Abstract:
The present invention incorporates the use of model-driven and data-driven methodologies to attenuate multiples in seismic data utilizing a prediction model which includes multiply-reflected, surface-related seismic waves. The present invention includes beam techniques and convolving a predicted multiples beam with a segment of a modeled pegleg beam to obtain a convolved multiples beam. The convolved multiples beam can then he deconvolved to attenuate the multiples that are present in the original input beam.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    This invention relates to seismic exploration and processing, and more specifically to imaging with beams and a method to predict multiples based on primaries by combining both model-driven and data-driven methodologies. 
         [0002]    In the petroleum industry, seismic prospecting techniques are commonly used to aid in the search for and the evaluation of subterranean hydrocarbon deposits. In seismic prospecting, one or more sources of seismic energy emit waves into a subsurface region of interest such as a geologic formation. These waves enter the formation and may be scattered, e.g., by reflection or refraction, by subsurface seismic reflectors (i.e., interfaces between underground formations having different elastic properties). The reflected signals are sampled or measured by one or more receivers, and the resultant data are recorded. The recorded samples may be referred to as seismic data or a set of “seismic traces”. The seismic data may be analyzed to extract details of the structure and properties of the region of the earth being explored. 
         [0003]    Seismic prospecting consists of three separate stages: data acquisition, data processing and data interpretation. The success of a seismic prospecting operation depends on satisfactory completion of all three stages. 
         [0004]    In general, the purpose of seismic exploration is to map or image a portion of the subsurface of the earth (a formation) by transmitting energy down into the ground and recording the “reflections” or “echoes” that return from the rock layers below. The energy transmitted into due formation is typically sound and shear wave energy. The downward-propagating sound energy may originate from various sources, such as explosions or seismic vibrators on land or air guns in marine environments. Seismic exploration typically uses one or more energy sources and typically a large number of sensors or detectors. The sensors that may be used to detect the returning seismic energy are usually geophones (land Surveys) or hydrophones (marine surveys). 
         [0005]    During a surface seismic survey, the energy source may be positioned at one or more locations near the surface of the earth above a geologic structure or formation of interest, referred to as shotpoints. Each time the source is activated, the source generates a seismic signal that travels downward through the earth and is at least partially reflected from discontinuities of various types in the subsurface, including reflections from “rock layer” boundaries. In general, a partial reflection of seismic signals may occur each time there is a change in the elastic properties of the subsurface materials. Reflected seismic signals are transmitted back to the surface of the earth, where they are recorded as a function of traveltime at a number of locations. The returning signals are digitized and recorded as a function of time (amplitude vs. time). 
         [0006]    One prevalent issue with the seismic energy recorded by the receivers during the data acquisition stage is that the seismic traces often contain both the desired seismic reflections (the: “primary” reflections) and unwanted multiple reflections which can obscure or overwhelm the primary seismic reflections. A primary reflection is a sound wave that passes from the source to a receiver with a single reflection from a subsurface seismic reflector. A multiple reflection is a wave that has reflected at least three times (up, down and back up again) before being detected by a receiver. Depending on their time delay from primary events with which they, are associated, multiples are commonly characterized as short-path, implying that they interfere with their own primary reflection, or long-path, where they appear as separate events. 
         [0007]    There are also a variety of multiple events which are well known in the art. There are signals which are “trapped” in the water layer between two strong reflectors, the free surface and the bottom of the water layer. There are “peg-leg” multiple events, which are reflections that are characterized by an additional roundtrip through the water layer just after emission or just before detection. There are “remaining” surface-related multiple events, where the first and last upward reflections are below the first (water) layer, and there is at least one reflection at the free surface in between. There are also “interbed” multiples which has a downward reflection occurring from a subsurface reflector. 
         [0008]    In most cases, multiples do not contain any useful information that is not more easily extracted from primaries. Moreover, water-bottom multiples have been recognized as the most serious noise problem in seismic data processing in many offshore areas. Multiples can severely mask primary reflection events for structural imaging and contaminate Amplitude vs. Offset (“AVO”) information. For those reasons, removal of multiples, or at least attenuation of multiples is a necessary part of the seismic data processing stage in many environments, particularly in marine settings where multiples are especially strong relative to the primaries. 
