Abstract:
One embodiment of the present disclosure includes a method for processing seismic data comprising the steps of receiving data representing seismic energy gathered from a formation by a plurality of seismic receivers, wherein the data include primary and multiple data. A copy of the received data is created and compensated to reduce amplitude attenuation effects due to transmission and absorption losses. A multiple prediction algorithm is applied to the received and compensated data to obtain a multiple data prediction. The multiple data prediction is subtracted from the received data to obtain primary data. The primary data is processed to reduce attenuation effects in the received data.

Description:
BACKGROUND 
       [0001]    The present disclosure generally relates to a method of improving Seismic data by reducing the effects of multiple reflected energy. Seismic exploration involves surveying subterranean geological formations for hydrocarbon deposits. A survey typically involves deploying seismic source(s) and seismic sensors at substantially predetermined locations. The sources generate seismic waves which propagate into the geological formations creating pressure changes and vibrations along their way. Changes in elastic properties of the geological formation scatter the seismic waves, changing the properties of the seismic waves. For example, the direction of propagation of the seismic wave may be altered. Part of the energy emitted by the sources are reflected from interfaces between subterranean formations. Some of the reflected waves reach the seismic sensors, which detect seismic waves. There are various types of seismic sensors. Some are sensitive to pressure changes (hydrophones) and others are sensitive to particle motion (geophones). Industrial surveys may deploy either one type of sensor or both types. In response to the detected waves, the sensors generate electrical signals to produce seismic data. Analysis of the seismic data (or traces), the shape, position, and composition of the subterranean formations can be determined and can then be indicative of the presence or lack thereof of probable locations of hydrocarbon deposits 
         [0002]    Some surveys are known as “marine” surveys because they are conducted in marine environments. However, “marine” surveys may be conducted not only in saltwater environments, but also in fresh and brackish waters. In a first type of marine survey called a “towed-array” survey, an array of streamers and sources is towed behind a survey vessel. In a second type of marine survey, an array of seismic cables, each of which includes multiple sensors, laid on the ocean floor, or sea bottom; and a source is towed behind a survey vessel. 
         [0003]    Oftentimes, seismic waves reflect from interfaces other than just those between subterranean formation, as would be desired. Seismic waves sometimes reflect from the water bottom and the water surface, and the resulting reflected waves themselves continue to generate further reflections. Waves that reflect multiple times are referred to as multiple reflections or “multiples”. Surface multiples are those waves that have reflected multiple times between the water surface and any upward reflectors, such as the water bottom or formation interfaces, before being senses by a receiver. Generally, surface multiples are considered undesirable noises that interfere with and complicate the desired data. 
         [0004]    Considerable effort is expended in the design of seismic data acquisition and the processing of seismic data to limit the effect of multiple reflections on seismic data. Nevertheless, in many instances, present methods of processing seismic data are not as efficient as they could be. Accordingly, a need exists for an efficient method for attenuating seismic data multiples. 
       SUMMARY 
       [0005]    In one embodiment of the present disclosure a method for processing seismic data includes the steps of receiving data representing seismic energy gathered from a formation by a plurality of seismic receivers, wherein the data include primary and multiple data and creating a copy of the received data. The method further includes the steps of compensating the copied data to reduce attenuation effects and applying a multiple prediction algorithm to the received and compensated copied data to identify the multiple data. Further, the method includes the steps of subtracting the multiple data from the received data and obtain the primary data and processing the primary data in the received data to reduce attenuation effects in the received data. 
         [0006]    In another embodiment of the present disclosure, a system for processing data includes a processor and a computer memory comprising instructions executable by the processor to receive data representing seismic energy gathered from a formation, wherein the data include primary and multiple data. The instructions further cause the computer to create a copy of the received data, compensate the copied data to reduce attenuation effects and apply a multiple prediction algorithm to the received and compensated signals to identify the multiple data. In addition, the computer subtracts the multiple data from the received data to identify the primary data and processes the primary data to reduce attenuation effects. 
         [0007]    In yet another embodiment of the present disclosure, a non-transitory computer-readable medium having instructions stored thereon, that when executed by a processor, performs the steps of receiving data representing seismic energy gathered from a formation from a plurality of seismic receivers, wherein the data include primary and multiple data and creating a copy of the received data. The processor compensates the copied data to reduce attenuation effects and applies a multiple prediction algorithm to the received and copied data to identify the multiple data. Further the processor subtracts the multiple data from the received signals to identify the primary data and processes the primary data to reduce attenuation effects. The processor also generates a model of the formation based in part on the processed primary data. 
         [0008]    Other or additional features will be apparent from the following description, from the drawings, and from the claims. The summary is provided to introduce a selection of concepts that are further described below in the detailed description. The summary is not to be intended to be used as an aid in limiting the scope of the claimed subject matter. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
         [0009]      FIG. 1  depicts a schematic view of marine seismic surveying deployed for acquiring seismic data; 
           [0010]      FIGS. 2A-2D  illustrate flow charts of various embodiments of methods of according to various embodiments of the present disclosure; 
           [0011]      FIGS. 3 and 3A  illustrate reflector models showing primary and multiple events that may be acquired by the equipment shown in  FIG. 1 ; 
           [0012]      FIG. 4  depicts a five layer seismic model; 
           [0013]      FIG. 5  illustrates results derived from implementing embodiments of the methods of  FIGS. 2A-2D ; 
           [0014]      FIG. 6A  shows a common shot gather of received seismic data as a function of offset and time; 
           [0015]      FIG. 6B  shows the common shot gather of  FIG. 6A  and the internal multiples predicted by the method of  FIG. 2A ; and 
           [0016]      FIG. 7  illustrates a computing system in capable of incorporating with some embodiments of the present disclosure. 
       
