-P data at the second horizon (about 4500 ft deep, but had too much scatter to be definitive at the deepest horizon (about 6500 ft deep).
So, in this first-ever test of SV-P versus P-P for fault detection, SV-P data appear to be the better choice for detecting and characterizing faults. This study will be published in the May issue of the Interpretation journal that is jointly sponsored by SEG and AAPG. I have never had a paper accepted so quickly. The review and acceptance phases were done in 2 months. One well-known reviewer wrote a note to the Editor stating that the paper should receive the Best Paper Award for 2021. I doubt that will occur, but it is an indication of the impact of the investigation. The paper also illustrates how SV-P reflections can be separated from P-P reflections in vertical-geophone data, which addresses a preceding question.
When were the seismic data acquired, and what kind of seismic data-processing was applied, PSTM or PSDM?
The data were acquired in 2001. We did not process the data until 2010, which is an example of extracting SV-P reflections from legacy data. The P-P and SV-P data that I show were imaged using PSTM procedures.
The SV-P seems wormy and smoothed. Is this normal or a processing artifact?
I recommend that you base your judgment by comparing P-P and SV-P data in their wiggle-trace form. Specifically, look at slide 5 of the Webinar presentation. Most people who have seen this comparison have concluded that the SV-P data are showing appropriate intra-turbidite details, but P-P data are excessively smoothing the data, which is the opposite of what you conclude. Opinions differ between interpreters about all issues, and you are not alone in being suspicious of SV-P data produced by a P source and recorded by vertical geophones. Suspicion is good. We all learn by being suspicious of a new imaging concept.
Regarding the possibility of a processing artifact, I need to say that the data used in this webinar were processed in 2011 and were the first-ever example of a converted-P (i.e., SV-P) image that is extracted from the same vertical-geophone data that provide direct-P (i.e., P-P) images. This initial data processing was done by Fairfield Nodal. Since 2011, we have conducted converted-P studies in 10 basins. Every SV-P image, except one, was created by a commercial data-processing shop, not by my research staff. The one exception is a converted-P image that was made by my last Ph.D. student. In these 10-basin results, each commercial data-processing group produced converted-P images that were exact matches to P-SV data if we were using 3C data. So far, all SV-P images have agreed with available subsurface control if we had no access to P-SV data. My conclusion is that SV-P data are not prone to processing artifacts that differ in any appreciable way from processing artifacts that can be embedded in any seismic image.
Slide 28. What is the basis for neuron picking that represented geology?
The logic that people use to see geological information in SOM data varies from interpreter to interpreter, as it should. Seismic interpretation is often more of an art than it is a science. I arrived at the illustrations shown in slide 28 by looking at the patterns produced by each of the 64 winning neurons, one at a time, to see what each winning neuron contributed to the SOM data volume. Generally, all interpreters do some form of this type of one-by-one examination of winning-neuron patterns to reach a decision about the geological information that is revealed by SOM data.
You must keep in mind that a winning neuron only identifies a natural cluster of a certain mixture of attributes. The interpreter then has to decide if that natural cluster is true geology. A natural cluster of attributes will occur at coordinates in real-data space where there is a group of organized wavelets. Go back to real-data space and look at the same coordinates where a winning neuron exists in the SOM volume. You may then be more comfortable in concluding that the winning neuron is, or is not, real geology.
What is the meaning of the dashed line in attributes of specific neurons? Why is it missing for some neuron lists?
The lists that you refer to are lists of “winning” neurons. I have labeled the lists with the single word “Neuron”. I need to modify the graphic so that the lists are titled “Winning Neuron”. At the present time, I am satisfied when the attributes embedded in a winning neuron’s search list total up to approximately 90-percent of the total information that a winning neuron can carry. When the percentages of attribute contributions reach that targeted level of 90%, I simply have a habit of drawing a dashed line and terminating the attribute list. The absence of a dashed line on a list means only that I was careless and inconsistent in my habit of indicating the cutoff of an attribute list.
The selection of winning neurons is too arbitrary. Is there a consistent procedure for inspecting winning neurons, or do you need such a procedure?
The reply to the preceding question applies to this question also. An interpreter has no ability to position a winning neuron at specific coordinates in attribute space. The size, shape, and location of each natural cluster that is defined by a SOM is controlled completely by SOM calculations.
An interpreter’s control of SOM results ends once she/he defines the number of searching neurons that SOM can use. This neuron number coincides with the number of neurons that appear on the color pallet used to make SOM displays. If you define the number of searching neurons to be 25, and then create a second SOM using 49 searching neurons, the two SOM results will be different. For example, a natural cluster that appeared as a single cluster when positioning 25 winning neurons in attribute space may appear as two natural clusters that combine to form that single cluster when SOM uses 49 searching neurons.