         [0009]    In the case of deep-water data, suppression of first-order and the next few orders of sea-bottom multiple and peg-leg reflections are of great importance. These rather strong multiples may have the same travel time as the primary reflections of target reflectors. 
         [0010]    There are several prior art methods to attenuate multiples depending on the attributes of the multiples utilized. One class of multiple attenuation methods is the predictive methods where the multiples are predicted from their respective primaries. Prior art predictive multiple attenuation techniques can be generally divided into two categories; model-driven methodologies and data-driven methodologies. Model-driven methodologies generally use an earth model and the recorded data to predict or simulate multiples utilizing the estimated sea-bottom reflectivity function and calculated amplitude functions to model water-layer multiple reflections, those predicted multiples are then subtracted from: the original data. Other model-driven technologies utilize an earth model or reflectivity model to predict the stationary multiples. The data-driven methodologies exploit the fact that primaries and multiples are physically related through a convolutional relationship and predict multiples by crossconvolving the relevant primaries thought to contain the stationary contributions for multiples. Data-driven methodologies can generally handle complex geometries and need little or no information about the properties of the subsurface. The model-based technologies are typically cost-effective compared to data-driven technologies, while the latter are typically more flexible. 
         [0011]    Some model-driven methodologies require structural information, i.e., information about the subsurface structure, the determination of which is the reason for doing seismic exploration in the first place. Other model-driven methodologies require the shape of the source wavelet that will not be a pure delta function because of the reverberations and frequency bandwidth limitation. Some model-driven methodologies require both structural and source wavelet information while others use a matching filter to account for a distorted source wavelet. 
         [0012]    Data-driven methodologies rely on the predictability of multiples from primary components. In effect, that methodology utilizes existing seismic data to generate multiples and those generated multiples are then subtracted from the existing data. One such prior art methodology that is data-driven is known as “surface-related multiple elimination” or “SRME”. In brief, this method operates by utilizing the existing data to create a dataset that contains only predictions of the multiples that are present in the data. Specifically, the method seeks to predict the seismic expression of multiples, and after adaptation to the existing multiples in the data the predicted multiples are subtracted from the original data leaving behind (at least theoretically) only the primary energy. 
         [0013]    Data-driven SRME techniques are attractive solutions for predicting multiples in complex geologic settings, they do no require any a-priori knowledge of the subsurface (reflectivity, structures and velocities). However, these methods do require one shot location for each receiver position, and this is not the case for most three dimensional (“3D”) acquisition geometries. SRME methodologies are generally challenged by complex 3D multiples because of large shot spacing, narrow spread length and/or wide cable spacing. The missing data can be interpolated or extrapolated from the existing data, but interpolation of extrapolation has trouble with aliased seismic data caused by the large shot and/or receiver spacing. Advanced interpolation or extrapolation methods can also be difficult to implement and expensive. A common cause of these complex 3D data that challenge 3D SRME methods is rugosity on the top of salt. But, any type of complex overburden can cause complex 3D seismic data that is hard to interpolate. 
         [0014]    Another data-driven methodology utilizes predictive deconvolution which is a filtering method that assumes that multiples are periodic while primaries are not. This assumption is usually met for data from water depths less than 500 msec (approximately 1,200 feet) and approximately layered subsurface geology. In areas of water depths greater than 500 msec where the velocity difference between primaries and multiples are significant, velocity-filtering methods (as opposed to predictive methods) such as tau-p and f-k filtering can be used, where the variable f represents frequency, k represents the wave-number, p represents the ray parameter, and tau represents the zero offset intercept time. 
         [0015]    However, filtering methods generally require determination, or at least an educated guess, of the apparent wave propagation velocities in the subsurface media through which the reflected seismic waves pass in their journey from the seismic source to a receiver. These velocities can differ significantly due to the combination of the variations of the subsurface structure and rock properties. In addition, predictive deconvolution often leads to inadvertent damage to the primaries due to the difficulty in separating the multiples and primaries. Moreover, predictive deconvolution often fails to take into account the nonlinear factor in the reflectivity, which are generally caused by peg-leg multiples. 