    
    
     DETAILED DESCRIPTION 
       [0017]    Turning now to  FIG. 1 , a schematic view of marine seismic survey  100  is shown. Subterranean formations  102 ,  104  targeted for exploration, are below a water body  106 . Seismic energy sources  108  and seismic receivers  110  are positioned in the body of water  106 , typically by one or more seismic vessels (not shown). A seismic source  108 , for example, an air gun, if fired to create seismic waves in the body of water  106 . A portion of the seismic waves travels through the body of water  106  in the direction of the subterranean formation  102 ,  104  underneath the water. When the seismic waves encounters a seismic reflector, a portion of the seismic waves is reflected upward and a portion of the seismic wave continues to propagate downward. A reflector is caused by changes in the earth parameters (e.g., density or velocity) of the subterranean structure. The seismic reflector could be the water bottom  112  or one of the interfaces between the subterranean formation  102 ,  104 , such as interface  114  between formations  102  and  104 . When the reflected waves travelling upward reach the water/air interface at the water surface  116 , a portion of the waves are again reflected downwards. Continuing in this manner, seismic waves can reflect multiple times between upward reflectors, such as the water bottom or formation interface  114 , and the downward reflector at the water surface  116 , as described further below. Each time the reflected waves propagate past the position of a seismic receiver  110 , the receiver senses the reflected waves and generated representative signals (or datapoints). 
         [0018]    Those seismic waves that have reflected from the water bottom  112  or an interface between subterranean formations only once before being recorded by a seismic receiver are considered primary reflections.  FIG. 1  illustrates an example of a primary reflection shown by raypaths  120  and  122 . These primary reflections are typically indicative of the desired information about the subterranean formation. On the other hand, those waves that have reflected more than once in the subsurface prior to being sensed by a receiver  110  are considered multiple reflections (“multiples”). An example of a free-surface multiple with downward reflection at the free surface (air-water interface,  116 ) and which is also a water bottom ( 112 ) multiple is illustrated by raypaths  130 ,  132 ,  134 , and  136 . Examples of interbed multiple are shown by raypaths  140 ,  142 ,  144 , and  146 . Interbed multiples reflect downward on interfaces that are deeper than the free surface. Although individual interbed multiples may have lower amplitudes than free-surface multiples with similar upward reflections, the combination of interbed multiples from many downward generators may have a significant effect on the seismic data. As previously mentioned, all such multiples are extraneous noise that obscures the desired primary reflection signal. 
         [0019]    We now consider methods that predict interbed multiples. Such methods include approaches based on the Inverse Scattering Series (Weglein et al., 2003), as well as related methods by Jakubowicz (1998), Ten Kroede (2002), Wu et al. (2011), Ramirez et al. (2012). It is recognized that such methods provide accurate predictions of the traveltimes (kinematics) of the multiples in the data within a specified range of conditions, but have theoretical limitations that lead to systematic under-estimation of the amplitudes of the predicted multiples (Ramirez and Weglein, 2008; Dragoset, 2014). Recently, Wu and Weglein (2014) have analyzed the amplitudes of the predicted multiples (for 1D media and normal incidence plane waves) and pointed out two factors that affect these amplitudes; a first factor is related to transmission losses, while a second factor is related to anelastic losses in absorptive media. 
