Patent Publication Number: US-6904367-B2

Title: Petroleum exploration and prediction apparatus and method

Description:
RELATED APPLICATIONS 
   This application claims the benefit of U.S. Provisional Application Ser. No. 60/416,342, filed Oct. 4, 2002, and entitled SEISMIC EVENT CONTRAST STACKING AND OTHER USES OF EVENT RESOLUTION IMAGING WITHIN THE OIL AND GAS INDUSTRY. 

   BACKGROUND 
   1. The Field of the Invention 
   This invention relates to signal processing and, more particularly, to novel systems and methods for pattern recognition and data interpretation relative to monitoring and categorizing patterns for predictably detecting and quantifying hydrocarbon deposits. 
   2. The Background Art 
   Seismic waves have been used to generate models of the earth&#39;s composition. In more recent times, seismic waves have been employed in an effort to located resources such as oil and gas deposits within the earth&#39;s surface formations. Well log data has also been applied to predicting resources within the earth. However, because of the low signal-to-noise ration (SNR) or high noise-to-signal ratio and complexity of seismic waves and well log data, generating accurate models of resource deposits has been difficult. 
   To facilitate the extraction of useful information, various types of signal processing strategies have been applied to seismic waves and well log data. Analysis strategies used by those skilled in the art have included spectral analysis, seismic trace stacking, various transforms, time-frequency distributions, spatial filtering methods, neural networks, fuzzy logic systems, and integrated neurofuzzy systems. As appreciated, each of these analysis techniques, however, typically relies on human inspection of the generated waveforms. Visual inspection may miss vital content that is implicit or hidden (e.g. time domain information). 
   Stacking of multiple seismic traces from pre-stack gathers generally employs summing or averaging signals acquired over many angles of incidence and many offsets. The end goal of stacking is to reduce noise and amplify certain, useful, seismic, waveforms. However, it further obscures other data. While useful for certain applications, averaging and stacking techniques have several significant drawbacks. Large quantities of information, just as valuable but less understood, are lost in the averaging or stacking. Only selected types of signals are able to survive massive averaging or summation over multiple offsets. Moreover, the averaging process only provides a comparison between groups of offsets or groups of angles rather than between the individual offsets or angles. 
   Alternative analysis approaches including Fourier Transforms; Hilbert Transforms; Wavelet Transforms; Short-Time Fourier Transforms; Wigner Functions; Generalized Time-Frequency Distributions; Parameter vs. Offset (PVO); and Amplitude vs. Offset (AVO) have been applied to seismic waves and well log data. While valuable for certain applications, these approaches typically require averaging over small groups of angles or small groups of offsets. Moreover, these approaches have not been fully integrated with computerized condition discrimination. Like spectral analysis techniques, these approaches rely on visual inspection of the generated waveforms, greatly increasing the possibility of error. 
   Spatial filtering methods, including: Principal Component Analysis; Singular Value Decomposition; and Eigenvalue Analysis have been applied to seismic waves and well log data. Such filtering methods tend to ignore frequency and temporal information. Additionally, these filtering techniques are usually applied only to seismic traces that have been averaged (post-stack seismic traces), otherwise the noise level is prohibitive. 
   Additional analysis techniques and methodology have been developed by those skilled in the art, to take advantage of recent increases in computer processing power. Neural networks have been developed to discover discriminate information. The traditional neural network approaches, however, generally take a long time to program and learn, are difficult to train, and tend to focus on local minima to the detriment of other more global and important areas. Moreover, most of these analysis techniques are limited by a lack of integration with time, frequency, and spatial analysis techniques. 
   Due to their inherent narrow ranges of applicability, prior methods of analysis have provided a fragmentary approach to seismic waves and well log data analysis. What is needed is an integrated waveform analysis method capable of extracting useful information from highly complex and irregular waveforms such as raw seismic data, pre-stack seismic gathers, post-stack seismic traces, and the variety of signal types comprising well log data sets. 
   BRIEF SUMMARY OF THE INVENTION 
   In accordance with the invention as embodied and broadly described herein, apparatus and methods in accordance with the present invention may include an event contrast stacker arranged to process seismic traces, well log data, and the like to produce reliable and accurate information about a geological formation. Particularly, characteristic signals relating to a geological formation may be gathered, amplified, processed, and recorded. Such signals may include seismic traces (raw traces, pre-stack gathers, post-stack gathers, and the like), well log data, and any other waveform or measured value believed to contain information as to the content, state, or composition of the geological formation. 
   The strategy of an event contrast stacker in accordance with the present invention is to apply several methods of analysis to each epoch (time period of interest) to find and exhibit consistent differences between epochs relating to different states and similarities between epochs related to similar states. An event contrast stacker may include a signal pre-processor, a learning system, a classification system, and an output generator. 
   A signal pre-processor may provide any filtering, amplification, and the like that may prepare the signal for further processing. Additionally, the signal pre-processor may divide the signal into time segments or epochs. Each epoch may be labeled according to the state, if known, of the geological formation from which the data pertaining to an epoch was collected. 
   A collection of data from epochs, where the physical system represented thereby is of a known state may be passed to a learning system. The learning system may use several waveform analysis techniques including, by way of example and not limitation, time-frequency expansion, feature coherence analysis, principal component analysis, and separation analysis. For convenience we may refer to any set of data recorded over an epoch of time and relating to the same sensed system as an “epoch,” even though an epoch is literally just the application time segment. Each epoch may be expanded by feature operators (mathematical manipulations applying waveform analysis techniques) to generate feature segments in an extended phase space representing spatial, time, frequency, phase, and interchannel relationships. The various feature segments corresponding to an epoch may be weighted in an effort to locate the feature segments containing information corresponding exclusively to the state of the epoch. Weightings or weights may be though of as respective coefficients for each mathematical function contributing to composite or sum of contributing functions. Thus a weight is a proportion of contribution of a function or value. 
   Once weighted, the feature segments corresponding to an epoch may be summed or superimposed. If successful, the superposition provides a resulting waveform containing a non-random feature or pattern uniquely corresponding to the state of the epoch. If unsuccessful, the operation provides no distinction and the learning system may begin another iteration and apply a different combination of feature operators, feature weights, or both feature operators and feature weights. The learning system may continue processing until the superimposed feature segments of an epoch result in a characteristic feature corresponding exclusively to the state of the epoch. Once the effective feature operators, feature weights, and the like have been determined, they may be incorporated into a separation key. A separation key provides feature operators and weights, along with a resulting waveshape or other characteristic that will reliably distinguish two opposing states. 
   In one embodiment of a system in accordance with the present invention, a classification system may use the separation key and apply the feature operators and weights (previously determined to be optimal) to a selected group of epochs referred to as classification epochs. Classification epochs may have known states or unknown states. True epoch state labels may be bound to analyzed epochs to enable a comparison with epoch classifications generated by the classification system. That is, the actual or true state associated with a particular epoch may provide a key to determine if that epoch has been correctly classified. Accordingly, this may provide a method of testing or validating the accuracy of an event contrast stacker. High classification accuracy of non-training epochs (separate and distinct from the learning epochs used in the creation of the separation key), indicates a valid, derived, separation key capable of repeatedly separating signals according to the state of the geological formation from which the signals were collected. 
