Abstract:
Disclosed herein are systems and methods for calibrating seismic data using seismic attribute pairs such as amplitude versus offset (AVO) attributes. In one embodiment, a method comprises: receiving traces from a seismic survey that covers a volume; determining a pair of seismic attributes for each of a plurality of positions within the volume (“survey pairs”); deriving pairs of seismic attributes from a source independent of the survey (“independent pairs”); calculating a rotation angle and one or more scale factors that calibrate the survey pairs relative to the independent pairs; and calibrating the traces with the rotation angle and the one or more scale factors. Thus, for example, the overall amplitude and relative AVO of pre-stack seismic gathers can be calibrated to match that of synthetic gathers by matching crossplots of AVO attributes generated from each dataset.

Description:
BACKGROUND  
       [0001]     Seismic surveys, when used in conjunction with other available geophysical, borehole, and geological data, provide information about the structure and distribution of subsurface rock types and their interstitial fluids. Oil companies rely on interpretation of such seismic data for selecting the sites in which to invest in drilling exploratory oil wells. Even though seismic surveys provide maps of geological structures rather than direct measurements of petroleum, seismic surveys have become a vital part of selecting the site of an exploratory and development well. Experience has shown that using seismic surveys greatly improves the likelihood of a successful venture.  
         [0002]     When borehole logs are available from nearby wells, seismic survey data can be enhanced by combining it with the log data. Various methods exist for combining the different data types, but at least some of the methods involve the use of a synthetic survey.  
         [0003]     To obtain a synthetic survey, analysts first employ the borehole logs to make determinations of density, porosity, fluid type, shear wave velocity and pressure wave velocity in each of the formation layers. The analysts then construct a mathematical model of the formation and simulate its response to a seismic survey. Just as in a real survey, in the simulation a seismic wave propagates through the model and reflects where the acoustic impedance changes. Energy from the reflected waves travels to receiver positions where the energy is recorded in the form of a seismic trace.  
         [0004]     The traces from a synthetic survey perfectly scaled and representative of reflection signal strengths. However, real world seismic surveys require the use of physical transducers, which introduce scaling errors. Scaling errors cause inaccuracies in seismic attributes calculated from seismic surveys. Synthetic surveys provide a means for identifying and correcting at least some of these scaling errors.  
         [0005]     At least some existing methods provide for normalization of seismic traces relative to synthetic traces, but to date these methods fail to adequately account for the dependence of scaling error on incidence angle. Such a dependence is common, and a method that provides for compensation of such an error dependence would be expected to significantly improve the accuracy of seismic attribute calculations, thereby further enhancing the likelihood of success in discovering and exploiting hydrocarbons, ores, water, and geothermal reservoirs.  
       SUMMARY  
       [0006]     Accordingly, disclosed herein are systems and methods for calibrating seismic data using seismic attribute pairs such as amplitude versus offset (AVO) attributes. In one embodiment, a method comprises: receiving traces from a seismic survey that covers a volume; determining a pair of seismic attributes for each of a plurality of positions within the volume (“survey pairs”); deriving pairs of seismic attributes from a source independent of the survey (“independent pairs”); calculating a rotation angle and one or more scale factors that calibrate the survey pairs relative to the independent pairs; and calibrating the traces with the rotation angle and the one or more scale factors. Thus, for example, the overall amplitude and relative AVO of pre-stack seismic gathers can be calibrated to match that of synthetic gathers by matching crossplots of AVO attributes generated from each dataset. Calibration in crossplot space may be an automatic process or an interactive process in which the user scales and rotates a cluster of points from the seismic data until it overlays the same cluster from the synthetic data. The scalars used to modify the attributes in crossplot space can then be used to scale the original seismic gathers. The resulting gathers should have an amplitude range similar to the synthetic data and an offset amplitude trend consistent with the model data. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0007]     A better understanding of the present invention can be obtained when the following detailed description is considered in conjunction with the following drawings, in which:  
         [0008]      FIG. 1  shows an illustrative seismic survey operation;  
         [0009]      FIG. 2  shows a block diagram of an illustrative seismic survey data gathering system;  
         [0010]      FIG. 3  shows a block diagram of an illustrative seismic survey data processing system;  
         [0011]      FIG. 4  shows a flowchart of an illustrative crossplot calibration method;  
         [0012]      FIG. 5  shows illustrative traces and their digitization;  
         [0013]      FIG. 6  shows an illustrative set of amplitude versus offset (AVO) gathers in wiggle-chart form;  
         [0014]      FIG. 7  shows an illustrative map of pressure wave reflectivity in wiggle-chart form;  
         [0015]      FIG. 8  shows an illustrative map of shear wave reflectivity in wiggle-chart form;  
         [0016]      FIG. 9  shows an illustrative crossplot comparing seismic survey calculations to synthetic survey calculations;  
         [0017]      FIG. 10  shows an illustrative crossplot comparing scaled seismic survey calculations to synthetic survey calculations;  
         [0018]      FIG. 11  shows an illustrative crossplot comparing scaled and rotated seismic survey calculations to synthetic survey calculations;  
         [0019]      FIG. 12  shows an illustrative graph comparing incidence angle dependence of seismic survey data (both calibrated and uncalibrated) to that of synthetic survey data; and  
         [0020]      FIG. 13  shows an illustrative graph comparing trends of incidence angle dependence for seismic survey data and synthetic survey data. 