         [0020]    Those of skill in the art are typically familiar with the work of Wu and Weglein (2014, 2015), to derive a method to predict interbed multiples for layered media and vertically propagating waves, using the Inverse Scattering Series (ISS) method. This ISS method is further described in U.S. Pat. No. 5,757,723, which is hereby incorporated by reference in its entirety. One example of a software implementation based on the ISS method is the Omega™ Seismic Functional Module (SFM) known as Inverse-Scattering Internal Multiple Prediction algorithm, (ISIMP). Another Omega™ SFM is XIMP (eXtended Interbed Multiples Prediction), which is based on related concepts to ISS, but provides models for subsets of internal multiples, related to particular multiples generators, defined as horizons or layers (Wu et al., 2011; Ramirez et al., 2012). 
         [0021]    In one embodiment of the ISIMP implementation, the equation for prediction of interbed multiples (b 3 (k z )) by the above method may be of the form: 
         [0000]        b   3 ( k   z )=∫ −∞   ∞   b   1 ( z ) e   ik     z     z   dz∫   −∞   z-ε   b   1 ( z   1 ) e   −ik     z     z     1     dz   1 ∫ z     1     +ε   b   1 ( z   2 ) e   ik     z     z     2     dz   2 .  (1)
 
         [0022]    For an incident plane wave at normal (vertical) incidence, with a spike wavelet, the recorded data D(t) are transformed to Fourier domain D(ω), defining 
         [0000]    
       
         
           
             
               
                 
                   b 
                   1 
                 
                  
                 
                   ( 
                   
                     
                       2 
                        
                       ω 
                     
                     
                       c 
                       0 
                     
                   
                   ) 
                 
               
               = 
               
                 D 
                  
                 
                   ( 
                   ω 
                   ) 
                 
               
             
             , 
           
         
       
     
         [0000]    and 
         [0000]        b   1 ( z )=∫ −∞   ∞   b   1 ( k   z ) e   −ik     z     z   dk   z , with
 
         [0023]    k z =2ω/c 0  being the vertical wavenumber, and 
         [0024]    b 1 (z) corresponding to an uncollapsed FK migration of the input data (normal-incident spike plane-wave data in this example). The term ε in the formula is used to make sure the events satisfy the lower-higher-lower relationship, and its value is chosen on the basis of the wavelength corresponding to the wavelet. 
         [0025]    Turning now to  FIG. 3 , a two-reflector model is illustrated where P (1)  and P (2)  are primaries; R 1  and R 2  are reflection coefficients; T 12  and T 21  are transmission coefficients. IM is the first order internal multiple. The two-reflector model of  FIG. 3  assumes the depths of the source and the receiver to be zero. 
         [0026]    Substituting the analytic form of data into equation (1), the prediction result is illustrated below in equation (2), 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       b 
                       3 
                     
                      
                     
                       ( 
                       
                         k 
                         z 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       - 
                       