   The classification system may forward certain data to an output generator to compile a statistical summary of the results. Additional outputs may include calculations of sensitivity, specificity and overall accuracy. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The foregoing features of the present invention will become more fully apparent from the following description and appended claims, taken in conjunction with the accompanying drawings. Understanding that these drawings depict only typical embodiments of apparatus and methods in accordance with the invention and are, therefore, not to be considered limiting of its scope, the invention will be described with additional specificity and detail through use of the accompanying drawings in which: 
       FIG. 1  is a schematic diagram of a geological formation having primary seismic waves propagated therethrough and reflected seismic waves recorded therefrom; 
       FIG. 2  is a schematic diagram of a well undergoing well log data collection; 
       FIG. 3  is a schematic block diagram illustrating a signal migrator in accordance with the present invention; 
       FIG. 4  is a perspective view of a three dimensional seismic volume comprising a collection of seismic traces; 
       FIG. 5  is a schematic block diagram of an embodiment of an event contrast stacker in accordance with the present invention; 
       FIG. 6  is a schematic block diagram of an embodiment of a learning system from an event contrast stacker in accordance with the present invention; 
       FIG. 7  is a graph of a feature operator comprising a weighting in a time space (domain); 
       FIG. 8  is a graph of a feature operator comprising a weighting in a frequency space (domain); 
       FIG. 9  is a table illustrating a feature map in accordance with the present invention wherein the signal epoch has been expanded into three time segments and twelve frequency segments to generate a total of thirty-six feature segments; 
       FIG. 10  is a table illustrating an embodiment of a weighting table have weights to be applied to the feature segments of  FIG. 9  in accordance with the present invention; 
       FIG. 11  is a schematic block diagram illustrating an example epoch corresponding to a state A before and after processing by an event contrast stacker in accordance with the present invention; 
       FIG. 12  is a schematic block diagram illustrating an example epoch corresponding to a state B before and after processing by an event contrast stacker in accordance with the present invention; 
       FIG. 13  is a table illustrating an embodiment of a separation key generated by a learning system in accordance with the present invention; 
       FIG. 14  is a graph of the separation key of  FIG. 13 ; 
       FIG. 15  is a schematic block diagram of an embodiment of a classification system from an event contrast stacker in accordance with the present invention; 
       FIG. 16  is an alternative embodiment of an event contrast stacker in accordance with the present invention; 
       FIG. 17  is a schematic block diagram of an alternative embodiment of a classification system from an event contrast stacker in accordance with the present invention; 
       FIG. 18  is a schematic block diagram of an embodiment of an output generator from an event contrast stacker in accordance with the present invention; 
       FIG. 19  is a graph of an activation value plot generated by an output generator in accordance with the present invention; 
       FIG. 20  is a graph of an alternative activation value plot generated by an output generator in accordance with the present invention; 
       FIG. 21  is a schematic block diagram illustrating the formation of a reliability matrix by an output generator in accordance with the present invention; 
       FIG. 22  is a schematic block diagram illustrating the formation of a discrimination matrix by an output generator in accordance with the present invention; 
       FIG. 23  is a schematic block diagram illustrating the formation of a dissimilarity matrix by an output generator in accordance with the present invention; 
       FIG. 24  is a schematic block diagram illustrating the formation of a similarity matrix by an output generator in accordance with the present invention; 
       FIG. 25  is a schematic block diagram illustrating an alternative embodiment of a similarity matrix in accordance with the present invention; 
       FIG. 26  is a schematic block diagram illustrating the formation of a contrast stacked signal by an event contrast stacker in accordance with the present invention; 
       FIG. 27  is a schematic diagram of a seismic contrast volume generated by an event contrast stacker in accordance with the present invention; 
       FIG. 28  is a schematic diagram of a three-dimensional image corresponding to the seismic contrast volume of  FIG. 27  in accordance with the present invention; 
       FIG. 29  is a schematic diagram of a two-dimensional, horizontal image corresponding to the seismic contrast volume of  FIG. 27  in accordance with the present invention; 
       FIG. 30  is a schematic diagram of a two-dimensional vertical image corresponding to the seismic contrast volume of  FIG. 27  in accordance with the present invention; 
       FIG. 31  is a schematic diagram of a number plot corresponding to the seismic contrast volume of  FIG. 27  in accordance with the present invention; 
       FIG. 32  is a schematic diagram of a color plot corresponding to the seismic contrast volume of  FIG. 27  in accordance with the present invention; 
       FIG. 33  is a schematic diagram of selected seismic traces containing a common event; 
       FIG. 34  is a schematic diagram of the selected seismic traces of  FIG. 33  migrated in accordance with the present invention to align common events; 
       FIG. 35  is a schematic diagram of selected seismic traces containing various events; 
       FIG. 36  is a schematic diagram of the selected seismic traces of  FIG. 35  migrated in accordance with the present invention to align the various events; 
       FIG. 37  is a two-dimensional, horizontal image derived, using prior art methods, from actual seismic data collected from an oil field; 
       FIG. 38  is a two-dimensional, horizontal image derived from data generated by an event contrast stacker in accordance with the present invention from seismic data collected from the oil field; 
       FIG. 39  is a two-dimensional, vertical image derived, using prior art methods, from actual seismic data from the oil field; 
       FIG. 40  is a two-dimensional, vertical image derived from data generated by an event contrast stacker in accordance with the present invention from seismic data collected from the oil field; 
       FIG. 41  is a table illustrating the status, time window examined, and number of traces processed in accordance with the present invention for each of the various wells drilled in the oil field; 
       FIG. 42  is a table illustrating a portion of a separation key found by an event contrast stacker in accordance with the present invention to be effective on seismic data collected from the oil field; 
       FIG. 43  is a graph of an activation value plot generated by an event contrast stacker in accordance with the present invention from seismic data collected from the oil field; 
       FIG. 44  is a table illustrating the status, time window examined, and number of traces processed in accordance with the present invention for each of the various wells drilled in a gas field; 
       FIG. 45  is a table illustrating a portion of one embodiment of a separation key found by an event contrast stacker, in accordance with the present invention, to be effective over an 80 millisecond window on seismic data collected from the gas field; 
       FIG. 46  is a table illustrating a portion of an alternative embodiment of a separation key found by an event contrast stacker in accordance with the present invention to be effective over a 200 millisecond window on seismic data collected from the gas field; 
       FIG. 47  is a two-dimensional, vertical image derived, using prior art methods, from actual seismic data collected from the gas field; 
       FIG. 48  is a two-dimensional, vertical image derived from data generated by an event contrast stacker in accordance with the present invention over an 80 millisecond window of seismic data collected from the gas field; 
       FIG. 49  is a two-dimensional, vertical image derived from data generated by an event contrast stacker in accordance with the present invention over a 200 millisecond window of seismic data collected from the gas field; 
       FIG. 50  is a table illustrating a portion of a separation key found by an event contrast stacker in accordance with the present invention to be effective in segregating seismic data pertaining to gas production above a selected economic value from seismic data pertaining to gas production below a selected economic value; and 
       FIG. 51  is a table illustrating a portion of a separation key found by an event contrast stacker in accordance with the present invention to be effective in segregating seismic data pertaining to hydrocarbon deposits from seismic data pertaining to water deposits. 
   

   DETAILED DESCRIPTION 
   It will be readily understood that the components of the present invention, as generally described and illustrated in the Figures herein, could be arranged and designed in a wide variety of different configurations. Thus, the following more detailed description of the embodiments of the system and methods in accordance with the present invention, as represented by  FIGS. 1 through 51 , is not intended to limit the scope of the invention, as claimed, but is merely representative of the presently preferred embodiments of the invention. 
   Certain embodiments of apparatus and methods in accordance with the present invention incorporate the hardware and software of the signal interpretation engine disclosed in U.S. Pat. No. 6,546,378, filed Apr. 24, 1997, and entitled SIGNAL INTERPRETATION ENGINE, incorporated herein by reference. The present application does not attempt to describe every detail of the signal interpretation engine. To this end, the details of the signal interpretation engine are contained in the patent specification directed thereto. Whereas, only a general description of selected modules and procedures is presented herewith. 
   Referring to  FIG. 1 , in general, a seismic study  10  may be conducted by positioning at least one source  12  and at least one receiver  14  on, above, or within the earth&#39;s surface  16 . A source  12  may generate a primary seismic wave  18  in a selected geological area  19  or geological formation  19 . As a primary wave  18  travels though the geological formation  19 , it may encounter reflectors  20 . Reflectors  20  may be changes in the earth&#39;s make-up, striations, strata, differentials in density, differentials in stiffness, differentials in elasticity, differentials in porosity, changes in phase, and the like. Various reflectors  20   a ,  20   b ,  20   c  may reflect the primary wave  18  creating corresponding reflected seismic waves  22   a ,  22   b ,  22   c . The reflected waves  22  may be recorded, in the order of their arrival, by a receiver  14 . Reflected waves  22  gathered by a receiver  14  may be used to interpret the composition, fluid content, extent, geometry, and the like of geological formations  19  far below the earth&#39;s surface  16 . 
   In general, sources  12  may be selected from any devices for generating a seismic wave  20 . Suitable sources  12  may include air guns, explosive charges, vibrators, vibroseis trucks, and the like. A receiver  14  may be any device that detects seismic energy in the form of ground motion (or a pressure wave in fluid) and transforms it to an electrical impulse  24  or signal  24 . Generally, receivers  14  are referred to as geophones, for use on land, and hydrophones, for use on water. The electrical impulse  24  recorded by a receiver  14  may be referred to as a seismic trace  24 . A trace  24  may, therefore, be defined as a recording of the response of the earth  19  to seismic energy passing from a source  12 , through subsurface layers (reflectors  20 ), and back to a receiver  14 . 
   The seismic waves  18 ,  22  produced by a source  12  and recorded by a receiver  14  are generally in the frequency range of approximately 1 to 120 Hz. Seismic waves  18 ,  22  may be divided into two main categories, namely, pressure waves and shear waves. Pressure waves are elastic body waves or sound waves in which particles oscillate in the direction the wave propagates. Shear waves are elastic body waves in which particles oscillate perpendicular to the direction in which the wave propagates. Shear waves may be generated when pressure waves impinge on an interface at non-normal incidence. Shear waves can likewise be converted to pressure waves. 
   Referring to  FIG. 2 , in certain applications, well log data  26  may be used to provide additional information about selected geological formations  19  below the earth&#39;s surface  16 . Well log data  26  may be collected by lowering an instrument array  28  into a well bore  30 . The instrument array  28  may measure or record any characteristic of the well environment  32 . For example, an instrument array  28  may emit various waves into the well environment  32  and record the response. Additionally, an instrument array  28  may measure temperature, pressure, conductivity, and the like of the well environment  32 . Well log data  26  may be used to better understand geological formations  19  penetrated by wells  30 . 
   Referring to  FIG. 3 , in certain embodiments of apparatus and methods in accordance with the present invention, a geologic study  10  may collect a first data bundle  34 , corresponding to a first geological formation  19  having state A. In a similar manner, a geological study  10  may collect a second data bundle  36 , corresponding to a second geological formation  19  having state B. The data bundles  34 ,  36  may contain seismic traces  24 , well log data  26 , some other measured signal, value, or the like, or any combination thereof. 