     
    
       [0021]     While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that the drawings and detailed description thereto are not intended to limit the invention to the particular form disclosed, but on the contrary, the intention is to cover all modifications, equivalents and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.  
       DETAILED DESCRIPTION  
       [0022]     Seismic data acquisition is routinely performed both on land and at sea. At sea, seismic ships deploy one or more cables (“streamers”) behind the ship as the ship moves forward. Each streamer includes multiple receivers in a configuration generally as shown in  FIG. 1 . Streamer  110  trails behind ship  100 , which moves in the direction of the arrow  102 . As shown in  FIG. 1 , source  112  is also towed behind ship  100 . Source  112  and receivers  114  typically deploy below the surface of the ocean  104 . Streamer  110  also includes electrical or fiber-optic cabling for interconnecting receivers  114  and seismic equipment on ship  100 . The streamers may be several miles long and often a seismic ship trails multiple streamers to increase the amount of seismic data collected. Data is digitized near the receivers  114  and is transmitted to the ship  100  through the cabling at rates of 7 (or more) million bits of data per second. Processing equipment aboard the ship controls the operation of source  112  and receivers  114 , and processes the acquired data.  
         [0023]     Source  112  emits seismic waves  116  which propagate downward through subsurface structures and reflect from boundaries (such as, e.g., formation boundary  106 ). The reflected waves are sensed by receivers  114  and recorded as a function of time from the triggering of source  112 . By determining the time it takes for seismic waves  116  to propagate from source  112  to (say) boundary  106  and back to receivers  112 , the position and topography of boundary  106  can be determined.  
         [0024]     The receivers used in marine seismology are commonly referred to as hydrophones, or marine pressure phones, and are usually constructed using a piezoelectric transducer. Synthetic piezoelectric materials, such as barium zirconate, barium titanate, or lead mataniobate, are generally used. A sheet of piezoelectric material develops a voltage difference between opposite faces when subjected to mechanical bending. Thin electroplating on these surfaces allows an electrical connection to be made to the device so that this voltage can be measured. The voltage is proportional to the amount of mechanical bending, which in turn is proportional to the pressure changes caused by seismic energy propagating through the water. The physical nature of the receivers causes the receivers to introduce scaling errors in their measurement of seismic energy.  
         [0025]      FIG. 2  shows a block diagram of seismic survey system electronics. The block diagram of  FIG. 2  is representative of electronics that may be used in land surveys as well as in marine surveys. The detectors  200  include transducers to convert the seismic wave energy into electric signals, and may further include electronics to filter, amplify, and convert the electric signals into digital data. The digital data may be communicated to the recording unit  206  via a bus  202 , or alternatively may be communicated via a dedicated information pathway or via a wireless connection. The recording unit  206  stores the digital data on an information storage medium, along with timing and position information for each of the detectors and any other parameters that may be useful in interpreting the stored data. The location information and other parameters may be provided via an independent interface  204  such as a user interface that allows manual entry of such information.  