                         T 
                         12 
                       
                     
                      
                     
                       T 
                       21 
                     
                      
                     
                       
                         R 
                         1 
                         * 
                       
                       
                         R 
                         1 
                       
                     
                      
                     
                        
                       
                         
                           - 
                           2 
                         
                          
                         
                           α 
                           1 
                         
                       
                     
                      
                     
                       
                         IM 
                          
                         
                           ( 
                           
                             k 
                             z 
                           
                           ) 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0027]    The expression IM(k z ) represents the internal multiples in the data. The term 
         [0000]    
       
         
           
             
               - 
               
                 T 
                 12 
               
             
              
             
               T 
               21 
             
              
             
               
                 R 
                 1 
                 * 
               
               
                 R 
                 1 
               
             
           
         
       
     
         [0000]    is defined as a transmission factor (TF), and the term e −2α     1    is the Q absorption factor (QF). Accordingly, those of ordinary skill in the art will recognize that equation (2) can be rewritten as follows: 
         [0000]    
       
         
           
             
               
                 
                   b 
                   3 
                 
                  
                 
                   ( 
                   
                     k 
                     z 
                   
                   ) 
                 
               
               
                 IM 
                  
                 
                   ( 
                   
                     k 
                     z 
                   
                   ) 
                 
               
             
             = 
             
               TF 
               * 
               
                 QF 
                 . 
               
             
           
         
       
     
         [0028]    It is contemplated that both expressions TF and QF typically have more complex forms in situations where there are more than two reflectors existing in a given earth model. TF is related to the transmission losses at the interfaces on and above a multiple generator; Ramirez and Weglein (2008, equation 3) provide the expression for the transmission factor in the case of overburden with J layers (where J equal or larger than 1). The expression for the transmission factor TF for cases where the overburden includes 1 or more layers is as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         { 
                         
                           
                             
                               
                                 
                                   T 
                                   01 
                                 
                                  
                                 
                                   T 
                                   10 
                                 
                               
                             
                             
                               
                                 
                                   for 
                                    
                                   
                                       
                                   
                                    
                                   j 
                                 
                                 = 
                                 1 
                               
                             
                           
                           
                             
                               
                                 
                                   ∏ 
                                   
                                     i 
                                     = 
                                     1 
                                   
                                   
                                     j 
                                     - 
                                     1 
                                   
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     ( 
                                     
                                       
                                         T 
                                         
                                           
                                             i 
                                              
                                             
                                                 
                                             
                                              
                                             i 
                                           
                                           - 
                                           1 
                                         
                                         2 
                                       
                                        
                                       
                                         T 
                                         
                                           i 
                                           - 
                                           
                                             1 
                                              
                                             
                                                 
                                             
                                              
                                             i 
                                           
                                         
                                         2 
                                       
                                     
                                     ) 
                                   
                                    
                                   
                                     T 
                                     
                                       
                                         j 
                                          
                                         
                                             
                                         
                                          
                                         j 
                                       
                                       - 
                                       1 
                                     
                                   
                                    
                                   
                                     T 
                                     
                                       j 
                                       - 
                                       
                                         1 
                                          
                                         
                                             
                                         
                                          
                                         j 
                                       
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   for 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                                 &lt; 
                                 j 
                                 &lt; 
                                 J 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Note that when J is equal or larger than 2, the transmission factor for each interface above the multiple generator are squared, thereby compensating for transmission losses for two round-trips through the overburden. 
         [0029]    The factor QF is related to the Q absorption or generalized transmission loss in the layers above the multiple generator. A plane wave of frequency ω travelling a distance x in a medium of constant Q factor and velocity c has its amplitude decreased by a factor of 
         [0000]    
       
         
           
             
               A 
                
               
                 ( 
                 
                   x 
                   , 
                   Q 
                 
                 ) 
               
             
             = 
             
               
                  
                 
                   
                     
                       - 
                        
                     
                      
                     
                        
                       ω 
                        
                     
                      
                     x 
                   
                   
                     2 
                      
                     
                         
                     
                      
                     cQ 
                   
                 
               
               . 
             