   Hereinafter, data processed in accordance with the present invention may be referred to generically as a signal  24 . However, it should be recognized that a signal  24  may include seismic traces  24  (e.g. raw traces, pre-stack gathers, post-stack gathers, attribute volumes, and the like), well log data  26 , and any other waveform or measured value containing information as to the content, state, or composition of a geological formation  19 . 
   In embodiments utilizing seismic traces  24 , the data bundles  34 ,  36  may be processed by a signal migrator  38 . In general, a signal migrator  38  may process traces  24  by applying filtering  40 , a pre-stack migration  42 , stacking  44 , a post-stack migration  46 , or any combination thereof. After processing of signals  24  by the signal migrator  38 , the signal migrator  24  may provide a first record  48  to store data corresponding to the first data bundle  34 . A second record  50  may be generated to store data corresponding to the second data bundle  36 . 
   A “migration”  42 ,  46  of a seismic trace  24  is a complex process to determine the location in three-dimensional space from which the trace  24  most likely originated. Migration  42 ,  46  often involves applying a predicted velocity profile for the geological area  19  being studied. That is, various materials transfer seismic waves  18 ,  22  at different velocities. By taking what is known about a particular geological formation  19 , an estimate may be formulated for how long it would take a primary seismic wave  18  to travel down to a particular reflector  20 , reflect, and travel as a reflected seismic wave  22  back to the surface  16 . The longer the time for a reflected wave  22  to arrive at the surface  16 , the deeper the reflector  20  and origin of the trace  24  is likely to be. This process may, however, be complicated by the ability of waves  18 ,  22  to reflect back and forth between reflectors  20  before arriving at the surface. Thus, the travel time of certain signals  24  may be artificially prolonged. 
   Using velocity profiles and various other techniques, geologists may provide an approximation of the location where a trace signal  24  was generated in three-dimensional space. This locating process may be important because it ties the information contained within a trace  24 , or a portion of a trace  24 , to a particular location. 
   Stacking  44  is often simply the averaging or summing of a signal  24  with other signals  24  collected by the same receiver  14  or by other receivers  14  in the same area. Stacking  44  is typically used in an attempt to amplify common characteristic of the signals  24 . However, in certain applications, stacking  44  by averaging or summing may destroy or cancel useful information. 
   The first and second records  48 ,  50  may be generated at various stages during processing by a signal migrator  38 . For example, the first and second records  48 ,  50  may be generated upon completion of the pre-stack migration  42 , stacking  44 , or the post-stack migration  46 . Traces  24  processed only through a pre-stack migration  42  may be referred to as pre-stack gathers. Pre-stack gathers may be rich with hidden information. However, traces  24  processed through a post-stack migration  46  (generally referred to as post-stack gathers) may also contain sufficient informational content to be useful. 
   In general, data  34 ,  36  not in the form of a seismic trace  24  collected from the surface  16  need not be processed by a signal migrator  38 . Migration  42 ,  46 , which is essentially an attempt to locate the source of signals  24  that have traveled large distances, is not necessary when the source of the data is already known. For example, well log data  26  by definition is tied to the area surrounding a well  30 , thus migration  42 ,  46  may not be needed. It should be recognized, however, that data  34 ,  36  in any form may be filtered, amplified, or otherwise processed as needed before the first  48  and second records  50  are generated. 
   Referring to  FIG. 4 , first and second data bundles  34 ,  36  in accordance with the present invention may represent any collection of information. In certain embodiments, a data bundle  34 ,  36  may comprise all, or any portion, of a three-dimensional seismic volume  52 . A three-dimensional seismic volume  52  may be any mathematical space (domain), defined by an X-axis  54 , Y-axis  56 , and Z-axis  58 , containing a selected number of signals  24  positioned therewithin. A three-dimensional seismic volume  52  may be aligned so increasing time  60  of the recorded signals  24  is aligned with the Z-axis  58 . Thus, progress in the negative direction along the Z-axis  58  may indicate increasing time  60  as well as increasing depth into the earth  19 . 
   As stated hereinabove, a data bundle  34 ,  36  may comprise all, or any portion, of a three-dimensional seismic volume  52 . Thus, a data bundle  34 ,  36  may represent a single signal  24 , a portion of a single signal  24 , multiple signals  24 , or portions of multiple signals  24 . If portions of multiple signals representing a particular value of time (depth) are utilized, the collection may be referred to as a horizon  62 . A data bundle  34 ,  36  comprising a horizon may be useful for extracting information about a particular “pay horizon” or other suspected hydrocarbon deposit. 
   Referring to  FIG. 5 , once processed as desired, the first and second records  48 ,  50  may be forwarded to a event contrast stacker  64 . In certain embodiments, an event contrast stacker  64  in accordance with the present invention applies several methods of analysis to the data bundles  34 ,  36  to find consistent similarities within signals  24  related to similar states and differences between signals  24  relating to different states. 
   In certain embodiments, an event contrast stacker  64  may begin by passing the first and second records  48 ,  50  through a signal pre-processor  66 . The signal pre-processor  66  may divide the records  48 ,  50  into epochs  68 . An epoch  68  may be defined as a time segment of a signal  24 . A label  70  may be applied to each epoch  68  to identify the state of the geological formation  19  from which the epoch  68  was collected. For example, epochs collected from a first geological formation  19  may have a label indicating that the epochs correspond to a state A. Similarly, epochs from a second geological formation  19  may have a label indicating that the epochs correspond to a state B, Not-A and distinct from A. 
   The state of a geological formation  19  may be any characteristic of the formation  19  whose presence or absence may be worth predicting, quantifying, or the like. In general, state A may be the presence of a characteristic, while state B is the absence of the characteristic. Thus, state B is typically the state Not-A. For example, state A may be the presence of a hydrocarbon deposit, while state B is the absence of a hydrocarbon deposit. State A may be oil production above an threshold value, while state B is oil production below a threshold value. Other suitable state pairs include: presence of sand, absence of sand; presence of shale, absence of shale; density above a threshold value, density below a threshold value; water content above a threshold value, water content below a threshold value; porosity above a threshold value, porosity below a threshold value; gas production above a threshold value, gas production below a threshold value; permeability above and below a threshold value; presence and absence of salt; presence and absence of absorbed noncondensible gases (fizz water); presence and absence of faults; or the like. 
   In selected embodiments, states A and B may be differentiated economically. For example, state A may be hydrocarbon production over $1000 per day, while state B may be hydrocarbon production below $50 per day. In another embodiment, state A may be an economically viable hydrocarbon well (production sufficient to cover operating costs), while state B is a non-economically viable hydrocarbon well (production insufficient to cover operating costs). In short, states A and B may be any two determinable conditions, qualities, characteristics, production rates, or the like of geological formations  19 . 
   In certain embodiments, the labels  70  applied to the epochs  68  may also contain location information. For example, a label  70  may contain a coordinate (e.g. ordered triplet), or other designation, to identify the location of the epoch  68  in a three-dimensional or other seismic volume  52 . 
   Once segmented and labeled, a selected number of the epochs  68 , each known to represent a known state A or state B, may be designated as learning epochs  72 . Similarly, a selected number of the epochs  68  unknown as to their representing state A or state B may be designated as classification epochs  74 . The learning epochs  72  may be forwarded to a learning system  76  while the classification epochs  74  may be forwarded to a classification system  78 . 
   In selected embodiments, the learning system  76  may operate on the learning epochs  72  until a suitable interpretation map  80  or separation key  80  is generated. A separation key  80  may be considered complete when, upon application thereof to the learning epochs  72 , a non-random pattern corresponding to one of state A or state B is generated. After formulation, the separation key  80  may be transmitted to the classification system  78 . In certain embodiments, the classification system  78  may provide a test to verify the utility of the newly generated separation key  80 . Additionally, the classification system  78  may analyze and expand the classification epochs  74  in accordance with the information supplied by the separation key  80 . 
   At any time during processing, selected information may be exported from the learning system  76 , the classification system  78 , or both the learning system  76  and the classifications system  78 , to an output generator  82  for conversion into a useful and easily accessible format. 
   In selected embodiments, an event contrast stacker  62  may be incorporated into a single unit incorporating both hardware and software in accordance with the present invention. In such a configuration, a drive, network connection, or the like may be provided for receiving the first and second records  48 ,  50 . In an alternative embodiment, an event contrast stacker  64  may simply be a personal computer having an appropriate hardware and software configuration sufficient to provide a desired level of data reception, recordation, amplification, and manipulation capabilities. 
   Those skilled in the art will readily recognize that various other modules or systems may be incorporated in connection with an event contrast stacker  64  in accordance with the present invention. It is intended, therefore, that the examples provided herein be viewed as exemplary of the principles of the present invention, and not as restrictive to particular structures, systems, modules, or methods for implementing those principles. 