         [0016]    One prior art method which has extended predictive deconvolution for applications in deep water has utilized beam techniques. That method applies local slant stacking (or other dip-discriminating methods) to the data to decompose the recorded wavefields into beam components. These components travel approximately along raypaths. Simple raytracing within the water layer describes the long-period reverberations and relate primary and multiple events occurring in the beam components of the wave-field. Based on the information from the raytracing the time series of the beam-component of the primary can be shifted according to raytraced traveltimes and then analyzed with a multi-channel prediction filter. The predicted time series is considered as multiple energies and is removed from the beam components of the original data after a multi-channel matched filtering. 
         [0017]      FIG. 1  illustrates a flowchart for one example of a prior art method wherein deconvolution is utilized with a beam technique for attenuating multiples. The prior art method includes initializing an earth model  4  which relates to a geological region of interest, and initiating a beam dataset  6  that has been determined from seismic data of the geological region of interest. The prior art method further includes a series of loops wherein an input beam  8 , a multiple-generating surface  10  and a time gate  12  are selected. One or more time gates (or windows) are selected to ensure that the signal within each gate is stationary. Trial rays are then “sprayed” from a detector location  14  and a stationary pegleg is determined  16 . The stationary pegleg is the pegleg that satisfies the Snell&#39;s law for reflection at the-multiple-generating surface. A primary beam corresponding to the stationary pegleg is obtained  18 , and the primary beam is transformed into a predicted multiples beam  20 . The predicted multiples beam is then deconvolved to remove multiples which are present in the input beam  22 . 
         [0018]    While the beam techniques have improved prior art multiple attenuation techniques, there is still a need for an improved method which provides a more accurate prediction of multiples and therefore allows for more accurate subtraction of those multiples from the data. The prior beam techniques assume that there is a single dominant multiple-generating surface  10  and the predicted multiples beams are related only to this multiple-generating surface  10  and do not contain predicted multiples from other multiple-generating surfaces. The current invention improves prior art beam techniques to incorporate predicted multiples beams from multiple-generating surfaces that were not explicitly utilized to determine to stationary peglegs. 
       SUMMARY OF THE INVENTION 
       [0019]    The present invention overcomes the above-described and other shortcomings of the prior art by providing a novel and improved method of predicting multiples based upon primaries which combines features from both model-driven and data-driven methodologies. It is accomplished by determining a model-driven stationary prediction based on the earth model and augmenting that prediction by a data-driven prediction around the stationary prediction. It should be appreciated that the model-driven stationary prediction can be replaced by an a-priori determination, of stationary predictions, such as assuming a layered model. 
         [0020]    One embodiment of the present invention includes a method for generating a prediction model of multiply-reflected, surface-related seismic waves which includes initializing an earth model related to a geological volume and selecting a beam dataset derived from seismic data related to the geological volume. The method also includes selecting an input beam from the beam dataset; a multiple-generating surface from the earth model, and a time gate. A stationary pegleg is determined utilizing the input beam, the multiple generating surface and the time gate. A primary beam which corresponds to the stationary pegleg is then obtained, and a modeled pegleg beam related to the primary beam is determined. The modeled pegleg beam is convolved with the primary beam to generate a convolved multiples beam. The convolved multiples beam is compared with the input beam to remove the multiples in the input beam by matched filtering. 
         [0021]    The convolved multiples beam is utilized to provide a more accurate method of predicting and removing multiples than prior art methods. The step of convolving the modeled pegleg beam with the primary beam is not included in the prior art methods, and enables the present invention to more accurately predict multiples. For example, in one embodiment of the present invention convolving the primary beam and the modeled pegleg beam to obtain the convolved multiples beam includes transforming the primary beam into a predicted multiples beam by travel time shifting, and convolving the predicted multiples beam with a segment of the modeled pegleg beam to obtain a convolved multiples beam, the segment of the modeled pegleg beam starting at the multiple-generating surface and ending at a detector location. 
         [0022]    “Convolution” is known in the art. In general, it is a mathematical operation on two functions that represents the process of linear filtering. Convolution can be applied to any two functions of time or space (or other variables) to yield a third function, the output of the convolution. Although the mathematical, definition is symmetric with respect to the two input functions, it is common in signal processing to say that one of the functions is a filter acting on the other function. The response of many physical systems can be represented mathematically by a convolution. For example, a convolution is commonly used to model the filtering of seismic energy by the various rock layers in the Earth. 