         [0026]     Recording unit  206  may use any suitable information storage medium. Due to the large volume of information to be stored, the information storage medium is generally some form of magnetic medium, e.g., disk drives or magnetic tape. However it is expected that the necessary storage capacity may also be provided by optical media or integrated circuit memories, though the associated cost may be somewhat higher. In an alternative embodiment, recording unit  206  simply gathers the data from the detectors and transmits the data in real time to a remote location such as a central storage facility.  
         [0027]     The data collected by recording unit  206  may be communicated to a general purpose digital data processing system  210 . System  210  may be responsible for performing each of the method operations after the relevant data has been acquired. Alternatively, the role of system  210  may be limited to preliminary processing of the seismic data, and some other computing entity may perform the disclosed method operations.  
         [0028]     The communication of seismic data to system  210  may take place in any of various ways  208 , including transmission via a wired or wireless communications link, and by physical transport of an information storage medium. System  210  may process the traces to combine information from multiple firings and to apply corrections to the traces for such effects as wave propagation delays. Resampling of the data may be performed to obtain evenly-spaced, time- or depth-synchronized samples on each of the traces, and to obtain estimated traces at interpolated positions within the detector array. The trace data may also be converted into any number of seismic attribute measurements including without limitation phase, peak amplitude, sound velocity, acoustic impedance, rock porosity, water saturation, and hydrocarbon content.  
         [0029]     To aid in the interpretation of trace data, additional data may be gathered from existing wells. The additional data may take various forms, including core samples and digital logs of measurements made by downhole tools. From this data, acoustic properties are determined and a formation model is constructed at one or more specific points within the survey area. The formation model includes some combination of acoustic properties from which reflection coefficients can be determined. System  210  (or some other computing system that implements an embodiment of the disclosed method) is provided with the formation model, or alternatively provided with synthetic seismograms generated from the formation model.  
         [0030]      FIG. 3  shows a block diagram of an illustrative digital data processing system  210 . To interact with a user, system  210  may be coupled to a text or graphical display  302 , and to an input device  304 . Display  302  and input device  304  may together operate as an interface between the user and system  210 . That is, system  210  may perform certain actions prompted by user actuation of input device  304  and provide the user with a response via display  302 .  
         [0031]     System  210  may include a central processing unit (CPU)  306  that is coupled by a bridge  308  to a system memory  310 . CPU  306  may also be coupled by bridge  308  to a video card  312  that in turn couples to display  302 . CPU  306  may be further coupled by bridge  308  to an expansion bus  314 . Also coupled to the expansion bus  314  may be a storage device  316  and an input/output interface  318 . Input device  304  may be coupled to system  206  via input/output interface  318 . CPU  306  may operate in accordance with software stored in memory  310  and/or storage device  316 . Under the direction of the software, the CPU  306  may accept commands from an operator via a keyboard or some alternative input device  304 , and may display desired information to the operator via display  302  or some alternative output device. CPU  306  may control the operations of other system components to retrieve, transfer, process, and store data.  
         [0032]     Bridge  308  coordinates the flow of data between components. Bridge  308  may provide dedicated, high-bandwidth, point-to-point buses for CPU  306 , memory  310 , and video card  312 . In systems having alternative architectures, the bridge  308  may be omitted and the communications between the CPU  306  and all the other system components may occur via bus  314 .  
         [0033]     Memory  310  may store software and data for rapid access. On the other hand, storage device  316  may store software and data for long-term preservation. Storage device  316  may be portable, may accept removable media, may be an installed component, or may be a integrated component on a main system circuit board. Storage device  316  may also be a removable memory device such as a memory card. In addition, alternatives for storage device  316  may include a nonvolatile integrated memory, a magnetic media storage device, an optical media storage device, or some other form of long-term information storage.  
         [0034]     Video card  312  may provide customized processing for graphics, along with data conversion from a memory-based format to a signal format suitable for display  302 . Display  302  may provide data in a visual format for use by an operator. For example, display  302  may display, inter alia, seismograms and crossplots such as those described with reference to  FIGS. 6-11 . Alternatively, display  302  may show a two or three dimensional volumes of various seismic attributes. The three-dimensional volumes may be displayed by providing a perspective view and/or by animating a two-dimensional image to illustrate data variation as a function of position.  