   Referring to  FIGS. 6-13 , the learning system  76  may receive and process learning epochs  72  to compile an optimized formula (i.e. separation key  80 ) for segregating epochs  72  by state. Within a learning system  76 , learning epochs  72  may first be processed in a feature expansion module  84 . A feature expansion module  84  may provide  86  a collection of feature operators  88  comprising various mathematical manipulations. The collection of feature operators  88  may be stored within the feature expansion module  84  or input by a user. Additionally, a feature expansion module  84  may also be arranged to store a collection of feature operators  88  as well as receive feature operators  88  input by a user. 
   By processing each epoch  72  through a multitude of feature operators  88 , unique characteristics  90  or features  90  corresponding to a particular state may be magnified to the point that they become easily discernable to a computerized criterion or to a discerning user. A feature  90  may be any non-random pattern corresponding exclusively to epochs  72  of a particular state, as opposed to “not that particular state.” While certain feature operators  88 , or combinations of feature operators  88 , may be effective to produce repeatable features  90  in epochs  72  of a common state, other feature operators  88  may be ineffective. By processing the epochs  72  with a collection of feature operators  88 , the most effective feature operators  88  or combination of feature operators  88  may be identified. 
   In selected embodiments, the feature expansion module  84  may process each epoch  72  individually. In other embodiments, the feature expansion module  84  may consolidate epochs  72  before processing. For example, when multiple input signals  24  are contained within an epoch  72 , the feature expansion module  84  may superimpose any combination of the input signals  24  to create a composite signal. Selected signals  24  of an epoch  72  may be processed individually while others may be combined and analyzed in superposition. 
   In certain embodiments, a feature expansion module  84  may process a learning epoch  72  with feature operators  88  utilizing multiple waveform analysis techniques including time-frequency expansion, feature coherence analysis, principal component analysis, separation analysis, or the like. For example, processing learning epochs  72  with feature operators  88  may include applying frequency weighting factors, phase weighing factors, amplitude weighting factors, selective superposition of signals  24 , or the like. In selected embodiments, processing learning epochs  72  with feature operators  88  may also include comparing spacial pattern, signal  24  shape, area under the curve of selected signals  24 , or the like. 
   During processing by a feature operator  88 , each learning epoch  72  may be decomposed into feature segments  92  in an extended phase space representing space, time, frequency, phase, or the like. The feature segments  92  pertaining to a selected epoch  72  may be collected to generate  94  a feature map  96 . For example, in the illustrated embodiments of  FIGS. 7 and 8 , two feature operators  88  may expand an epoch  72 . The first feature operator  88   a  may expand the epoch  72  into three time segments  98 . The second feature operator  88   b  may expand each time segment  96  into twelve frequency bands  100 . 
   The first and second operators  88   a ,  88   b  may expand the epoch  72  into time segments  98  and frequency bands  100  by any suitable method. For example, in the illustrated embodiments of  FIGS. 7 and 8 , a Gaussian weighting  102  may be used to define the bounds of the time segments  98  and frequency bands  100 . The Gaussian weighting  102   a  of the first feature operator  88   a  may be defined in terms of a central time  104  and a time width  106 . If desired, the time width  106  may represent the location where the weighting of the Gaussian distribution  102   a  is half the maximum weighting. Similarly, the Gaussian weighting  102   b  of the second feature operator  88   b  may be defined in terms of a central frequency  108  and a frequency width  110 . If desired, the frequency width  110  may also represent the location where the weighting of the Gaussian distribution  102   b  is half the maximum weighting. 
   A feature map  96  may be generated  94  in any suitable manner. In the illustrated embodiment of  FIG. 9 , rows  112  may represent the various frequency bands  100  into which the epoch  72  was expanded. Columns  114  may represent the various time segments  98  into which the epoch  72  was expanded. Thus, each feature segment  92  may be charted according to its central frequency  108  and central time  104 . 
   Once completed, a feature map  96  may be forwarded to a weighting module  116 . Within a weighting module  116 , a weight table  118  may be generated  120 . A weight table  118  and accompanying weights  122  may be based on some manipulation of the signal data  24 ,  26  of an epoch  72  that will tend to self-neutralize. For example, certain resonance frequencies may occur at a frequency higher or lower than that of the background noise. Thus, shifting signal data  24 ,  26  slightly forward or backward within an epoch  72  and adding or multiplying the signal data  24 ,  26  together may provide enhancement of certain features  90 , while minimizing others relative thereto. 
   As in the illustrated embodiment of  FIG. 10 , a weight table  118  contains a value of weight  122  for each feature segment  92  contained within a feature map  96 . The weights  122  are arranged within the weight table  118  according to the feature segments  92  to which they apply. That is, the weights become coefficients. For example, the weight  122   a  contained in the first row and first column of the weight table  118  corresponds to the feature segment  92   a  in the first row and first column of the feature map  96 . The weights  122  illustrated in  FIG. 10  determine contributions or emphasize certain feature segments  92  while minimizing or virtually eliminating the effect of others. 
   In certain embodiments, upon leaving a weighting module  116 , feature segments  92  may enter a consolidation module  124 . In certain embodiments, the consolidation module  124  may apply  126  the weight table  118  to the feature map  96 . Additionally, a consolidation module  124  may act to compile what was previously separated by the feature expansion module  84 . For example, if an epoch  72  was expanded into feature segments  92  in the feature expansion module  84 , then the consolidation module  124  may collect the feature segments  92  in an effort to form a feature  90 . 
   A consolidation module  124  may consolidate feature segments  92  by any suitable method or mathematical manipulation. In certain embodiments, consolidation may include superposition  128  of the feature segments  92 . This can be a weighted sum of values. If the feature operators  88  and weights  122  were effective, when the feature segments  92  are assembled back together (e.g. added, consolidated), a feature  90  (e.g. a non-random shape of a waveform) unique to the state of the epoch  72  (and not existing when that state does not exist) may appear. 
   In the embodiments of  FIGS. 11 and 12 , example learning epochs  72   a ,  72   b  corresponding to mutually exclusive states A and B are illustrated. Both epochs  72   a ,  72   b  may contain a signal  24  appearing to be random. After processing by one or more effective feature operators  88  and weights  122 , a feature  90  corresponding to one state (A or B) and not the other (B or A) may be generated. In certain embodiments, recognizable, non-random patterns  90  or features  90  may be generated in epochs  72  corresponding to both states. In such cases, the feature operators  88  and weights  122  may still be considered effective so long as the feature  90  corresponding to state A is discernibly different from the feature  90  corresponding to state B. 
   In certain embodiments, before or after the feature segments  92  are superimposed  128 , the consolidation module  124  may aggregate  130  the feature segments  92  or the resulting feature  90 . Aggregation  130  may employ any method or mathematical manipulation directed to reducing the feature segments  92  or features  90  to a single numeric value characterizing the epoch  72 . In certain embodiments, aggregation  130  may involve assigning a numerical value corresponding to the magnitude of the presence or non-presence of a particular feature  90 . 
   In certain embodiments, after processing by a feature expansion module  84 , a weighting module  116 , and a consolidation module  124 , a typing confidence module  132  may evaluate the ability of the various feature operators  88 , weights  122 , or the like to generate or extract features  90  that reliably segregate epochs  72  according to their state. Evaluation of the processing may be accomplished in any suitable manner. 
   In one embodiment, the assigned numerical values corresponding to each epoch  72  may be plotted. A distribution  134  of epochs  72  corresponding to state A may be compared to a distribution  136  of epochs  72  corresponding to state B. If desired, an optimal threshold value  138  that best divides the two distributions  134 ,  136  may be selected. The percentage of epochs  72  corresponding to state A falling on the correct side of the threshold value  138  may be calculated. Similarly, the percentage of epochs  72  corresponding to state B falling on the correct side of the threshold value  138  may be calculated. If the calculated percentages surpass a selected level of statistical significance, the processing may be considered effective. The learning system  76  may continue to iterate through various feature operators  88  and weights  122  until an optimal procedure or formula for segregating epochs  72  by state is determined. 
   In certain embodiments, the optimized procedure or formula for segregating epochs  72  by state may be forwarded to a separation key  80 . For example, as illustrated in  FIG. 13 , a separation key  80  may outline the feature operators  88   a ,  88   b  successfully and reliably applied to generate a feature map  96 . The separation key  80  may indicate the weights  122  successfully applied to the feature segments  92 . A separation key  80  may also contain the optimal threshold value  138 , superposition  130  procedure, aggregation  130  procedure, or the like that were found by the learning system  76  to be the most effective. In general, a separation key  80  contain anything learned by the learning system  76 . 
   It may be noted that the portion of the separation key  80  illustrated in  FIG. 13  has been found by an event contrast stacker  64  in accordance with the present invention to be effective in segregating portions of a signal  24  pertaining to geological formations  19  containing sand from portions of a signal  24  pertaining to geological formations  19  containing little or no sand. That is, by expanding an epoch  68  into the twelve noted frequency bands  100  and three noted time segments  98  and applying the noted weights  122 , a feature  90  corresponding to the presence of absence of sand may be generated. 