         [0023]    One embodiment of the present invention determines the stationary pegleg utilizing rays which are sprayed from a detector location, the detector location being based on the input beam, and the stationary pegleg is related to one of the rays sprayed from the detector location. 
         [0024]    As one skilled in the art will appreciate, the phrase “time gate” is used herein to describe the entire beam or one of a plurality of segments included in the beam. 
         [0025]    It should also be appreciated that utilizing beam techniques to process seismic data are well known in the art, and those techniques are within the scope of the present invention. Beams in general are defined as energy components that are partially localized in space and dip. Some examples of beams are Gaussian beams and other non-Gaussian beams, such as beams with complex rays, controlled beams and beams as a finite-difference solution of some version of the wave equation. 
         [0026]    In one embodiment of the present invention, a segment of a modeled pegleg beam is convolved with the predicted multiples beam to generate a convolved multiples beam. The segment of the modeled pegleg beam starts at the multiple-generating surface and involves a time interval that is either explicitly specified or determined by another horizon in the model. 
         [0027]    In another embodiment of the present invention, the convolved multiples beam can be obtained by directly convolving the time sequences of the predicted multiples and the predicted modeled pegleg beams. 
         [0028]    It should also be appreciated that the present invention is intended to be used with a system which includes, in general, a computer configuration including at least one processor, at least one memory device for storing program code or other data, a video monitor or other display device (i.e., a liquid crystal display) and at least one input device. The processor is preferably a microprocessor or microcontroller-based platform which is capable of displaying images and processing complex mathematical algorithms. The memory device can include random access memory (RAM) for storing event or other data generated or used during a particular process associated with the present invention. The memory device can also include read only memory (ROM) for storing the program code for the controls and processes of the present invention. 
         [0029]    Additional features and advantages of the present invention are described in, and will be apparent from, the following Detailed Description of the Invention and the Figures. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0030]    These and other objects, features and advantages of the present invention will become better understood with regard to the following description, pending claims and accompanying drawings where; 
           [0031]      FIG. 1  illustrates a flow chart of a prior art method of attenuating multiples in seismic data; 
           [0032]      FIG. 2  illustrates a flow chart of one embodiment of the present invention for attenuating multiples in seismic data; 
           [0033]      FIG. 3  illustrates one embodiment of the present invention which includes transforming a primary beam into a predicted multiples beam; 
           [0034]      FIG. 4  illustrates one embodiment of the present invention wherein rays are sprayed from a detector location and are reflected off the water bottom surface of a marine environment; 
           [0035]      FIG. 5  illustrates one embodiment of me present invention wherein a primary beam corresponding to a given pegleg is determined through raytracing; 
           [0036]      FIG. 6  illustrates a method utilized by one embodiment of the present invention to determine the stationary pegleg; 
           [0037]      FIG. 7  illustrates a schematic drawing of the above method of determining the stationary pegleg used by one embodiment of the present invention; 
           [0038]      FIG. 8  illustrates one embodiment of the present invention wherein the primary beam is being convolved with the pegleg beam; 
           [0039]      FIG. 9  illustrates a schematic drawing of a single-beam deconvolution that is utilized by one embodiment of the present invention; 
           [0040]      FIG. 10  illustrates a flow chart of another embodiment of the present invention for attenuating multiples in seismic data; 
           [0041]      FIG. 11  illustrates a flow chart of a further embodiment of the present invention for attenuating multiples in seismic data; 
           [0042]      FIG. 12  illustrates a flow chart of one embodiment of the present invention for attenuating multiples in seismic data; 
           [0043]      FIG. 13  illustrates a flow chart of another embodiment of the present invention for attenuating multiples in seismic data; and 
           [0044]      FIG. 14  illustrates one embodiment of the invention wherein a primary beam corresponding to a pegleg is determined without raytracing. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0045]    While this invention is susceptible to embodiments in many different forms, there are shown in the drawings, and will herein be described in detail, preferred embodiments of the invention with the understanding, that the present disclosure is to be considered as an exemplification of the principles of the invention and is not intended to limit the broad aspect of the invention to the embodiments illustrated. 