           
         
       
     
         [0000]    The compensation for absorption losses for a wave travelling from the measurement surface to the generator of multiples P (1)  is given by the factor e −α     1   . Thus, the transmission TF factor is the square of factor for absorption attenuation in the overburden. 
         [0030]    Referring to the definitions of attenuation (Wu and Weglein, 2014), it is established that the e −2α     1    term in equation (2) above compensates for attenuation accumulated in two round trips through the overburden (layers above the generator for the internal multiples), similar to the situation described above for the transmission losses. 
         [0000]    With reference to  FIG. 3A , it is contemplated that compensation for attenuation in the overburden may be necessary for two round trips through the overburden, in the case of normal incidence wave propagation as analyzed theoretically, as well as in a more general case (for example, 3D media and/or point sources) An internal multiple is shown by the raypath from source S to receiver R, with a downward reflection on an interface Z 1 . Events E 1 , E 2 , and E 3  contribute to the prediction of the internal multiple. Event E 1  is the raypath from S′ to R′ with an upward reflection on the interface Z 1 , event E 2  is the raypath from S to R′ with an upward reflection on an interface Z 2 , and event E 3  is the raypath from S′ to R with an upward reflection on an interface Z 3 . The interface Z 1  where downward reflections occur may be an interpreted horizon provided by the user, or it may be a horizon set at a constant time (or depth, or pseudo depth) or interpolated between interpreted horizons. In the ISIMP implementation, each constant depth level is considered a potential interface generating downward reflection. The events E 2  and E 3  can be concatenated together by convolution and the event E 1  can be removed by cross-correlation to derive an event that occurs at traveltime T=T 3 +T 2 −T 1 .
 
The extent of attenuation experienced by a seismic event depends on the raypath for that event. For the internal multiple in  FIG. 3A , the raypath length L is equal to L 2 +L 3 −L 1 . However, for the multiple predicted by equation (1) the attenuation (transmission as well as absorption) is cumulated along raypaths of events E 1 , E 2 , and E 3 , with combined length of L 2 +L 3 +L 1 . The difference between these lengths (combined length of events E 1 , E 2 , and E 3  minus the length L of the internal multiple) is 2L 1 . This difference in lengths explains the underprediction of the amplitudes of interbed multiples by a factor corresponding to amplitude attenuation during two round trips through the overburden.
 
         [0031]    Another embodiment of the present disclosure contemplates reducing the effect of TF and QF on amplitude prediction. Unlike the ISIMP formula shown in equation 1, this embodiment of the present disclosure uses two different datasets as inputs for multiple prediction. For example, the modified inverse scattering series (ISS) (as described in Weglein (2003)) internal multiple attenuation algorithm may be expressed as: 
         [0000]        b   3 ( k   z )=∫ −∞   ∞   b   1 ( z ) e   ik     z     z   dz∫   −∞   z-ε   c   1 ( z   1 ) e   −ik     z     z     1     dz   1 ∫ z     1     +ε   ∞   b   1 ( z   2 ) e   ik     z     z     2     dz   2 ,  (4)
 
         [0000]    where the term c 1 (z) is computed from modified data {tilde over (d)}(t) via the same transform applied to compute b 1 (z) from original data d(t);
       a) when {tilde over (d)}(t)=d (t), equation (4) provides a similar prediction as equation (2);   b) when {tilde over (d)}(t) is equal to primaries in an overburden section, the predicted multiples are less affected by spurious events (events in the interbed multiples model that are not in the data), as noted in Melo et al. (2014) for the cascaded application of interbed multiples prediction using the ISIMP implementation, and variations on the ISS concepts.   c) Consider d(t) to be input data or estimated primaries to which amplitude corrections have been applied as the inverse of the factors TF and QF, such that the predicted multiples by equation (4) match the input data.       
 