   Referring to  FIG. 14 , a separation key  80  may be presented graphically, if desired. For example, a vertical axis  140  may represent the weighting  122 . A horizontal axis  142  may represent the frequency bands  100 . Each graph  144   a ,  144   b ,  144   c  may represent one of the various time segments  98 . A height  146  applied to a column  148  for each frequency band  100  may equal the weight  122  to be applied to that frequency band  100  for that time segment  98 .  FIG. 14  is arranged to be a graphical representation of the separation key  80  of FIG.  13 . 
   Referring to  FIG. 15 , the learning system  76 , once completed, may forward the separation key  80  to the classification system  78 . The classification system  78  may receive and process classification epochs  74  in accordance with the procedures contained within the separation key  80 . 
   In typical embodiments, the classification epochs  74  may be different from the learning epochs  72 . Thus, the classification system  78  may test the separation key  80  on epochs  74  that the event contrast stacker has never “evaluated” to provide a more rigorous tester validation. If the state of each epoch is known, the process is a validation. If not, classification epochs  74  are prediction outputs for use. Additionally, the number of classification epochs  74  may be greater than the number of learning epochs  72 . Classification epochs  74  may or may not be provided with a label  70  indicating the state of the geological formation  19  from which they were collected. During evaluation of a separation key  80 , labels  70  containing state information may be helpful in comparing actual state segregation against state segregation generated by the separation key  80 . Once a separation key  80  has been evaluated and proven reliable, any epoch  74  corresponding to geological formations  19  of unknown state may be received and processed by the classification system  78 . 
   In certain embodiments, similar to a learning system  76 , a classification system  78  may contain a feature expansion module  84  and a consolidation module  124 . Unlike a learning system  76 , however, a classification system  78  need not iterate through various procedures to collect the most effective feature operators  88 , weights  122 , superposition  128  procedures, aggregation  130  procedures, optimal threshold value  138 , or the like. A classification system  78  in accordance with the present invention applies the feature operators  88 , weights  122 , superposition procedures  128 , aggregation procedures  130 , optimal threshold value  138 , or the like that are provided in the separation key  80 . 
   Accordingly, unlike the feature expansion module  84  of the of the learning system  76 , the feature expansion module  84  of the classification system  78  does not apply a multitude of feature operators  88  to expand the epochs  74 . The feature expansion module  84  of the classification system  78  simply applies the effective feature operators  88  delivered thereto as part of the separation key  80 . 
   In selected embodiments, a weighting module  116  need not be included in a classification system  78 . A consolidation module  124  of the classification system  78  may apply the weight table  118  contained in the separation key  80 . Similarly, the consolidation module may apply the superposition procedure  128  and aggregation procedure  130  provided in the separation key  80 . Upon completion of processing by the consolidation module  124 , the resulting data may be passed to an output generator  82  to be converted into useful and easily accessible information. 
   Referring to  FIGS. 16 and 17 , in certain applications, after sufficient confidence is developed in a particular separation key  80 , it may not be necessary to enter the learning system  76  every time a new signal  24  is classified. Thus, an event contrast stacker  64  may be formed without a learning system  76 . In such embodiments, a proven separation key  80  may be coded within the classification system  78 . 
   For example, once a separation key  80  is generated for distinguishing between geological formations  19  containing oil above a desired production level and geological formations with no oil or with oil below a desired production level, a data bundle  152  contain signals  24  from a geological formation  19  having an unknown state may be analyzed. If desired, the data bundle  152  may be processed before entering an event contrast stacker  64 . In one embodiment, the data bundle  152  may be processed by a signal migrator  38 . A record  153  of the data bundle  152  may be generated. The record  153  may be forwarded to an event contrast stacker  64  and be divided by a signal pre-processor  66  into classification epochs  74 . Since the state of the epochs  74  is unknown, the epochs  74  cannot be labeled therewith. However, each classification epoch  74  may be labeled with a coordinate (e.g. ordered triplet) or other designation indicating the location from which the epoch  74  originated. 
   Upon processing by a classification system  78  having the internal separation key  80 , it may be determined whether the geological formation  19  corresponds more to a geological formations  19  containing oil above a desired production level or not, that is a geological formation with no oil or with oil below a desired production level. Accordingly, a user may determine which geological formations  19  are likely to produce oil as desired when tapped by a well. 
   As discussed hereinabove, certain embodiments of systems in accordance with the present invention may incorporate an event contrast stacker  64  into a single unit having a simple user interface. Such embodiments may be supplied with an internal database  150  containing various separation keys  80  for differentiating between hundreds or thousands of state pairs likely to be found in geological formations. A display and user interface may provide to a user the ability to select which separation key  80  is used. In an alternative embodiment, an event contrast stacker  64  may query the database  150  to find a separation key  80  most suited to a particular state comparison selected by a user. 
   An internal database  150  containing multiple separation keys  80  may also be supplied in addition to a learning system  76 . An event contrast stacker  64  containing both an internal database  150  and a learning system  76  may more quickly analyze common states using separation keys  80  recorded in the database  150 , while still providing the hardware and software to learn how to segregate additional states of geological formations  19 . In selected embodiments, an event contrast stacker  64  in accordance with the present invention, may store a copy of every new separation key  80  generated in an internal database  150  for future reference. In such a manner, the event contrast stacker  64  may quickly build up a database  150  of effective feature operators  88 , weights  122 , and so forth. 
   Referring to  FIG. 18 , an event contrast stacker  64  in accordance with the present invention may present data in multiple useful formats. The following output formats are presented as exemplary models and are not to be interpreted as being restrictive of the available formats. For example, these formats may include activation value plots  154 , reliability matrices  156 , contrast stacked signals  158 , contrast seismic volume  160 , and so forth. Additionally, several useful matrices may be derived from a reliability matrix  156 . These derivatives may include a discrimination accuracy matrix  162 , similarity matrix  164 , and dissimilarity matrix  166 . Furthermore, in certain embodiments, it may be desirable to simply output a plot of the feature  90  produced by the event contrast stacker  64  before it is aggregated  130  to a numerical value. 
   Referring to  FIG. 19 , an activation value plot  154  may have a spacing axis  168  and a magnitude axis  170 . The spacing axis  168  may simply allow a plotted point  172  to be slightly spaced in the horizontal direction from neighboring plotted points  172 . Thus, the plotted points  172  may be arranged to avoid entirely overlapping one another. The magnitude axis  170  may have a range  176  selected to illustrate a magnitude of the presence or non-presence of a particular distinguishing feature contained in each classified epoch  74 . 
   In certain embodiments, the spacing axis  168  may also be divided according to geological formations  19 . For example, a first section  174   a  of the spacing axis  168  may correspond to a first geological formation  19  penetrated by a first well. A second section  174   b  of the spacing axis  168  may correspond to a second geological formation  19  penetrated by a second well, and so on. The presence of a well may provide information concerning the state of the geological formation. For example, in the illustrated embodiment, wells one through three may be known gas producing wells  178 , while wells four and five are known to be dry holes  180  or non-producing wells  180 . Wells six and seven may be prospective wells  182  that are yet to be drilled. 
   To create an activation value plot  154 , an assigned numerical value for each classified epoch  74  may be scaled or otherwise manipulated to fit in the magnitude range  176  of the plot  154 . In one embodiment of a system in accordance with the present invention, the assigned numerical value is manipulated to fit within the range  176  from −1 to +1. The optimum threshold value  138  may be normalized to zero. Each small circle  172  or plotted point  172  may represent an epoch  74  of highly processed signal activity. 
   In the illustrated embodiment of  FIG. 19 , the producing wells  178  exhibit mostly positive (from 0 to +1) spectrum activation values. In contrast, the non-producing wells  180  exhibit mostly negative (from 0 to −1) spectrum activation values. The activation value plots  154  of prospective wells  182  may be compared to activation value plots for the producing and non-producing wells  178 ,  180 . Well six shows a strong correlation to the producing wells  178 . Thus, it may likely be profitable to drill well six. On the other hand, well seven shows a strong correlation to the non-producing wells  189 . Thus, it is likely to be unprofitable to drill well seven. 
   The ability to non-invasively and accurately predict the state of a geological formation  19  may be profitable. Drilling a hydrocarbon well can be very expensive. By more accurately predicting which prospective wells are likely to produce, large sums of money may be saved by not drilling in unproductive sites. 
   Referring to  FIG. 20 , activation value plots  154  may be used to create a “fingerprint” corresponding to a particular state. Activation value plots  154  illustrate the relative probability that an epoch  74  corresponding to a particular state will have a particular magnitude. From the illustrated activation value plot  154 , it can be seen that well eight has produced a dense concentration of plotted points  172  having values between 0.5 and 1.0 on the magnitude axis  170 . While the plotted points  172  of  FIG. 20  are similar to those shown in  FIG. 19  for the producing wells  178 , the point distribution  172  for the producing wells  178  in  FIG. 19  is more spread out. 
   Thus, by examining the finger print illustrated in an activation value plot  154 , a range of information may be extracted. For example, well eight is very different from the non-producing wells  180 , but is not exactly like the producing wells  178 . Further analysis may show that well eight is an exceptionally high producing gas well. Accordingly, variations in the activation value plots  154  may provide a spectrum of information. 