An interpreter can do nothing but wait until SOM calculations end to see where a winning neuron is located in multi-dimensional attribute space. This is why a SOM procedure is called “unsupervised” machined learning. An interpreter has no ability to “supervise; i.e., control” SOM results; she/he can only wait to see what SOM calculated. Once SOM calculations end, the interpreter then has 100-percent control and supervision of the colors to use to display objects found by winning neurons. It will be unusual for any two interpreters to agree on what color pallet is best for viewing where a SOM positioned the winning neurons.
Have you considered any other unsupervised approach, e.g. tSNE or applying Topical Data Analysis, e.g. UMAP?
The Webinar lecturer, Bob Hardage, does not know the history of the research that Geophysical Insights has done to determine which machine learning (ML) procedures should be provided by Paradise software. Consequently, I defer to Rocky Roden, who has been engaged in developing most of the Paradise applications, and to Dr. Tom Smith, President of Geophysical Insights, to provide you an accurate picture of the various ML approaches that Geophysical Insights has investigated.
Geophysical Insights has not yet tested tSNE (t-distributed stochastic neighbor embedding), which is a relatively new non-linear, dimension-reducing approach. We have tested other topical approaches like U-Matrix. We have found that U-Matrix works best in identifying relationships between neurons, or groups of neurons when a large number of neurons (usually >200) are employed. In applications with seismic attributes, we have found that seldom should more than 100 neurons be employed. When there are more than 100 neurons, some neurons begin to identify themselves as individuals, not as a data point that is associated with a cluster. This behavior implies that too many neurons are being used in the analysis.
Kohonen’s self-organizing map was a breakthrough in machine learning (ML for short) as a classification of high-dimensional data samples. After training, the neural network itself exhibits features of clustering. Prior to this and to the best of my knowledge (TAS, [email protected]), ML algorithms (both supervised and unsupervised) worked to classify data samples, but there was nothing to look at in the neural network itself. SOM neural networks exhibit an organization such that nearby, trained, neurons in the network are traced back to samples in nearby regions in the original data space. In other words, SOM neurons in the lower-left corner of the SOM map might be traced to samples in one portion of the original data space, while SOM neurons in the lower right corner might be traced to samples in another part of the data space. A nice introduction to high-dimensional classification may be found in Wikipedia (Cluster analysis – Wikipedia).
Indeed, natural clusters of samples in the original data space map to SOM winning neurons (see Haykin, Neural Networks, and Learning Machines, 3rd ed., 442-444 for discussion on how SOM neurons gravitate to natural clusters in attribute space). SOM training neurons are attracted to samples that stack (cluster) in the original data space (Smith, Taner, and Treitel, Self-Organizing Maps of Multi-Attribute 3D Seismic Reflection Surveys, SEG 2009 Workshop on “What’s New in Seismic Interpretation”).
We exploit this feature following the observation that certain trained neurons, or groups of nearby trained neurons, are associated with geologic-looking features in the seismic survey. This association has been confirmed by the drill bit many times and published several times in our peer-reviewed journals. If you have an electrical engineering background, you might be familiar with the concept of using a probe at various points on an operating “breadboard” circuit to track how a signal is modified across its various components.
Similarly, probe a self-organizing map to relate a trained winning neuron to seismic samples in the survey.
In general, there are three evolutionary stages of ML – self-adaptation, self-organization, and self-awareness (self-adaptation self-organization and self-awareness – Bing). Neural network recipes which exploit both dimensionality reduction and dimensionality expansion (autoencoders) were early examples of supervised neural networks that self-adapted to data. Today, an explosion of deep-learning algorithms has resulted in a variety of self-adaptations in supervised, semi-supervised, and unsupervised training sessions. SOM stands out as one of the earliest, and regrettably, one of only a few MLs with self-organization.
The concept of self-organization and probing neurons for geology is not restricted to SOM alone. While K-means is not self-organizing, tSNE is self-organizing. So, to get to your question, we are actively investigating tSNE as an area of research interest. Perhaps it will be a useful alternative to SOM.
I am not familiar with Topical Data Analysis and will have a look (Topological data analysis – Wikipedia).
UMAP is a display technique to look for separations between natural clusters.
Reports of UMAP are associated with SOM, but I see no reason why UMAP could not identify empty regions in an original data space for any self-organizing ML. UMAP detects separations between natural cluster regions by displaying the distance between adjacent winning neurons. Of course, as Rocky points out above, separations are more apparent when you have lots of neurons. Lots of trained neurons decompose parts of geologic geobodies into finer details that might result in missing the geobodies. SOM is a great tool for investigating geologic geobodies at different levels of detail. Our users typically run SOMs with a variety of neuron topologies (say 4×4, 6×6, 8×8, and perhaps 10×10) for their interpretation.
Fundamentally, our job is to deliver the very best ML tools to interpreters for them to make better predictions.
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