         [0035]     Expansion bus  314  may support communications between bridge  308  and multiple other computer components. Bus  314  may couple to removable modular components and/or components integrated onto a circuit board with bridge  308  (e.g., audio cards, network interfaces, data acquisition modules, modems). In systems that include a network interface, the CPU  306  may access software and data via a network, thereby making it possible for system  210  to use information storage and processing resources external to system  210 .  
         [0036]     Input/output interface  318  may support communications with legacy components and devices not requiring a high-bandwidth connection. Interface  318  is coupled to input device  304 , which may provide data to interface  318  in response to operator actuation. Input device  304  may be a keyboard or some other input device (e.g., pointing devices, buttons, sensors). Multiple input devices may be concurrently coupled to input/output interface  318  to provide data in response to operator actuation. Output devices (e.g., parallel ports, serial ports, printers, speakers, lights) may also be coupled to input/output interface  318  to communicate information to the operator.  
         [0037]     In the current context, system  210  may be configured with software that processes seismic data to generate maps of seismic attributes. The software may be stored in storage device  316 , and some or all of the software may be copied into memory  310  as needed for use by CPU  306 . CPU  306  may retrieve the software instructions a few at a time from memory  310 , and follow the procedures laid out by the software instructions to generate the desired maps. These procedures may include opportunities for interaction with a user of system  210 , such as displaying fields that allow a user to identify the seismic data file to be operated on, or displaying controls that allow a user to alter processing parameters and change display characteristics.  
         [0038]      FIG. 4  illustrates an embodiment of a crossplot calibration method that may be implemented by system  210  to correct for scaling errors in seismic survey data. Though the contemplated implementation of the crossplot calibration method involves software, other implementations are possible. For example, the crossplot calibration method may be implemented in firmware or hardware. Users may employ programmable logic devices (PLDs) or application specific integrated circuits (ASICs) in contexts where speed is a priority. Although  FIG. 4  shows operations in a particular order, the actual implementation may re-order some of the operations, may overlap the execution of sequential steps, and/or may execute different operations in parallel. As an example, the operations for blocks  402 - 412  may be conducted independently of, and thus in parallel with, the operations for blocks  414 - 424 . Some implementations may employ multiple processing units that execute operations of a single block in parallel.  
         [0039]     In block  402 , system  210  obtains (digital) seismic survey data. The survey data is obtained in the form of digitized seismic traces, each trace having an associated receiver position and seismic source position.  FIG. 5  shows an illustrative collection of survey traces. The seismic source is originally fired at position S 0 , causing receivers at locations R 0 -R 2  to receive seismic reflections from formation boundaries. The received signals are sampled and digitized as indicated by the dots on each of the traces. The seismic source is then fired at position S 1 , producing another set of seismic traces at each of the receivers. Typically, although not necessarily, the traces of the seismic survey are subjected to some preliminary processing to maximize their signal to noise ratio before being provided to system  210 . If not, the preliminary processing may be performed at this stage.  
         [0040]     In block  404  ( FIG. 4 ), system  210  combines seismic traces to form amplitude versus offset (AVO) gathers. This operation begins with the determination of midpoints between the receiver and source positions for each trace. Those traces that share a common midpoint (to within some predetermined tolerance) are combined to form a gather, and in this manner a gather is formed for each midpoint. The set of traces for a given midpoint may be ordered in terms of offset (defined as the distance from the receiver to the midpoint, or alternatively, defined as the angle between rays drawn from the reflector to the receiver and midpoint). Traces sharing a common offset and midpoint are “stacked”, i.e., averaged together. The final step of forming an AVO gather involves time compression or expansion of traces as a function of offset to compensate for differences in travel time through the formation, often termed “normal move-out” or NMO. After the operations of block  404 , the seismic data has been organized into an AVO gather for each midpoint, with the traces in each gather showing the dependence of amplitude on offset.  