   Referring to  FIG. 21 , in certain embodiments of a system in accordance with the present invention, the classification accuracy of a particular separation key  80  may be determined by creating a reliability matrix  156 . A reliability matrix  156  may be created by comparing the classification of an epoch  74  as corresponding to a particular state with the actual state associated with that epoch  74 . For example, if a particular epoch  74  was classified as a “state A” epoch, then one of two things can be true. The epoch  74  can either correspond to a state A or state B. The same may be true for an epoch  74  classified as state B. 
   After comparing classification data against actual data, four numbers may be produced: the number  184  of state B epochs  74  erroneously classified as a state A epochs  74 ; the number  186  of state A epochs  74  correctly classified as state A epochs  74 ; the number  188  of state A epochs  74  erroneously classified as a state B epochs  74 ; and the number  190  of state B epochs  74  correctly classified as state B epochs  74 . By dividing these numbers (i.e., the numbers indicated by the identifiers  184 ,  186 ,  188 ,  190 ) by the total number of actual epochs  74  related to their predicted state, accuracy or reliability percentages  192  may be calculated. 
   Reliability percentages  192  may be incorporated into a reliability matrix  156 . For example, if 100 epochs  74  of state A where classified and 94 where correctly classified as corresponding to state A, then the AA (matrix notation) reliability percentage  192   a  would be 94%. That would leave 6 epochs  74  of state A that where erroneously classified as state B. The AB reliability percentage  192   b  would be 6%. The remaining BB and BA reliability percentages  192   c ,  192   d  may be calculated in a similar manner. 
   A reliability matrix  156  may provide the user a better understanding of the extent to which a particular classification may be trusted. In the illustrated example, a user may be quite comfortable that, using this particular separation key  80 , a epoch  74  of state A will indeed be classified as a state A epoch  74  as the reliability matrix  156  indicates that 94% of all state A epochs  74  were correctly classified. 
   Referring to  FIG. 22 , multiple reliability matrices  156   a ,  156   b ,  156   c , . . . ,  156   n  may be used to generate a discrimination accuracy matrix  162 . Reliability matrices  156  provide the probability that two states (A and B, B and C, C and D, or the like) will be classified correctly. A discrimination matrix  162 , on the other hand, may provide information about how well a particular separation key  80  is able to differentiate several states. 
   For example, a particular reliability matrix  156   b  may state that when compared with state B, an event contrast stacker  64  may correctly classify 88% of all state A epochs  74 . When compared with state A, that same event contrast stacker  64  may correctly classify 90% of all state B epochs  74 . A total classification accuracy  194   b  of the event contrast stacker  64  with respect to states A and B may be determined by averaging the two correct reliability percentages  192 . In the illustrated embodiment of  FIG. 22 , the generation of various total classification accuracies  194  is shown in a matrix notation  196  as well as a numeric example  198 . In applications where the number of state A epochs  74  analyzed does not equal the number of state B epochs  74  analyzed, a total classification accuracy  194  may be determined by adjusting, such as by dividing the total number of correct classifications (regardless of state) by the total number of epochs  74  analyzed. 
   Once a total classification accuracy  194  has been generated for a particular pair of states, this value  194  may be inserted in the appropriate locations of the discrimination accuracy matrix  162 . It may be noted that discrimination matrices  162  are symmetric, thereby reducing the number of calculations necessary to complete the matrix  162 . Reliability matrices  156  may be generated and total classification accuracies  194  calculated using selected state pairs until the discrimination matrix  162  is complete. 
   A complete discrimination matrix  162  may provide the user with a comparison of the similarities of a variety of states. It may be noted that the diagonal  200  of the discrimination matrix  162  may often contain values near 50%. The diagonal  200  contains total classification accuracies  194  of a particular state compared against itself. As would be expected, an event contrast stacker  64  may not repeatably distinguish a given state from itself. Therefore, it is typically right half the time and wrong half the time. 
   Referring to  FIG. 23 , a discrimination matrix  162  may be converted to a dissimilarity matrix  166  by a dissimilarity transformation  202 . Dissimilarity matrices  166  provide a method for comparing how different a particular state is from another state. As can be seen, the diagonal  200  contains low dissimilarity values. This is to be expected as states have a low (theoretically zero) dissimilarity with themselves. 
   Referring to  FIG. 24 , a discrimination matrix  162  may be converted to a similarity matrix  164  by a similarity transformation  204 . As can be seen, the diagonal  200  contains high similarity values. This is to be expected as states are similar to themselves. Similarity matrices  164  may be particularly useful. A similarity matrix  164  enables a user to objectively calculate how similar a particular state is to another state. This comparison may have a profound impact on the ability of a user to predict and quantify states. 
   Referring to  FIG. 25 , a similarity matrix  164  may be presented as a bar graph. The bar graph provides a visual representation of areas of similarity and dissimilarity between various geological formations  19  having various states. For example, in the illustrated embodiment, two geological formations  19  known to contain oil, two geological formations  19  known to contain gas, and three geological formations  19  having prospective well sites are compared. As expected, the geological formations  19  containing oil show a high similarity to one another. Similarly, the geological formations  19  containing gas show a high similarity to one another. The first prospective well shows no similarity to oil or gas. The second prospective well shows a similarity to oil. The third prospective well shows similarity to gas. 
   Referring to  FIG. 26 , an output generator  82  of an event contrast stacker  64  in accordance with the present invention may output information in the form of a contrast stacked signal  158  or contrast stacked trace  158 . As discussed hereinabove, in certain embodiments, an event contrast stacker  64  may receive a complex and apparently random signal  24 . The event contrast stacker  64  may divided the signal  24  into epochs  68 . Each epoch  68  may be processed by the event contrast stacker  64  in an effort to reveal features  90  (inherent characteristics indicating non-random information encoded within the signal  24 ) that correspond to a particular state of the formation  19  from which the signal  24  was collected. 
   Once the features  90  of each epoch  68  have been expanded, the epochs  68  may be reassembled in the order they were taken from the signal  24 . This reassembly may result in the formation of a contrast stacked signal  158 . That is, a signal  158  that is stacked, collected, summed, or otherwise processed in a manner to draw out contrasts between portions  206  of the signal  158  pertaining to state A and portions  208  of the signal  158  pertaining to state B. 
   Referring to  FIGS. 27-30 , if desired, a collection of contrast stacked signals  158  may be arranged in their proper relative locations in three-dimensional Euclidean space. A collection of properly positioned contrast stacked signals  158  may constitute a contrast seismic volume  160 . In certain embodiments, a contrast seismic volume  160  may represent a map of a selected physical volume of a geological formation  19 . The contrast seismic volume  160  may indicate locations corresponding to different states. 
   Various methods may be used to operate on a contrast seismic volume  160  and generate three dimension images  210  or two dimensional images  212  of a geological formation  19 . In selected embodiments, three dimensional images  210  may be generated by interpolating between the collection of contrast stacked signals  158 . The illustrated embodiment of  FIG. 28  provides a three dimension image  210  of volumes  214  corresponding to state A and volumes  216  corresponding to state B. In certain embodiments, volumes  214  corresponding to state A may represent an oil deposit that will produce oil above a selected threshold rate, while volumes  216  corresponding to state B may be formations that will not produce oil at a rate above a selected threshold value. 
   As stated hereinabove, a contrast seismic volume  160  may be used to generate two dimensional images  212 . In the illustrated embodiment of  FIG. 29 , a horizontal, two dimensional slice  212  provides views of regions  218  corresponding to state A and regions  220  corresponding to state B at a certain physical depth. In the illustrated embodiment of  FIG. 30 , a vertical, two dimensional slice  212  provides additional views of regions  218  corresponding to state A and regions  220  corresponding to state B at a certain distance. 
   Referring to  FIGS. 31 and 32 , in certain embodiments, it may be desirable to divide a contrast seismic volume  160  into various sub-volumes  222 . The size or number of the sub-volumes  222  may vary according to the desired resolution. In selected embodiments, each sub-volume  222  may be labeled with a number  224  indicating the correspondence of that sub-volume  222  to a particular state. The resulting collection of numbered sub-volumes  222  may form a numeric plot  226 . 
   The number  224  may be selected by quantifying the presence or absence of a feature  90  in a portion  206 ,  208  of the contrast stacked signal  158  contained within the sub-volume  222 . If desired, the number  224  may be the numerical value assigned the portion  206 ,  208  in the aggregation  130  process. In selected embodiments, more than one contrast stacked signal  158  may pass through a sub-volume  222 . In such situations, the number  224  may be selected to represent the presence or absence of a feature  90  in selected portions  206 ,  208  of the various contrast stacked signals  158  contained within the sub-volume  222 . In one embodiment, the number  224  may be an average of the numerical value assigned to the selected portions  206 ,  208  in the aggregation  130  process. 
   In selected embodiments, each sub-volume  222  may have a color  228  applied thereto. The color  228  may provide a visual key indicating the correspondence of that sub-volume  222  to a particular state of interest. The resulting collection of colored sub-volumes  222  may be combined to form a color plot  230 . For example, in one embodiment, the various colors  228  applied to the sub-volumes  222  may represent a spectrum or scale of color. Sub-volumes  222  containing portions  206 ,  208  of the contrast stacked signal  158  representing a high probability of the desired state, represented by the high incidence of a particular feature  90 , may be assigned a color  228  at one end of the selected color spectrum. Conversely, sub-volumes  222  containing portions  206 ,  208  of the contrast stacked signal  158  representing a low incidence of the particular feature  90  may be assigned a color  228  at the other end of the color spectrum or other contrasting color. Sub-volumes  222  containing portions  206 ,  208  of the contrast stacked signal  158  representing an intermediate incidence of the particular feature  90  may be assigned a corresponding color  228  from the interior of the color spectrum. 