         [0046]    One embodiment of the present invention  30  is illustrated in  FIG. 2 . The embodiment includes initializing an earth model that corresponds to a geological area of interest  32  and selecting a beam dataset derived from seismic data collected in the geological area of interest  34 . An input beam from the beam dataset  36 , a multiple-generating surface from the earth model  38 , and a time gate  40  are selected. A stationary pegleg is determined utilizing the input beam, the multiple generating surface and the time gate  42 . A primary beam corresponding to the stationary pegleg is then obtained  44 . A modeled pegleg beam related to the primary beam is obtained  46 . The modeled pegleg beam is convolved with the primary beam to determine a convolved multiples beam  48 . The convolved multiples beam is deconvolved with the input beam to remove the multiples in the input beam  50 . 
         [0047]    In another embodiment of the present invention, the predicted primary beam can be directly convolved with the modeled pegleg beam. 
         [0048]    In yet another embodiment of the present invention, rays are sprayed from a detector location and the stationary pegleg is determined based upon one of the rays. The detector location in that embodiment is based upon the input beam. 
         [0049]    In a further embodiment of the present invention, a segment of the modeled pegleg beam is convolved with the primary beam to obtain a convolved multiples beam. The segment of the modeled pegleg beam starts at the multiple-generating surface and involves a time interval that is either explicitly specified or is determined by another horizon in the model. The convolved multiples beam is then deconvolved with the input beam to remove the multiples in the input beam. 
         [0050]    As described-above, prior art methods have used local slant stacking or other dip-discriminating methods for seismic traces to separate a recorded wavefield into beam components and those methods are known in the art. The present invention utilizes local slant stacking to separate the recorded wavefield into components that are localized in both position and dip. These components are what would be recorded at the center of a beam arrival  54 ,  56  at locations A  58  and B  60  as illustrated in  FIG. 3 . The beam energy  54  that arrives at location B  60  reverberates in the water layer  64  and is assumed to arrive as multiples  62  within a beam  56  recorded at location A  58 . Shifting beam B  54  by the raytrace traveltime T AB    66  from location B  60  to location A  58  will line up the events in beam B  54  with the multiples  68 ,  70  in beam A  56 . Once the events have been aligned and the multiples  68 ,  70  are identified, the multiples  68 ,  70  can then be removed. 
         [0051]    When the local slant stacking described-above is used for 3D acquisition, the recorded energy cannot be completely steered into beams because the wavefield is not densely sampled along all recording directions, thus there is an issue of missing data or severe aliasing that is needed to accurately determine the raytrace traveltime T AB . For example, as one skilled in the art will appreciate, the local slant stacking is accomplished in the common-offset domain but, not in the common-midpoint domain. In one embodiment of the present invention, an assumption is made that stacking velocities describe the dip of primary events in common-midpoint (“CMP”) gathers. In general, stacking velocities are a reasonable description of primaries from geological structures above the subsurface salt formations, which can reverberate in marine environments to become the strongest multiples. 
         [0052]      FIGS. 4 ,  5  and  6  illustrate me manner in which this embodiment of the present invention calculates the raytrace traveltime for the determination of the stationary pegleg. An input beam is selected with a source location “S”  74  and a detector location “D”  76  as illustrated in  FIG. 4 . A multiple generating surface is determined, in this embodiment it is the water bottom (“wb”)  78 . Rays  80  are sprayed from the detector D  76  which are reflected back from the multiple-generating surface wb  78  and reach the free surface  82 . The angular interval for the rays  80  is predetermined to be dp x  in the x (vertically downward from the free surface  82 ) direction and dp y  in the y direction (perpendicular to the sheet). An individual ray  84  is selected with a given ray parameter or detector raypath dip p d  and an arrival location Q  86  of the ray  84  is determined at the free surface  82  as illustrated in  FIG. 5 . The arrival direction (ray parameter p q′   88 ) of the ray  84  is determined at the arrival location Q  86 . The reflection at location Q  86  is determined and an outgoing ray parameter p q    90  is calculated. The locations S  74  and Q  86  and their ray parameters p s    92  and p q    90  determine the primary corresponding to the pegleg with locations D  76  and Q  86  and ray parameters p d    84  and p q′   88 . 
         [0053]    Finding the stationary raypaths that describe the reflection at location Q  86  requires a raypath search. The search is performed to find the separate reflections that occur at the various locations S  74 , Q  86  and D  76 . In this particular embodiment, the search compares the ray traced p h  with the calculated p h  (p h  being the offset dip). The raytraced p h  calculated as; 
         [0000]    
       