         [0041]      FIG. 6  shows illustrative AVO gathers in the form of “wiggle traces”. The midpoints are numbered sequentially (gathers shown for midpoints  3474 - 3477 ), with a 45-trace gather shown for each midpoint. The vertical scale corresponds to recording time in milliseconds. Finally, the negative portions of the wiggle traces are “filled in” to aid in visual interpretation.  
         [0042]     In block  406  ( FIG. 4 ), system  210  processes the AVO gathers to determine reflection coefficients or other seismic attributes as a function of position, time/depth, and offset. In one embodiment, the system  210  determines reflection coefficients for shear waves and pressure waves, denoted as Rs and Rp, respectively. One method for determining reflection coefficients from AVO gathers is disclosed in P. M. Gidlow, G. C. Smith, and P. J. Vail, “Hydrocarbon Detection Using Fluid Factor Traces: A case history”, Expanded Abstracts of the Joint SEG/EAEG Summer 1992 Research Workshop on “How Useful Is Amplitude-Versus-Offset (AVO) Analysis?”, pp. 78-89. Other methods are known and may be used.  
         [0043]      FIG. 7  shows illustrative Rp data in the form of wiggle traces.  FIG. 8  shows illustrative Rs data for the same region. In both views, the horizontal axis corresponds to horizontal displacement, and the vertical axis corresponds to recording time. Although Rp and Rs data are employed for this example, other seismic attribute pairs may alternatively be used.  
         [0044]     In block  408  ( FIG. 4 ), system  210  isolates a region of the reflection coefficient (or other seismic attribute) data to serve as a basis for the calibration. This region may be selected by a user, or some algorithmic selection technique may be employed. The region is selected subject to two constraints. The first constraint is the availability of synthetic seismic survey data for the region. The second constraint is that the region contain primarily formation data that satisfies (within some tolerance) a linear relationship. For example, the user may select a region containing primarily wet sand/shale reflectors, which are known to have an approximately linear relationship between their reflection coefficients.  
         [0045]     In an alternative embodiment, the whole set of seismic attribute data is used as a basis for the calibration, with certain regions excluded. These regions typically represent possible pay zones, and they exhibit attribute relationships that deviate significantly from the background. For example, system  210  may be configured to use a ratio of shear wave reflectivity to pressure wave reflectivity as an indicator of hydrocarbon concentrations. Throughout the bulk of the data, this ratio will be substantially constant. Regions having ratios outside a predetermined tolerance may represent possible pay zones, and may be excluded.  
         [0046]     In block  410 , system  210  forms a crossplot, i.e., system  210  combines seismic attributes in the region as an (x,y) pair. In the present example, zero-offset pressure wave reflectivity Rp is combined with zero-offset shear wave reflectivity Rs. In  FIG. 9 , a diamond symbol is plotted at coordinates corresponding to (Rp,Rs), the reflectivity pairs for the selected region.  
         [0047]     When AVO attributes such as Rp and Rs are displayed in a crossplot, the cluster of points from wet sand/shale reflections form a linear trend. This is often called the background trend. Smith and Gidlow, in “Weighted Stacking for Rock Property Estimation and Detection of Gas” (Geophys. Prosp., v. 35, pp. 993-1014, 1987), showed that at least in the case of Rp and Rs, this background trend is directly related to the relationship between compressional velocity (Vp) and shear velocity (Vs). The cluster of points that make up the background trend has a principal axis that is the long axis through the cloud. Outliers from the background trend are from reflectors that don&#39;t share this Vp, Vs relationship. Hydrocarbon saturation is one factor that alters the Vp, Vs relationship.  
         [0048]     System  210  operates on AVO attributes derived from seismic data. In this example, P-wave Reflectivity (Rp) and S-wave Reflectivity (Rs) are used to calibrate the data. Other attribute pairs such as Intercept and Gradient, Normal Incidence and Poisson&#39;s Reflectivity, or Lambda and Mu Reflectivity could be used as well.  