   Various colors  228  or color spectra may be applied to any output generated by an output generator  82  in accordance with the present invention. For example, in addition to the color plots  230  described hereinabove, colors  228  and color spectra may be applied to activation value plots  154 , reliability matrices  156 , contrast stacked signals  158 , contrast seismic volumes  160 , three dimensional images  210 , two dimensional images  212 , or the like. Colors  228  and color spectra may be used to immediately communicate information to a viewer regarding the degrees of presence or absence of a particular state within a geological formation  19 . 
   In selected embodiments, traces  24  that are migrated may be combined with color coded contrast stacker signals  158 . The end result may be a combination of information available in seismic traces  24  before processing by an event contrast stacker  64  and information obtained after processing by an event contrast stacker  64 . The color coded contrast stacked signals  158  may enhance the seismic traces  24  and indicate what locations in the seismic traces  24  represent a particular state of the geological formation. 
   In certain embodiments, activation value plots  154 , reliability matrices  156 , contrast stacked signals  158 , contrast seismic volumes  160 , three dimensional images  210 , two dimensional images  212 , numeric plots  226 , color plots  230 , or the like may be used to quantify the portions  206 ,  208 , volumes  214 ,  216 , and regions  218 ,  220  corresponding to different states. For example, if state A represents the presence of an oil deposit in a geological formation  19 , a three dimensional image  219  may provide the ability to quantifying the number of barrels of oil that may be contained in a volume  214  corresponding to state A. 
   Additionally, signals  24  may be collected from a particular geological formation  19  at different times. By using the methods and structures in accordance with the present invention, the portions  206 ,  208 , volumes  214 ,  216 , and regions  218 ,  220  pertaining to a particular state may be calculated for each time the signals  24  are collected. The portions  206 ,  208 , volumes  214 ,  216 , and regions  218 ,  220  may be compared between different collections of signals  24  to determine how the geological formation  19  is changing. For example, the volume  214  corresponding to the presence of an oil deposit may be quantified in a first year. In subsequent years, such as after each year of pumping, signals  24  may again be collected and the volume  214  corresponding to the presence of an oil deposit may again be quantified. By comparing the quantities, the impact of pumping on the oil deposit may be evaluated. 
   Referring to  FIGS. 33-36 , in certain embodiments, an event contrast stacker  64  may migrate or to assist in migrating seismic traces  24 . As discussed hereinabove, migration is an attempt to locate the source of signals  24  that have traveled large distances (e.g. long times). One of the techniques that may be used to migrate seismic traces is event aligning. An event  232  may be defined as a section of a seismic trace  24  corresponding to the reflected wave  22  caused by a particular reflector  20 . A seismic trace  24  is, in reality, a collection of events  232  represented by a shape of a waveform, obscured by noise. 
   In certain applications, selected traces  24   a ,  24   b ,  24   c  may contain common events  232 . Common events  232  may be defined as reflected waves  22  originating from a common reflector  20 . By locating waveshapes or recognizable common events  232  in multiple traces  24   a ,  24   b ,  24   c , the traces  24  may be adjusted until common events  232  are aligned, such as in time. Aligning may facilitate piecing together the various traces  24  to form a collection of fully migrated traces  24 . 
   An event contrast stacker  64  in accordance with the present invention may be used to compare signals  24  and identify signals  24   a  having an information content that is either more readily exposed or simply stronger than others. Signals  24   a  having such high information content and visibility may then be used for facilitating processing of other signals  24   b ,  24   c . For example, a plurality of events  232   b ,  232   c  may be identified along a signal  24   a  of high information visibility. Other low information signals  24   b ,  24   c  may contain one of the plurality of events  232 . It may be difficult to align two low information signals  24   b ,  24   c  if a common event  232  is not readily located. However, the high information signal  24   a  may contain an event  232   b  in common with a low information signal  24   b  as well as an event  232   c  from another low information signal  24   c . Thus, using the high visibility or simply high information signal  24   a , the low information signals  24   b ,  24   c  may be aligned with respect to one another. 
   The following examples will illustrate the invention in further detail. It will be readily understood that the present descriptions of certain aspects of the invention, as generally described and illustrated in the Examples herein, are merely exemplary of embodiments of apparatus and methods in accordance with the present invention. Thus, the following more detailed description of certain embodiments of methods and formulations in accordance with the present invention, as represented in Examples I through IV, is not intended to limit the scope of the invention, as claimed, but is merely representative of possible embodiments and applications of the present invention. 
   EXAMPLE I 
   Referring to  FIGS. 37-43 , in the present example, signals  24  (post-stack gathers) were provided from a twenty square mile area of an operating oil field. The signals had previously been used to generate conventional seismic volumes illustrated in  FIGS. 37 and 39 . Twelve wells  30  were drilled based on the seismic volumes. As can be seen, all the wells  30  are positioned in areas  234  that the seismic volumes indicated are likely locations for oil. 
   Of the twelve bores  30  or wells  30 , two resulted in oil wells  30   a ,  30   b , two resulted in dry holes  30   c ,  30   d , and two resulted in wet holes  30   e ,  30   f  (water filled). The states of the remaining six wells  30   g ,  30   h ,  30   i ,  30   j ,  30   k ,  30   m  were known to the owners of the oil field, but were withheld until processing in accordance with the present invention was completed. 
   As illustrated in  FIG. 41 , selected signals  24  corresponding to each of the wells  30  were provided for processing. The number  236  of signals  24  provided for each well  30  ranged from 154 to 177. The signals  24  were processed by an event contrast stacker  64  in accordance with the present invention. 
   The area of interest, or pay horizon  62 , of the oil field of the present example was located about 1.1 seconds from the surface  16 . As a result, an epoch  68  was taken from each of the signals  24  in the range extending from 0.1 seconds before the pay horizon  62  to 0.1 seconds after the pay horizon  62 . Thus, each epoch  68  represented 0.2 seconds (200 milliseconds) of a signal  24 . Since the pay horizon  62  of the actual oil field did not remain at a constant depth, the exact location of the various epochs  68  varied for different wells  30 . For example, the epochs  68  corresponding to well one  30   a  extended from time 0.976 to time 1.176 while the epochs  68  from well two  30   b  extended from time 0.964 to time 1.194. 
   The geological formation  19  containing well two  30   b , an oil well, was considered an example of state A (i.e. an oil producing location). The geological formations  19  containing well three  30   c , a dry hole, and well five  30   e , a wet hole, were considered examples of state B (i.e. non oil producing locations). Epochs  68  corresponding to wells two  30   b , three  30   c , and five  30   e  were used as learning epochs  72  and processed by a learning system  76  in accordance with the present invention. Epochs  68  corresponding to wells one  30   a , four  30   d , and six  30   f  through twelve  30   m  were used as classification epochs  74  and processed by a classification system  78  in accordance with the present invention. 
   After processing the learning epochs  72 , the learning system  76  produced a separation key  80  illustrated in part by FIG.  42 . It was determined that each epoch  72  may be weighted in time space with a Gaussian distribution  102  centered at time 100 milliseconds (halfway though the epoch  72 ) with a time width  106  of 100 milliseconds. It was also determined that each epoch  72  may be divided in a frequency space into five frequency bands  100 . The frequency bands  100  may be weighted with Gaussian distributions  102  centered at 25 Hz, 50 Hz, 75 Hz, 100 Hz, and 120 Hz, all with frequency widths  110  of 5 Hz. Weights  122  for the resulting feature segments  92  may be applied as illustrated. 
   The learning epochs  72  and the classification epochs  74  were processed by the classification system  78  using the separation key  80  developed by the learning system  76 . Each epoch  68  was expanded into feature segments  92 . The feature segments  92  corresponding to a particular epoch  68  were weighted, superimposed  128 , and aggregated  130  to a numerical value. The numerical values were normalized and plotted in the activation value plot  154  of FIG.  43 . Each processed epoch  68  is represented by a plotted point  172 . Plotted points  172  between 0.0 and 1.0 indicate a correspondence to an oil producing state. Plotted points  172  between 0.0 and −1.0 indicate a correspondence to a non oil producing state. 
   As seen in  FIG. 43 , wells one  30   a  and two  30   b  were properly classified as oil wells. Wells three  30   c  though six  30   f  were properly classified as non-producing wells. Of the unknown test wells (i.e. wells seven  30   g  though twelve  30   m ), wells eight  30   h  and eleven  30   k  were classified as oil wells, while wells seven  30   g , nine  30   i , ten  30   j , and twelve  30   m  were classified as non-producing wells. Upon viewing the data, the oil field owners confirmed that wells eight  30   h  and eleven  30   k  were indeed oil wells and wells seven  30   g , nine  30   i , ten  30   j , and twelve  30   m  were indeed non producing wells. Thus, the processing of the event contrast stacker  64  in accordance with the present invention was validated. 
   A horizontal, two dimensional slice  212  of the oil field as processed in accordance with the present invention is illustrated in  FIG. 38. A  vertical, two-dimensional slice  212  of the oil field as processed in accordance with the present invention is illustrated in FIG.  40 . As can be seen in  FIGS. 38 and 40 , all the oil wells  30   a ,  30   b ,  30   h ,  30   k  are positioned in areas  238  that an event contrast stacker  64  in accordance with the present invention predicted to contain oil. All of the dry and wet holes  30   c ,  30   d ,  30   e ,  30   f ,  30   g ,  30   i ,  30   j ,  30   m  are positioned in areas  240  that an event contrast stacker  64  in accordance with the present invention predicted not to contain oil. Additionally, other areas  242  are illustrated to indicate where future wells  30  may be drilled with a high likelihood of finding extractable oil. 
   EXAMPLE II 
   Referring to  FIGS. 44-49 , in the present example, traces (post-stack gathers) were collected from an eight square mile area of an operating gas field. The data was used to form the conventional seismic volume illustrated in FIG.  47 . Five wells  30  were drilled based on that seismic volume. As can be seen, all the wells  30  are positioned in areas  234  that the seismic volume indicated as likely locations for gas. 
   Of the five wells  30 , well one  30   a  resulted in a gas well and well two  30   b  resulted in non-producing wet hole (producing water not gas). The states of the remaining three wells  30   c ,  39   d ,  30   e  were known to the owners of the gas field, but were withheld until completion of processing in accordance with the present invention. 
   As illustrated in  FIG. 44 , selected signals  24  corresponding to each of the wells  30  were provided for processing. The number  236  of signals  24  provided for each well  30  ranged from 431 to 606. The signals  24  were processed by an event contrast stacker  64  in accordance with the present invention. 
   The area of interest, or pay horizon  62 , of the gas field of the present example was located about 0.85 seconds from the surface  16 . In a first application of an event contrast stacker  64  in accordance with the present invention, an epoch  68  was taken from each of the signals  24  in the range extending from 0.1 seconds before the pay horizon  62  to 0.1 seconds after the pay horizon  62 . Thus, each epoch  68  of the first application represented 0.2 seconds (200 milliseconds) of a signal  24 . Thus, the epochs  68  corresponding to the wells  30  extended from approximately time 0.75 to time 0.95. 
   In a second application of an event contrast stacker  64  in accordance with the present invention, an epoch  68  was taken from each of the signals  24  in the range extending from 0.04 seconds before the pay horizon  62  to 0.04 seconds after the pay horizon  62 . Thus, each epoch  68  of the first application represented 0.080 seconds (80 milliseconds) of a signal  24 . Thus, the epochs  68  corresponding to the wells  30  extended from approximately time 0.81 to time 0.89. 
   The geological formation  19  containing well one  30   a , a gas well, was considered an example of state A (i.e. a gas-producing location). The geological formation  19  containing well two  30   b , a wet hole, was considered an example of state B (i.e. a non-gas-producing location). Epochs  68  corresponding to wells one  30   a  and two  30   b  were used as learning epochs  72  and processed by a learning system  76  in accordance with the present invention. Epochs  68  corresponding to wells three  30   c , four  30   d , and five  30   e  were used as classification epochs  74  and processed by a classification system  78  in accordance with the present invention. 
   After processing the learning epochs  72  corresponding to the 200 millisecond time window, the learning system  76  produced a separation key  80   a  illustrated in part by FIG.  45 . It was determined that each epoch  72  may be weighted in time space with a Gaussian distribution  102  centered at a time of 40 milliseconds (halfway though the epoch  72 ) with a time width  106  of 40 milliseconds. It was also determined that each epoch  72  may be divided in frequency space into five frequency bands  100 . The frequency bands  100  may be weighted with a Gaussian distribution  102   s  centered at 25 Hz, 50 Hz, 75 Hz, 100 Hz, and 120 Hz, all with frequency widths  110  of 5 Hz. Weights  122  for the resulting feature segments  92  may be applied as illustrated. 
   After processing the learning epochs  72  corresponding to the 80 millisecond time window, the learning system  76  produced a separation key  80   b  illustrated in part by FIG.  46 . It was determined that each epoch  72  may be weighted in time space with a Gaussian distribution  102  centered at time 100 milliseconds (halfway though the epoch  72 ) with a time width  106  of 100 milliseconds. It was also determined that each epoch  72  may be divided in frequency space into three frequency bands  100 . The frequency bands  100  may be weighted with Gaussian distributions  102  centered at 9.09 Hz, 18.18 Hz, and 27.27 Hz, all with frequency widths  110  of 15 Hz. Weights  122  for the resulting feature segments  92  may be applied as illustrated. 
   The learning epochs  72  and the classification epochs  74  corresponding to the first and second applications were processed by the classification system  78  using the respective separation keys  80   a ,  80   b  developed by the learning system  76 . For both applications, each epoch  68  was expanded into feature segments  92 . The feature segments  92  corresponding to a particular epoch  68  were weighted, superimposed  128 , and aggregated  130  to a numerical value. From the resulting data, an output generator  82  in accordance with the present invention generated respective vertical, two-dimensional slices  212   a ,  212   b.    
   As seen in  FIGS. 47 and 48 , in both the first and second applications, well one  30   a  was properly positioned in an area  238  classified as gas producing and well two  30   b  was properly positioned in an area  240  classified as non gas producing. Additionally, other presently untapped areas  242  were classified as likely to be gas producing. Of the unknown, test wells (i.e. wells three  30   c , four  30   d , and five  30   e ), wells four  30   d  and five  30   e  were classified as gas wells, while well three  30   c  was classified as a non-producing well. Upon viewing the data, the gas field owners confirmed that wells four  30   d  and five  30   e  were indeed gas wells and well three  30   c  was indeed a non-producing well. Thus, the processing of the event contrast stacker  64  in accordance with the present invention was validated. 
   EXAMPLE III 
   Referring to  FIG. 50 , in the present example, signal  24  was provided from a first geological formation  19  having gas production rates above a selected economic value and a geological formation  19  having gas production rates below a selected economic value. Epochs  68  corresponding to the first and second geological formations  19  were used as learning epochs  72  and processed by a learning system  76  in accordance with the present invention. 
   After processing, the learning system  76  produced a separation key  80  effective to separate geological formations  19  having gas production above a selected value from geological formations  19  having gas production below a selected value. The separation key  80 , illustrated in part in  FIG. 50 , instructs that each epoch  72  be divided in both time and frequency space. In time space, each epoch  72  may be divided into four time segments  98 . The time segments  98  may be weighted with Gaussian distributions  102  centered at 25 ms, 50 ms, 75 ms, and 50 ms. The time segments may have time widths  106  of 6 ms, 6 ms, 6 ms, and 50 ms, respectively. 
   In frequency space, each epoch  72  may be divided into six frequency bands  100 . The frequency bands  100  may be weighted with Gaussian distributions  102  centered at 20.83 Hz, 41.67 Hz, and 83.33 Hz, all with frequency widths  110  of 10 Hz, and at 20.83 Hz, 41.67 Hz, and 83.33 Hz, all with frequency widths  110  of 5 Hz. Weights  122  for the resulting feature segments  92  may be applied as illustrated. 
   EXAMPLE IV 
   Referring to  FIG. 51 , in the present example, signal  24  was provided from a first collection of geological formations  19  producing hydrocarbons (i.e. gas, oil, or gas and oil) and a second collection of geological formations  19  producing water. Epochs  68  corresponding to the first and second collections were used as learning epochs  72  and processed by a learning system  76  in accordance with the present invention. 
   After processing, the learning system  76  produced a separation key  80  effective to separate geological formations  19  producing a hydrocarbon from geological formations  19  producing water. The separation key  80 , illustrated in part in  FIG. 51 , instructs that each epoch  72  be divided in both time and frequency space. In time space, each epoch  72  may be divided into three time segments  98 . The time segments  98  may be weighted with Gaussian distributions  102  centered at 50 ms, 100 ms, and 150 ms, all with time widths  106  of 100 ms. In frequency space, each epoch  72  may be divided into three frequency bands  100 . The frequency bands  100  may be weighted with Gaussian distributions  102  centered at 10 Hz, 20 Hz, and 30 Hz, all with frequency widths  110  of 10 Hz. Weights  122  for the resulting feature segments  92  may be applied as illustrated. 
   From the above discussion, it will be appreciated that the present invention provides an integrated waveform analysis method and apparatus capable of extracting useful information from highly complex, irregular, and seemingly random or simply noise-type waveforms such as seismic traces and well log data. Unlike prior art devices, the present invention provides novel systems and methods for signal processing, pattern recognition, and data interpretation by means of observing and correlating the affects of a particular state on a geological formation. 
   The present invention may be embodied in other specific forms without departing from its essential characteristics. The described embodiments are to be considered in all respects only as illustrative, and not restrictive. The scope of the invention is, therefore, indicated by the appended claims, rather than by the foregoing description. All changes within the meaning and range of equivalency of the claims are to be embraced within their scope.