         [0035]    To compensate for QF, the present disclosure contemplates applying twice Q compensation using the estimated Q model, or alternatively applying Q compensation once with a Q/2 model. The Q model may be estimated from analysis of VSP data at well locations and interpolation between wells, or by Q tomography from surface seismic data, or by a combination of both approaches. To compensate for amplitude compensation for transmission through the overburden may be applied twice. A model for transmission losses may also be obtained from well logs or from VSP data, or from acoustic impedances estimated from surface seismic data by inversion. In the application described above we apply amplitude correction to seismic data before computations of the multiples models according to equation (2) and to the flowchart shown in and described with respect to  FIG. 2B . By applying the above described, process, compensation for amplitude losses in the medium above specified generators is achieved, thus making the models of multiples not only comparable to the data, but also more consistent and comparable to each other. 
         [0036]    Another embodiment contemplates using the result of equation (2) to equalize the amplitudes of models of different subsets of interbed multiples. For example, using the XIMP approach (Wu et al., 2011) two interbed multiples models may be computed, for horizon generators Z 1  and Z 2 , respectively ( FIG. 3A ). These models may require compensation with different correction factors, as shown in equation (2). The amplitude correction factors for both models depends on at least medium properties between the two horizon generators. Once the amplitude correction factors are derived, the ratios of the amplitude correction factors can be used to compensate amplitude losses for the interface at a larger depth (Z 2  interface), such that now both models require a similar correction when matched to the data. One advantage of this approach is that it doesn&#39;t require knowledge of material properties up to the measurement surface, but can be readily used with log or VSP data available only over a limited depth interval. 
         [0037]    Numerical tests for waves emitted from a point source in a layered medium provide justification (as discussed with reference to  FIGS. 4 and 5  below) for applying the method disclosed herein beyond the conditions set for theoretical analysis. The methods disclosed herein may also be applied for media that are not layered media. 
         [0038]    Note that the present disclosure differs from the disclosure of Zou and Weglein (2014) where an approach to correct iteratively for the transmission losses and estimating the transmission losses from the data as part of their multiples elimination procedure is disclosed. Further the Zou and Weglein (2015) approach is directed to non-absorptive media. One or more implementations of various techniques for removing internal multiples from seismic data according to the principles and equations described above will now be described in more detail with reference to the figures in the following paragraphs. 
         [0039]      FIG. 2A  illustrates one embodiment of a method  200  for attenuating or removing multiple data representing signals recorded in a seismic survey in accordance with implementations of various techniques described herein. In one implementation, seismic data  210  is loaded onto a computer system (described below in connection with  FIG. 7 ) at a block  212 . The seismic data  210  may include primary reflections and internal multiple reflections as described above with respect to  FIG. 1 . A block  214  applies amplitude compensation to the seismic data  210 . As is known to those of ordinary skill in the art, a model of attenuation factors (transmission losses or Q-attenuation) characterizing an area of interest may be derived from seismic survey data. In other embodiments, the Q-values may be modelled from well data such as vertical seismic profiles at well locations, interpolation between wells, Q-tomography, or from any combination of each of these methods. The prediction of interbed multiples including the use of a model for anelastic attenuation (Q model) is explained in greater detail below. Following the partial compensation by the block  214 , the partially compensated seismic data is transmitted to a block  216  that applies an internal multiple attenuation algorithm to the partially compensated seismic data and a copy of the seismic data from the block  212  to derive an internal multiple estimate that models the internal multiples in the seismic data  210 . The internal multiple attenuation algorithm implemented in the block  216  may include the ISIMP implementation or the modified ISS implementation discussed above. 
         [0040]    Next, the estimated multiple model derived in the block  216  is adaptively subtracted from the seismic data  210  at a block  216  to derive seismic data that is substantially free of multiples in a block  220 . Note that the seismic data  210  has not been corrected for absorption or transmission losses at this point during the processing. 