      
       p 
       h 
       =p 
       q 
       −p 
       s  
      
     
         [0000]    
       
      
       p 
       m 
       =p 
       q 
       +p 
       s  
      
     
         [0000]    where p m  (the midpoint dip) at a given location corresponds to a particular beam. The calculated p h  obtained from the normal moveout equation (“NMO”): 
         [0000]    
       
         
           
             
               p 
               n 
             
             = 
             
               
                 
                   ∂ 
                   t 
                 
                 
                   ∂ 
                   h 
                 
               
               = 
               
                 
                   ∂ 
                   
                     ∂ 
                     h 
                   
                 
                  
                 
                   
                     
                       T 
                       0 
                       2 
                     
                     + 
                     
                       
                         ( 
                         
                           
                             2 
                              
                             h 
                              
                             
                                 
                             
                              
                             cos 
                              
                             
                                 
                             
                              
                             
                               θ 
                               m 
                             
                           
                           V 
                         
                         ) 
                       
                       2 
                     
                   
                 
               
             
           
         
       
     
         [0000]    where: 
         [0054]    t is time; 
         [0055]    h is the half offset; 
         [0056]    V is the NMO velocities; and 
         [0057]    T o  is zero-offset traveltime. 
         [0000]    V and T o  are derived from the stacking velocities obtained from the earth model.  FIG. 6  illustrates the determination of p h  where p h  is the local slope  96  of the curve  98  in the h-t plot  94 . The beam with the closest match between the raytraced p h  and the calculated p h  is selected as the stationary pegleg. 
         [0058]      FIG. 7  illustrates a schematic of the method in which the stationary pegleg is determined by this embodiment of the present invention. A midpoint dip p m  is selected  102 , and a trial direction p d  is selected from the detector location D that corresponds to the p m  is chosen  104 . The parameter p d  is used to perform a raytrace from the detector location D to a point Q selected between the source location S and the detector location D  106 . The raytrace results in a raytraced offset dip p h  which is compared to a calculated offset dip p h    108 , if the raytraced p h  closely matches the calculated p h  then this process is complete and the beam corresponding to p m  is selected as the stationary pegleg  110 . If the raytraced p h  does not match the calculated p h  then another trial direction p d  is chosen and the process is performed again  112  until a satisfactory match between the raytraced p h  and the calculated p h  is obtained. 
         [0059]    This embodiment of the present invention also includes convolving the predicted multiples beam with a segment of the modeled beam to obtain the convolved multiples beam. As illustrated in  FIG. 8 , the predicted multiples beam B  114  is convolved with the a segment of the modeled pegleg beam C  116  starting at the multiple-generating surface  118 . The result of the convolution is beam E  120  which is the convolved multiples beam that is deconvolved with input beam A  122  to remove multiples that are present in the input beam A  122 . 
         [0060]    A schematic illustration of this embodiment is provided in  FIG. 9 , wherein beam B  114  is utilized as the source side prediction  124 , and beam Q  116  is utilized for the detector side prediction  126 . This embodiment utilizes a Wiener Filter  128  and inputs from beams A  122 , B  114  and C  116  to generate an estimation of the multiples present in beam A  122 . A Wiener filter is known in the art. In general, it is a causal filter which will transform an input into a desired output as closely as possible, subject to certain constraints. As one skilled in the art will appreciate there are other filters or means that can perform this particular function and they are intended to be within the scope of the present invention. Once the multiples in Beam A  122  have been determined, the multiples are then removed  130  from Beam A  122 . 
         [0061]    One embodiment of the present invention is illustrated in  FIG. 10  wherein an earth model is initialized  134  which correlates to a specific geological region of interest. A beam dataset  136  that has been determined from seismic data of the geological region of interest is also initiated. This embodiment of the present invention includes a series of loops wherein an input beam  138 , a multiple-generating surface  140  and a time gate  142  are selected. Rays are sprayed from a detector location that is based on the input beam  144  and a stationary pegleg is selected from one of the rays  146 . A primary beam corresponding to the pegleg is obtained  148 , and the primary bean is transformed into a predicted multiples beam  150  by a shift corresponding to the traveltime of the ray corresponding to the stationary pegleg. A modeled pegleg beam related to the predicted multiples beam is then generated  152 . A segment of the modeled pegleg beam which starts at the multiple-generating surface is convolved with the predicted multiples beam to obtain a convolved multiples beam  154 . The convolved multiples beam is then either accumulated or deconvolved with the input beam to remove the multiples in the input beam  162 . The accumulated beams can be used to reconstruct the multiple prediction as a seismic trace or be used to deconvolve with the input beam at a later time. 
         [0062]    This embodiment of the present invention allows a number of different points after convolution to either accumulate the convolved multiples, beam or deconvolve the convolved multiples beam to remove the multiples in the input beam  162 . Depending on the data being processed, those steps can occur before the end of the For loop for selecting the time gate  142 - 156  or immediately after that loop  142 - 156 . Those steps can also occur after For loop for selecting the multiple-generating surface  140 - 158  or after the For loop for selecting the input beam  138 - 160 . 
         [0063]    Another embodiment of the present invention is illustrated in  FIG. 11 , that embodiment includes choosing a pegleg which is in a narrow range around a selected stationary pegleg  176 . A primary beam which corresponds to the chosen pegleg is obtained  178 , and that primary beam is transformed into a predicted multiples beam  180 . The modeled pegleg beam which relates to the predicted multiples beam is obtained  182 . The predicted multiples beam is then convolved with a segment of the modeled pegleg beam to obtain a convolved multiples beam. The segment of the modeled pegleg beam utilized by this step starts at the multiple-generating surface and ends at the detector location. Within the For loop for selecting the pegleg  176 - 186 , the predictions or convolved multiples beam for the narrow range around the stationary are stacked. The steps of accumulating the convolved multiples beam or deconvolving the convolved multiples beam to remove the multiples in the input beam  194  can occur in this embodiment after the For loop for selecting the pegleg  176 - 186 , the For loop for selecting, the time gate  172 - 188 , the For loop for selecting the multiple-generating surface  170 - 190 , or the For loop for selecting the input beam  168 - 192 . 
         [0064]    Another embodiment of the present invention is illustrated in  FIG. 12 , wherein the pegleg that is selected  208  is not tied to a stationary pegleg. That pegleg is used to obtain a corresponding primary beam  210 . The primary beam is transformed into a predicted multiples beam  212  and a modeled pegleg beam is obtained  214 . A segment of the modeled pegleg beam that starts at the multiple-generating surface is convolved with the predicted multiples beam to obtain a convolved multiples beam  216 . The convolved multiples beams that are generated within the For loop pegleg  208 - 218  are accumulated. In this embodiment, the steps of accumulating the convolved multiples beam or deconvolving the convolved multiples beam to remove the multiples in the input beam  226  can occur in this embodiment after the For loop for selecting the pegleg  208 - 218 , the For loop for selecting the time gate  204 - 220 , the For loop for selecting the multiple-generating surface  202 - 222 , or the For loop for selecting the input beam  200 - 224 . 
         [0065]    Both the stationary pegleg and the pegleg can be determined for a variety of multiples. One embodiment of the present invention determines the stationary pegleg or pegleg for a source-side multiple. Another embodiment determines the stationary pegleg or pegleg for a detector-side multiple. A further embodiment determines the stationary pegleg or pegleg for both source-side and the detector-side multiples. 
         [0066]    As one skilled in the art will appreciate, there may be situations in which an earth model is not readily available, in such instances, the present invention is still able to predict and attenuate multiples. One embodiment of the present invention does not include the use of an earth model. In that embodiment, an input beam is selected  230  from an opened beam dataset  228  as illustrated in  FIG. 13 . A time gate is selected  232  and the pegleg selection  236  is aided by an a-priori determination of stationary predictions  234 , such as assuming a layered earth model or determining the areal coverage of the source and detector locations. A pegleg is selected  236  and a primary beam corresponding to the pegleg is obtained  238 . A modeled pegleg beam corresponding to the primary beam is calculated  240 , and the primary beam is convolved with the modeled pegleg beam  242 . The above-described steps can either be repeated,  230 - 248 ,  232 - 246 ,  336 - 244  with the convolved multiples beam being accumulated or the convolved multiples beam is deconvolved with the input beam to remove the multiples from the input beam  250 . 
         [0067]    The above-described embodiment convolves a plurality of primary and pegleg beams for a range of locations Q  252  and a range of ray parameter values P q    254  and P s    256  as illustrated in  FIG. 14 . The range of Q  252  and the ranges P q    254  and P s    256  (or P d    258 ) is predetermined from an analysis of the input data. The ranges are determined so that enough beams are included to contain the stationary contribution for the modeled multiples that is amplified after summation of the stationary contribution with other non-stationary contributions. In  FIG. 14  a beam with a given ray parameter P m =P s    280 +P d    258 , a location Q  252 , and ray parameters P q    254  and P s    256  (or P d    258 ) are selected. The primary beam, P m1 =P s   256 +P q    254 , and the pegleg beam, P m2 =P d    258 +P q    254 , are determined. In this embodiment, there is an assumption made that the surface reflection at Q  252  is from P q    254  to −P q    260 . The primary beam can then be convolved with the pegleg beam. In this embodiment, the primary beam and the pegleg beam are convolved for a range of location Q  252  values beginning at Q  252 =(S  262 + 264 )/2 or some other predetermined locations. In addition, the primary beam and the pegleg beam are convolved for a range of ray parameter P q    254  values. 
         [0068]    As described-above, the embodiments of the present invention depicted in  FIGS. 10-13  incorporate loops which illustrate that certain steps of those embodiments can be repeated depending on the data which is being processed. 
         [0069]    Certain embodiments of the present invention described-above include spraying rays from the detector location to select the stationary pegleg or pegleg, it should be understood that there are another means of selecting the stationary pegleg or pegleg, for example, random selection, and those means are considered to within the scope of the present invention. 
         [0070]    While in the foregoing specification this invention has been described in relation to certain preferred embodiments thereof, and many details have been set forth for purpose of illustration, it will be apparent to those skilled in the art that the invention is susceptible to alteration and that certain other details described herein can vary considerably without departing from the basic principles of the invention.