         [0049]     In block  412 , system  210  parameterizes the collection of crossplotted points. In one embodiment, the parameterization process involves: 1) taking the mean of the collection to determine the center (xC,yC); 2) determining a least-squares fit of a straight line (through the center) to the collection of points; 3) taking this straight line as the major (primary) axis of the collection, and measuring σ1, the standard deviation of the collection along the major axis; 4) taking a line perpendicular to the major axis and through the center as the minor (secondary) axis of the collection, and measuring the σ2, standard deviation of the collection along the minor axis. These four parameters (center, major axis, standard deviation along the major axis, and standard deviation along the minor axis) can be summarized and displayed as an ellipse.  FIG. 9  shows an ellipse  904  having the least-squares fit line as the major axis, having the dimension along the major axis equal to two times the standard deviation along this axis, and having the dimension along the minor axis equal to two times the standard deviation along that axis.  
         [0050]     In block  414  ( FIG. 4 ), system  210  obtains an acoustic model of the formation. In block  416 , system  210  generates synthetic AVO gathers from the acoustic model. Methods for generating synthetic AVO gathers are well known and may be found in standard texts. See, e.g., K. Aki and P. G. Richards,  Quantitative Seismology: Theory and Methods , W.H. Freeman and Co., 1980. In one embodiment, a full-offset synthetic is constructed from the log data using a ray-tracing algorithm to calculate incidence angles and Aki and Richards equations (Id. at p. 150) to calculate reflection amplitude. Offsets are chosen to mimic the actual seismic data. The reflection series is convolved with a zero-phase wavelet extracted from the seismic data at the well location.  
         [0051]     In block  418 , the operations of block  406  are applied to the synthetic AVO gathers to determine the reflectivity coefficients (or other seismic attributes). In block  408 , system  210  isolates a region of the reflection coefficient (or other seismic attribute) data to serve as a reference for the calibration. The selection of this region was discussed above.  
         [0052]     In block  420 , system  210  combines seismic reference attributes from the selected region to form a crossplot. In block  422 , system  210  parameterizes the collection of reference crossplot points.  FIG. 9  shows a circle symbol at coordinates corresponding to (Rp,Rs), the reference reflectivity pairs from the selected region.  FIG. 9  further shows ellipse  902 , which represents the parameters for the collection of reference points.  
         [0053]      FIG. 9  illustrates the significant difference between the reflectivities determined from the seismic survey, and the reflectivities determined from the synthetic, or model, survey. Although the model formation&#39;s lack of detail may account for some of the differences, the bulk of the differences are due to scaling errors in the seismic survey. Accordingly, system  210  modifies the seismic survey crossplot distribution to match the synthetic survey crossplot distribution.  
         [0054]     In block  426  ( FIG. 4 ), system  210  scales and rotates the crossplot from the seismic survey to match that from the synthetic survey. In one embodiment, the scale factor along the major axis is σ IM /σ IS , the ratio of the model data&#39;s standard deviation along the major axis to the ratio of the seismic data&#39;s standard deviation along the major axis. Similarly, the scale factor along the minor axis is σ 2M /σ 2S , the ratio of the standard deviations along the minor axis. The scaling may be viewed conceptually as rotating the major and minor axes to align with the coordinate axes, scaling the coordinate axes, and rotating the major and minor axes back into position. Thus the coordinates of the scaled crossplot are:  
           [           x   scaled               y   scaled           ]     =           [           cos   ⁢           ⁢   θ             -   sin     ⁢           ⁢   θ               sin   ⁢           ⁢   θ           cos   ⁢           ⁢   θ           ]     ⁡     [             σ     1   ⁢   M       /     σ     1   ⁢   S             0           0           σ     2   ⁢   M       /     σ     2   ⁢   S               ]       ⁢     
     ⁢           [           cos   ⁢           ⁢   θ           sin   ⁢           ⁢   θ                 -   sin     ⁢           ⁢   θ           cos   ⁢           ⁢   θ           ]     ⁡     [         x           y         ]         ,       
 
 where (x,y) are the original crossplot coordinates for the seismic survey data, and θ is the angle between the major axis and the x-axis.  FIG. 10  compares the scaled seismic survey crossplot with the model crossplot. 
 
         [0055]     The scaled crossplot is then rotated to align with the model crossplot. System  210  determines φ, the angle measured counterclockwise from the major axis of the model crossplot to the major axis of the survey crossplot. System  210  then determines the coordinates of the rotated crossplot as:  
         [           x   calibrated               y   calibrated           ]     =         [           cos   ⁢           ⁢   φ           sin   ⁢           ⁢   φ                 -   sin     ⁢           ⁢   φ           cos   ⁢           ⁢   φ           ]     ⁡     [           x   scaled               y   scaled           ]       .         
 
         [0056]      FIG. 11  compares the scaled and rotated crossplot with the model crossplot. Note that the ellipses  902 ,  904  are offset from each other for illustrative purposes, but mathematically they would coincide. The scale factors σ 1M /σ 1S  and σ 2M /σ 2S , and the rotation angle φ, are stored for later use.  
         [0057]     In block  428  ( FIG. 4 ), system  210  processes the seismic survey AVO gathers to separate the AVO trend from the AVO “noise”. That is, the AVO gathers provide at each position and time an indication of reflected wave intensity R as a function of offset angle α: 
 
 R (α)= R   T (α)+ R   N (α), 
 
 where R T  is the trend as determined by a least-squares second-order polynomial fit, and R N  is the difference between R and R T . 
 
         [0058]     In block  430 , system  210  employs the scale factors and the rotation angle determined from the calibration process to determine a new AVO trend and AVO noise. The new (calibrated) trend is:  
             R   CT     ⁡     (   α   )       =         Rp   2     ⁢     (       σ     1   ⁢   M         σ     1   ⁢   S         )     ⁢       sec   2     ⁡     (   α   )       ⁢     cos   ⁡     (   φ   )         -       Rp   ⁡     (       σ     2   ⁢   M         σ     2   ⁢   S         )       ⁢       sin   2     ⁡     (   α   )       ⁢     sin   ⁡     (   φ   )         -     
     ⁢           ⁢       Rs   2     ⁢     (       σ     2   ⁢   M         σ     2   ⁢   S         )     ⁢       sec   2     ⁡     (   α   )       ⁢     sin   ⁡     (   φ   )         -       Rs   ⁡     (       σ     1   ⁢   M         σ     1   ⁢   S         )       ⁢       sin   2     ⁡     (   α   )       ⁢     cos   ⁡     (   φ   )             ,       
 
 where Rp is the (unscaled) zero-incidence pressure wave reflectivity (see  FIG. 7 ) and Rs is the (unscaled) zero-incidence shear wave reflectivity (see  FIG. 8 ). The new (calibrated) noise is:  
           R   CN     ⁡     (   α   )       =       (       σ     1   ⁢   M         σ     1   ⁢   S         )     ⁢         R   N     ⁡     (   α   )       .           
 
         [0059]     In block  432  ( FIG. 4 ), system  210  combines the calibrated trend and calibrated noise to obtain calibrated AVO gathers. The calibrated gathers are: 
 
 R   C (α)= R   CT (α)+ R   CN (α). 
 
         [0060]      FIG. 12  shows the dependence of reflected wave intensity R on offset angle α for a raw AVO gather ( FIG. 6 ), a synthetic AVO gather, and for the calibrated AVO gather.  FIG. 13  compares the AVO trends for each of these curves.  
         [0061]     The calibrated AVO gathers generated by the method of  FIG. 4  can then be used for calculations of stacks or other seismic attributes. When the calibrated AVO gathers are used to calculate fluid factors (e.g., the ratio of Rp to Rs), the results have proven to be cleaner and more interpretable. In this manner, system  210  highlights proven hydrocarbon concentrations with greater accuracy, and is expected to significantly enhance success probabilities for future exploration ventures.  
         [0062]     In the foregoing description, the scale factors were expressed as ratios of standard deviations. In alternative embodiments, the scale factors (and rotation angles) may be determine visually, e.g., by interactive rotation and scaling by a computer user who visually determines when the survey attribute pairs are calibrated to the independent attribute pairs. The visual alignment may be aided by the use of geometric shapes such as ellipses or rectangles having orientations and dimensions determined by the distribution of attribute pairs. In another embodiment, the scale factors (and rotation angle) may be determined by correlation coefficient matching.  
         [0063]     Numerous variations and modifications will become apparent to those skilled in the art once the above disclosure is fully appreciated. It is intended that the following claims be interpreted to embrace all such variations and modifications.