         [0041]    Turning now to  FIG. 2B , another embodiment of a method  240  for attenuating multiples in seismic data is shown. A block  242  receives seismic data, then a copy of the seismic data is transmitted to a block  244 . The block  244  performs amplitude compensation on the copy of the seismic data received from the block  242 . In this embodiment of the method  240 , the block  244  may receive a data input  246  from other software modules that estimate a Q model (e.g. Omega™ SFM Q-TOMO module). Such Q-models are used for instance by depth migrations that compensate for attenuation as part of the migration (Omega™ SFMs Q-RTM, Q-KDM). Following the block  244 , control is passed to a block  248  that applies the modified ISS internal multiple attenuation algorithm to the seismic data received in the block  242  and the partially Q-compensated data from the block  244  to derive a model of the multiples in the seismic data. Next, a block  250  adaptively subtracts the multiples model from the seismic data from the block  242  to derive seismic data that is substantially free of multiples in a block  252 . 
         [0042]    Yet another embodiment of a method  270  for attenuating multiples in seismic data is described in connection with  FIG. 2C . A block  272  receives seismic data. A copy of the seismic data is transmitted to a block  274 . The block  274  compensates the seismic data for any losses that may have occurred due to transmission or the Q-factor of the transmission medium. Following the block  274 , control is passed to a block  276  that applies the modified ISS internal multiple attenuation algorithm to the seismic data received in the block  274  and the partially Q-compensated data from the block  274  to derive a model of the multiples in the seismic data. Next a block  278  adaptively subtracts the multiples from the seismic data from the block  272  to derive seismic data that is substantially free of multiples in a block  280 . A block  282  applies additional Q-compensation to the seismic data derived in the block  280  to remediate any attenuation that may still be present in the seismic data and a block  284  renders an image of the subsurface region of interest using the compensated data from the block  284 . 
         [0043]      FIG. 2D  illustrates another embodiment of a method  290  for attenuating multiples in seismic data. A block  292  receives seismic data. A copy of the seismic data is transmitted to a block  294 . The block  294  compensates the seismic data to reduce the effect of any transmission losses that may have occurred to the data. Following the block  294 , control is passed to a block  296  that applies the modified ISS internal multiple attenuation algorithm to the seismic data received in the block  274  and the partially Q-compensated data from the block  294  to derive a model of the multiples in the seismic data. Next a block  298  adaptively subtracts the multiples model from the seismic data from the block  292  to derive seismic data that is substantially free of multiples in a block  300 . A block  302  applies additional Q-compensation to the seismic data derived in the block  300  while the subsurface region characterized by the seismic data is being imaged in a block  302 . The Q-compensation in the block  302  remediates attenuation that may be present in the seismic data and renders an image of the subsurface region of interest. 
         [0044]      FIG. 5  shows results of an evaluation of one embodiment of the method of compensating Q-amplitude. A 1D normal incidence plane wave propagates in the acoustic, absorptive, horizontally layered medium with parameters shown in  FIG. 4 . Reflection data are received in the top layer of the model (medium  1 ). The received data is indicated by reference numeral  504 . The multiple prediction  502  results from the application of one embodiment of the method disclosed herein. A result from a known method of predicting multiples is indicated by reference  506 . The prior art method does not take into account absorption in the medium. By observing the areas marked  508  in  FIG. 5 , those of ordinary skill in the art will readily notice that the amplitude of the data derived from the subtraction of the multiples prediction  502  derived by the implementation of an embodiment of the present disclosure is significantly improved compared to the amplitude of the data derived by the prior art method indicated by  506  in  FIG. 5 . It is understood that the modified multiple prediction  502  still has a smaller amplitude than the original attenuated data indicated by  504  due to the transmission factor (TF) as discussed above. 
         [0045]    Another example of an evaluation of one embodiment of the method disclosed herein is described with respect to  FIGS. 6A and 6B  using data with offset. The shot gather record is generated using a software Plane Wave transverse Isotropic Modelling (PWTIM) as is known to those of skill in the art. Parameters to produce a 1D earth shot gather with a point spike source are chosen and the Omega™ Seismic Function Module INV_Q_Filter is used to obtain this compensated dataset. The prediction results can be seen from  FIGS. 6A and 6B , where P 1 -P 4  represent four primary events generated at three interfaces and the arrows  602  represent internal multiples. Those of ordinary skill in the art will observe a similar improvement as the previous 1D example in  FIG. 5 . Specifically, the internal multiple prediction in  FIG. 6B  shows relatively high accuracy in comparison to the input data shown in  FIG. 6A   
         [0046]      FIG. 7  illustrates an example computing system arrangement  700  in accordance with some embodiments. Computing system arrangement  700  may be an individual computer system or an arrangement of distributed computer systems. Computer system  701 A includes one or more noise mitigation modules  702  that are configured to perform various tasks according to some embodiments, such as one or more methods disclosed herein. To perform these various tasks, noise mitigation module  702  executes independently, or in coordination with, one or more processors  704 , which is (or are) connected to one or more storage media  706 . The processor(s)  704  is (or are) also connected to a network interface  707  to allow the computer system  701 A to communicate over a data network  708  with one or more additional computer systems and/or computing systems, such as  701 B,  701 C, and/or  701 D (note that computer systems  701 B,  701 C and/or  701 D may or may not share the same architecture as computer system  701 A, and may be located in different physical locations, e.g., computer systems  701 A and  701 B may be in the field and/or on a laboratory, while in communication with one or more computer systems such as  701 C and/or  701 D that are located in one or more data centers, and/or located in varying countries on different continents and/or on various marine vehicles). Processors  704  may include a microprocessor, microcontroller, processor module or subsystem, programmable integrated circuit, programmable gate array, or another control or computing device. 
         [0047]    The storage media  706  may be implemented as one or more computer-readable or machine-readable storage media. Note that while in the example embodiment of  FIG. 7  storage media  706  is depicted as within computer system  701 A, in some embodiments, storage media  706  may be distributed within and/or across multiple internal and/or external enclosures of computing system  701 A and/or additional computing systems. Storage media  806  may include one or more different forms of memory including semiconductor memory devices such as dynamic or static random access memories (DRAMs or SRAMs), erasable and programmable read-only memories (EPROMs), electrically erasable and programmable read-only memories (EEPROMs) and flash memories, magnetic disks such as fixed, floppy and removable disks, other magnetic media including tape, optical media such as compact disks (CDs) or digital video disks (DVDs), BluRays, or other types of optical storage, or other types of storage devices. Note that the instructions discussed above may be provided on one computer-readable or machine-readable storage medium, or alternatively, may be provided on multiple computer-readable or machine-readable storage media distributed in a large system having possibly plural nodes. Such computer-readable or machine-readable storage medium or media is (are) considered to be part of an article (or article of manufacture). An article or article of manufacture may refer to any manufactured single component or multiple components. The storage medium or media may be located either in the machine running the machine-readable instructions, or located at a remote site from which machine-readable instructions may be downloaded over a network for execution. 
         [0048]    It should be appreciated that computing system arrangement  700  is only one example of a computing system, and that computing system arrangement  700  may have more or fewer components than shown, may combine additional components not depicted in the example embodiment of  FIG. 7 , and/or computing system arrangement  700  may have a different configuration or arrangement of the components depicted in  FIG. 7 . The various components shown in  FIG. 7  may be implemented in hardware, software, or a combination of both hardware and software, including one or more signal processing and/or application specific integrated circuits. 
         [0049]    Further, the steps in the processing methods described herein may be implemented by running one or more functional modules in information processing apparatus such as general purpose processors or application specific chips, such as ASICs, FPGAs, PLDs, or other appropriate devices. These modules, combinations of these modules, and/or their combination with general hardware are all included within the scope of protection of the invention. 
         [0000]    The foregoing description, for purpose of explanation, has been described with reference to specific embodiments. However, the illustrative discussions above are not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations are possible in view of the above teachings. The embodiments were chosen and described in order to best explain the principles of the invention and its practical applications, to thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated.