Patent Publication Number: US-2015085603-A1

Title: Systems and methods for determining the far field signature of a source in wide azimuth surveys

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit under 35 U.S.C. §119(e) of U.S. Provisional Application Ser. No. 61/882,111 filed on Sep. 25, 2013, which is incorporated by reference in its entirety for all purposes. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates generally to seismic exploration and, more particularly, to systems and methods for determining the far field signature of a source in wide azimuth surveys. 
     BACKGROUND 
     In recent years, offshore drilling has become an increasingly important method of locating and retrieving oil and gas. But because drilling offshore involves high costs and high risks, marine seismic surveys are used to produce an image of subsurface geological structures. While the image may not directly show the location of oil or gas, those trained in the field can use such images to more accurately predict the location of oil and gas and thus reduce the chance of drilling a non-productive well. 
     Marine seismic surveys are usually accomplished by marine survey ships towing a signal source and/or seismic sensors. Some marine seismic surveys may involve multiple marine survey ships and may include source vessels that tow signal sources and recording vessels that tow seismic sensors and can, in some configurations, also tow sources. Each seismic sensor, or “sensor,” may be a hydrophone, which detects variations in pressure below the ocean surface. The sensors are contained within or attached to a cable that is towed behind the moving ship. The cables are often multiple kilometers in length and each has many sensors. The towing process is referred to as “streaming” the cable, and the cables themselves are referred to as “streamer cables” or “streamers.” For example, typically streamers can be approximately three to twelve kilometers in length. The distance between streamers perpendicular to the direction of movement of the recording vessel may be referred to as the “crossline streamer separation.” The total crossline distance from the first streamer to the last streamer may be referred to as “spread width.” For example, a recording vessel may tow approximately eight streamers at approximately seventy-five meter crossline streamer separation for a total spread width of approximately 500 hundred to 600 hundred meters. Spread widths can be designed up to approximately 1,200 meters. 
     A recording vessel may tow streamer cables at the same depth or at different depths. One or multiple depth positioning devices can act to hold portions of the streamer cable below the ocean surface at a desired depth. Streamer cables may be positioned at a constant depth below the ocean surface, or they may have a variable depth profile, according to the design of the survey. For example, a particular sensor may be towed on a towing line or a streamer cable at an approximately constant depth of 250 meters. 
     Source vessels can also tow one or more sources. The source generates a seismic signal, which is a series of seismic waves that travel in various directions including toward the ocean floor. The seismic waves penetrate the ocean floor and are at least partially reflected by interfaces between subsurface layers having different seismic wave propagation speeds. Sensors detect and receive these reflected waves. Sensors transform the seismic waves into seismic traces suitable for analysis. Sensors are in communication with a computer or recording system, which records the seismic traces from each sensor. 
     Each seismic trace typically contains contributions corresponding to multiple reflected waves that travel different paths from the source to the seismic sensor. For example, a given sensor may detect waves reflected from an interface at a shallow depth below the surface at one time, and detect waves reflected from an interface at a deeper depth at a later time. The arrival times of the waves travelling along each path may be affected by a variety of factors including the composition of the subsurface layers along each path, the depths and thicknesses of the layers along each path, the angle of the incoming wave, and other factors. 
     A seismic source has a characteristic far field signature that assists in processing of seismic data acquired by sensors. A signature for a particular source is the shape of the signal emitted by the seismic source and transmitted in the body of water. The signature varies with distance and azimuth from the seismic source. When the signature achieves and maintains a stable shape, it is referred to as the “far field” signature. This occurs at a certain distance from the point of source signal emission and when the water depth is sufficient to avoid the perturbation of the wave refracted by the sea floor. 
     Different techniques can be used to obtain the far field signature. For example, the far field signature can be modelled through dedicated source modelling software, reconstructed with a mathematical method from the individual signal recorded on each air gun, or in some cases, directly measured. In the case of direct measurement, a single sensor (hydrophone) or a group of single sensors positioned in the body of water at a certain distance from the source may be used to record the “true” signal emitted by the source. The sensors transform the waves emitted by the source into a signal suitable for analysis. When the sensor is positioned at a distance sufficiently far from the source, e.g., approximately 250 meters, the sensor may be used to determine the “true” far field signature of the source. 
     In wide azimuth (WAZ) survey, an increase in azimuthal range is accomplished by acquiring data over the same subsurface area using multiple recording vessels and source vessels. Azimuth is defined as the angle in a horizontal plane between the seismic source and the place where the reading is taken, relative to some datum angle, for example north. For WAZ surveys, multiple passes are acquired with increasing lateral separation between the recording vessels and source vessels to build up a range of offsets and azimuths. Thus, WAZ surveys use one or more recording vessels to tow sensors to detect and record seismic signals, and one or more source vessels that generally travel parallel to, but at some specified distance from the recording vessels. By making successive passes over the target, increasing the offset between the recording vessels and the source vessels by the width of the streamer spread each time, a wider range of azimuths and offsets are obtained. 
     However, in WAZ surveys, determining the far field signature at the azimuth angles may be difficult. Additionally, approximating the far field signature for these angles produces inferior data regarding the subsurface than would be obtained using the actual far field signature. Thus, there is a need for a technique to improve determination of the far field signature of a source at relevant angles from vertical for identification and analysis of subsurface formations. 
     SUMMARY 
     In accordance with some embodiments of the present disclosure, a method for seismic data processing is disclosed. The method includes determining a position of a first sensor and a source. The first sensor is attached to a first vessel and the source is attached to a second vessel. The method further includes calculating a reflected incidence angle between the first sensor and the source, determining a position for a second sensor based on a direct incidence angle between the second sensor and the source approximating the direct incidence angle. The method also includes determining a far field signature for the source based on the direct incidence angle. 
     In accordance with another embodiment of the present disclosure, a seismic survey system includes a source configured to emit seismic waves, a first sensor and a second sensor configured to transform seismic waves into a recorded signal, and a computing system. The computing system includes a processor, a memory communicatively coupled to the processor, and instructions stored in the memory. The instructions, when executed by the processor, cause the processor to determine a position of the first sensor and the source. The first sensor is attached to a first vessel and the source is attached to a second vessel. The processor is also caused to calculate a reflected incidence angle between the first sensor and the source, determine a position for a second sensor based on a direct incidence angle between the second sensor and the source approximating the reflected incidence angle, and determine a far field signature for the source based on the direct incidence angle. 
     In accordance with another embodiment of the present disclosure, a non-transitory computer-readable medium includes instructions that, when executed by a processor, cause the processor to determine a position of a first sensor and a source. The first sensor is attached to a first vessel and the source is attached to a second vessel. The processor is also caused to calculate a reflected incidence angle between the first sensor and the source, determine a position for a second sensor based on a direct incidence angle between the second sensor and the source approximating the reflected incidence angle, and determine a far field signature for the source based on the direct incidence angle. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present disclosure and its features and advantages, reference is now made to the following description, taken in conjunction with the accompanying drawings, which may include drawings that are not to scale and wherein like reference numbers indicate like features, in which: 
         FIG. 1A  illustrates an elevation view of an example marine seismic survey system used for conducting a wide azimuth (WAZ) survey and measuring the far field signature in accordance with some embodiments of the present disclosure; 
         FIG. 1B  illustrates an exemplary side view of the example marine seismic survey system of  FIG. 1A  in accordance with some embodiments of the present disclosure; 
         FIG. 1C  illustrates an exemplary elevation view of an example marine seismic survey system used for measuring the far field signature at varied direct incidence angles in accordance with some embodiments of the present disclosure; 
         FIGS. 2A-2E  illustrate exemplary views of configurations of source vessels and recording vessels used to determine the far field signature of a source in accordance with some embodiments of the present disclosure; 
         FIG. 3  illustrates a flow chart of an example method for determining the far field signature of a source in accordance with some embodiments of the present disclosure; and 
         FIG. 4  illustrates a schematic of an example seismic imaging system that can be used to determine the far field signature of a source in accordance with some embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     The present disclosure is directed to methods and systems of determining the far field signature of a seismic source at varied direct incidence angles. The system of the present disclosure can be utilized to determine the far field signature of a source at angles other than vertical. The system is useful in wide azimuth (WAZ) surveys because the far field signature can be determined with similar azimuths that are used in gathering seismic data during production. As discussed above, determining the far field signature of a source for an increased range of direct incidence angles seen during WAZ surveys provides additional details that can be used to improve the resulting seismic data. For example, for data gathered at a specified angle from vertical, the far field signature for that angle may be applied to the data rather than the far field signature measured at vertical leading to improvements in accuracy of the resultant data. 
       FIG. 1A  illustrates an elevation view of an example marine seismic survey system  100  used for conducting a WAZ survey and measuring the far field signature in accordance with some embodiments of the present disclosure. Source vessel  104  and recording vessel  102  are oriented to show the rear of the vessels. Source vessel  104  includes signal source  106 . Although only one source  106  is shown, it should be understood that system  100  may comprise multiple sources  106 . Sources  106  may also be referred to as “seismic sources,” “energy sources,” or “seismic energy sources.” Seismic survey system  100  may include sensors  108   a - 108   e  (collectively referred to as “sensors  108 ”). Source  106  and sensors  108  may be configured to conduct a WAZ survey. Sensors  108  may be attached to and towed behind recording vessel  102  and positioned relative to source  106   
     In some embodiments, seismic survey system  100  may include a single hydrophone (or closely spaced group of hydrophones) shown as sensor  110  to measure the far field signature of source  106 . Sensor  110  may be attached to recording vessel  102  via towing line  118 . Sensor  110  may be towed behind recording vessel  102  and positioned relative to source  106 . 
     In some embodiments, sensors  108  may be positioned with any appropriate combination of crossline streamer offset (perpendicular to direction of travel of recording vessel  102 ), inline offset (along the direction of travel of recording vessel  102  discussed with reference to  FIG. 1B ), and depth offset from sources  106  or water surface  114 . Sensors  108  may be attached or connected to recording vessel  102  via streamer lines  116   a - 116   e  (collectively “streamer lines  116 ”). Although only one sensor  108  is shown per streamer line  116 , any appropriate number of sensors  108  may be coupled to a particular streamer line  116 . In some embodiments, sensors  108  may be maintained in a selected position or location using any suitable positioning system. Sensors  108  may be configured to receive seismic signals to generate seismic data, but may not be configured to determine a far field signature. 
     In some embodiments, sensor  110  may be configured to determine the far field signature of source  106 . Sensor  110  may be attached or connected to recording vessel  102  with towing line  118  (or towing lines  118  for several closely spaced sensors  110 ). Towing line  118  may also be combined with a data line to provide real time monitoring of the acquired data. Sensor  110  may be positioned and maintained at a particular depth. For example, sensor  110  may be maintained at sensor depth  120  of approximately 250 meters. In some embodiments, sensor  110  may consist of multiple closely spaced sensors  110 . Although shown in the illustrated embodiments to be on the same recording vessel  102  as sensors  108 , in some embodiments, recording vessel  102  may not include sensors  108 . 
     In some embodiments, source  106  may be at a particular source depth  122  below the water surface  114 , for example approximately ten meters. Source  106  may be attached to source vessel  106  via source towing line  124 . Source  106  can include an array of seismic energy sources towed behind source vessel  104 . Multiple sources  106  may be at varied depths below surface  114 . Although only one source  106  is shown on source towing line  124 , any appropriate number of sources  106  may be connected to a particular source towing line  124 . Additionally, multiple sources  106  may be positioned at a predetermined distance from one another, for example approximately three meters. 
     In some embodiments, the positions of sources  106  and sensors  108  and  110  are monitored using one or more position-measurement mechanisms. For example, system  100  may include an ultra-short baseline (USBL), which measures an angle and distance to each source  106  or sensor  108  and  110  using acoustic pulses. System  100  may also include depth sensors, GPS sensors, visible light or infrared transceivers, or any other mechanisms suitable for measuring the positions of sources  106  and sensors  108  and  110 . 
     Seismic survey system  100  illustrates one of the possible vessel arrangements during a WAZ survey. A WAZ survey may include multiple source vessels  104  and recording vessels  102  arranged such that multiple passes are performed over a survey area. With each successive pass, offset distance  126  (also referred to as “lateral separation”) between sources  106  and sensors  108  may increase to build up the range of offsets and azimuths. For example, two source vessels  104  may be operated to tow different sets of sources  106  parallel to each other. Two recording vessels  102  may be operated on either side of the two source vessels  104 , such that with each successive pass the offset distance  126  between a particular sensor, and a source  106  is increased by spread width  128 . Spread width  128  may be the total distance of the separation between streamer lines  116 . For example, spread width  128  may be the distance between streamer line  116   a  and  116   e , or approximately 600 meters. In some embodiments, seismic survey system  100  is configured to measure the far field signature of a source used in a WAZ survey and not conducting the WAZ survey itself. For example, a configuration that does not include sensors  108  or streamer lines  116  may be operated to determine the far field signature of a source used in a WAZ survey as discussed in detail with reference to  FIG. 1C . 
     During a WAZ survey, signals emitted from source  106  are reflected from the ocean bottom  140  and received by sensors  108  as reflected waves  130 . The distance between sensors  108  and source  106  and the water depth  136  creates a reflected incidence angle α 1  from vertical  138 , which is a vertical line from source  106  to ocean floor  140 . Because the seismic signals are received at sensors  108  based on the reflected incidence angle α 1 , understanding the far field signature at the reflected incidence angle α 1  allows for increased accuracy in analysis of seismic data. The reflected incidence angle α 1  for reflected wave  130  may be calculated using the following: 
     
       
         
           
             
               ∝ 
               1 
             
              
             
               = 
               
                 
                   tan 
                   
                     - 
                     1 
                   
                 
                  
                 
                   ( 
                   
                     
                       
                         ( 
                         
                           D 
                           + 
                           SW 
                         
                         ) 
                       
                       / 
                       2 
                     
                     WD 
                   
                   ) 
                 
               
             
           
         
       
     
     where D is offset distance  126 , SW is streamer width  128 , and WD is water depth  136 . 
       FIG. 1B  illustrates an exemplary side view of the example marine seismic survey system  100  of  FIG. 1A  in accordance with some embodiments of the present disclosure. System  100  in the view of  FIG. 1B  includes recording vessel  102  and source vessel  104 . Recording vessel  102  and source vessel  104  are oriented to show the sides of the vessels. Source  106  is towed on line  124  at source depth  122  from water surface  114 . Sensors  108  are towed by streamer lines  116 . Sensor  110  is towed by towing line  118  at sensor depth  120 . Inline offset  142  is the inline distance between source  106  and sensor  110 . In some embodiments, source vessel  104  (and source  106 ) may be positioned in front of recording vessel  102  (and sensor  110 ). In some embodiments, source vessel  104  and recording vessel  102  may be positioned such that source  106  and sensor  110  are substantially parallel (e.g., inline offset  142  may be approximately zero meters). 
       FIG. 1C  illustrates an elevation view of an example marine seismic survey system  150  used for measuring the far field signature at varied direct incidence angles in accordance with some embodiments of the present disclosure. Seismic survey system  150  is configured to measure the far field signature to be used in analysis of seismic data obtained during a WAZ survey. As such, seismic survey system  150  may not include sensors  108  and streamer lines  116  that are shown with reference to  FIG. 1A . Source vessel  104  and recording vessel  102  are oriented to show the rear of the vessels. Source vessel  102  includes signal source  106 . Although only one source  106  is shown, it should be understood that system  150  may comprise multiple sources  106 . Sensor  110  may include a single hydrophone (or closely spaced group of hydrophones) and may be towed behind recording vessel  102  and positioned relative to source  106 . 
     In some embodiments, sensor  110  may be positioned with any appropriate combination of crossline offset (perpendicular to direction of travel of recording vessel  102 ), inline offset (along the direction of travel of recording vessel  102  discussed with reference to  FIG. 1B ), and depth offset from sources  106  or water surface  114 . Sensor  110  may be connected to recording vessel  102  with towing line  118  (or towing lines  118  for several closely spaced sensors  110 ). Towing line  118  may also be combined with a data line to provide real time monitoring of the acquired data. Sensor  110  may be positioned and maintained at a particular depth. For example, sensor  110  may be maintained at sensor depth  120  of approximately 250 meters. In some embodiments, sensor  110  may consist of multiple closely spaced sensors  110 . In some embodiments, source  106  may be at a particular source depth  122  below the water surface  114 , for example approximately ten meters. Source  106  can include an array of seismic energy sources towed behind source vessel  104 . Multiple sources  106  may be at varied depths below surface  114 . Although only one source  106  is shown on source towing line  124 , any appropriate number of sources  106  may be connected to a particular source towing line  124 . Additionally, multiple sources  106  may be positioned at a predetermined distance from one another, for example approximately three meters. 
     In some embodiments, source  106  emits a signal that propagates in all directions. Signals received by a sensor, such as sensor  110 , may include direct arrival waves (W(t))  152 , and surface ghost waves (G(t))  154 . The far field signature may be expressed as: F(t)=W(t)+G(t). Bottom ghost waves  156  may be detected at sensor  110  when water depth  136  is not sufficiently large. For example, bottom ghost waves  156  may be seen when water depth  136  is less than approximately 800 meters. In some embodiments, when water depth  136  is sufficiently large, the effect of bottom ghost waves  156  is negligible. Thus, in embodiments of the present disclosure, the effect of bottom ghost waves may be disregarded. 
     In some embodiments, since the far field signature of a source is based on both direct arrival waves  152  and surface ghost waves  154 , a change in position of either the source or sensor results in a change to the far field signature for that source. The change in position of either the source or sensor can be characterized by the direct incidence angle α. The far field signature for a source determined at a particular direct incidence angle α may then be used to analyze azimuthal seismic data gathered during a WAZ survey in which the sensors receive reflected signals from a source at reflected incidence angle α 1 , (discussed with reference to  FIG. 1A ) approximately equivalent to direct incidence angle α. Direct incidence angle α may be determined based on a geometrical equation or set of equations. 
     For example, a signal may be received at sensor  110  from source  106 . The position information for source  106  and sensor  110  may be determined and direct incidence angle α may be calculated as approximately 15°. The far field signature for source  106  may be determined for the particular direct incidence angle α. The far field signature at the particular direct incidence angle α can be subsequently used to analyze data collected during a survey in which a sensor receives reflected waves from a source at a similar or equivalent angle, for example approximately 15°. 
       FIGS. 2A-2E  illustrate exemplary views  200   a - 200   e  of configurations of source vessels  204  and recording vessels  202  used to determine the far field signature of source  206  in accordance with some embodiments of the present disclosure. Each view  200   a - 200   e  includes vessels that are traveling in a direction shown by directional arrow  230 .  FIG. 2A  illustrates side view  200   a  of recording vessel  202  with sensor  210  approximately directly below source  206 . In side view  200   a , source  206  and sensor  210  are on the same vessel. Recording vessel  202  may or may not be towing streamers. View  200   a  may allow generation of a far field signature of source  206  for direct incidence angles 0°≦α≦10°. 
       FIG. 2B  illustrates top view  200   b  of recording vessel  202  towing both source  206  and sensors  210   a  and  210   b  laterally offset from source  206 . For example, each sensor  210   a  and  210   b  may be offset approximately forty meters from source  206 . In top view  200   b , source  206  and sensors  210  are on the same vessel. Recording vessel  202  may or may not be towing streamers. View  200   b  may allow generation of a far field signature of source  206  for direct incidence angles 10°≦α≦15°. 
       FIG. 2C  illustrates top view  200   c  of recording vessel  202  with sensor  210  and source vessel  204  with source  206 . Recording vessel  202  and source vessel  204  may travel approximately parallel to each other. Also, sensor  210  may be positioned at a particular depth, for example approximately 250 meters. Recording vessel  202  may or may not be towing streamers. Further, recording vessel  202  and source vessel  204  may be operated such that crossline distance  226  may vary. Different crossline distances  226  may allow different ranges of angles α to be utilized. For example, Table 1 below illustrates various maximum direct incidence angles α max  based upon crossline distance  226  and sensor  210  at a depth of approximately 250 meters: 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Crossline distance (m) 
                 α max  (degrees) 
               
               
                   
                   
               
             
            
               
                   
                 100 
                 22 
               
               
                   
                 200 
                 39 
               
               
                   
                 350 
                 54 
               
               
                   
                   
               
            
           
         
       
     
       FIG. 2D  illustrates top view  200   d  of recording vessel  202  with sensor  210  and source vessel  204  with source  206 . Recording vessel  202  and source vessel  204  may travel along approximately the same path, e.g., inline. Recording vessel  202  and source vessel  204  may be operated such that inline distance  242  may vary. Recording vessel  202  may or may not be towing streamers. Different inline distances  242  may be adjusted to allow different operational angles to be utilized. Operational angle is the direct incidence angle in the inline direction, as opposed to the crossline direction. For example, Table 2 below illustrates various operational angles achieved based upon inline distances  242  and sensor  210  at a depth of approximately 250 meters: 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Inline distance (m) 
                 Angle (degrees) 
               
               
                   
                   
               
             
            
               
                   
                 100 
                 40 
               
               
                   
                 200 
                 58 
               
               
                   
                 350 
                 70 
               
               
                   
                   
               
            
           
         
       
     
       FIG. 2E  illustrates top view  200   e  of recording vessel  202  with sensor  210  and source vessel  204  with source  206 . Recording vessel  202  and source vessel  204  may travel approximately parallel and with a separation defined by both offset distance  226  and offset length  242 . Recording vessel  202  may or may not be towing streamers. In this embodiment, the crossline distance may be varied as discussed above with reference to  FIG. 2C  and the inline distance may be varied as discussed above with reference to  FIG. 2D . 
       FIG. 3  illustrates a flow chart of an example method  300  for determining the far field signature of a source in accordance with some embodiments of the present disclosure. For illustrative purposes, method  300  is described with respect to source  106  in seismic survey system  150 , discussed with respect to  FIG. 1C ; however, method  300  may be used to determine the far field signature of any appropriate source. The steps of method  300  can be performed by a user, electronic or optical circuits, various computer programs, models, or any combination thereof, configured to process seismic traces. The programs and models may include instructions stored on a non-transitory computer-readable medium and operable to perform, when executed, one or more of the steps described below. The computer-readable media can include any system, apparatus, or device configured to store and retrieve programs or instructions such as a hard disk drive, a compact disc, flash memory, or any other suitable device. The programs and models may be configured to direct a processor or other suitable unit to retrieve and execute the instructions from the computer readable media. Collectively, the user, circuits, or computer programs and models used to process seismic traces may be referred to as a “computing system.” For example, the computing system may be computing system  406 , discussed with reference to  FIG. 4  below. In some embodiments, the computing system is located elsewhere, and receives information stored during the seismic survey. For example, computing system  406  may record seismic signals and position information and deliver them to an on-shore computing system for processing at a later time. 
     At step  305 , the computing system receives a recorded signal from a sensor. For example, the computing system may receive a recorded signal from sensor  110 , discussed with reference to  FIG. 1C . In some embodiments, the computing system receives multiple recorded signals, each from a separate sensor. For example, the processing tool may receive separate recorded signals from multiple closely spaced sensors  110 . In some embodiments, the computing system receives the recorded signals indirectly from the sensor. For example, computing system  406 , discussed with reference to  FIG. 4  below, may store recorded signals from sensor  110  and deliver them to a different computing system at a later time. 
     At step  310 , the computing system determines the location of the sensor that provided the recorded signal and the source that emitted the signal that resulted in the recorded signal. For example, the computing system may determine the location and position of sensor  210  and source  206  in any of configurations discussed with reference to  FIGS. 2A-2E . The computing system may use information from a USBL, depth sensors, GPS sensors, visible light or infrared transceivers, or any other mechanisms suitable for measuring the positions of sensors to determine the location of the sensor that provided the recorded signal. 
     At step  315 , the computing system calculates the direct incidence angle α between the source and the sensor. For example, the computing system may use the position information from step  310  to determine the direct incidence angle α for direct arrival wave  152  as discussed with reference to  FIG. 1C . Such a determination may be based on constructing a geometric equation. 
     At step  320 , the computing system determines the far field signature for the source at the calculated direct incidence angle α. For example, as discussed with reference to  FIG. 1C , the far field signature may be determined by characterizing the portion of the recorded signal that reflects the arrival of direct arrival wave  152  and surface ghost wave  126 . 
     At step  325 , the computing system utilizes the far field signature at the angle α to process a seismic data set. In some embodiments, the far field signature at the calculated direct incidence angle may be used in a signature deconvolution process applied to a seismic data set received at a sensor configured to receive signals from the source at approximately the same reflected incidence angle. The seismic data set may be gathered based on a WAZ survey where the reflected incidence angle between the sensors and the source is calculated. 
     Modifications, additions, or omissions may be made to method  300  without departing from the scope of the present disclosure. For example, the steps may be performed in a different order than that described and some steps may be performed at the same time. For example, in some embodiments, a seismic data set may be gathered at a particular reflected incidence angle, e.g., reflected incidence angle α 1  as discussed in step  325 . Subsequently, the computing system may determine a configuration and locations for a source and sensor to determine the far field signature of the source. The configuration of the source and sensor may be based on producing a direct incidence angle that approximates the reflected incidence angle as discussed in step  310  and step  315 . Further, more steps may be added or steps may be removed without departing from the scope of the disclosure. 
       FIG. 4  illustrates a schematic of an example seismic imaging system  400  that can be used to determine the far field signature of a source in accordance with some embodiments of the present disclosure. System  400  includes sources  404 , sensors  402 , and computer system  406  communicatively coupled via network  414 , which can include one or more wired or wireless networks, or any suitable combination thereof. 
     Determining the far field signature of a source by computer system  406  can be used to improve seismic data and images generated from signals originating from sources  404 . Computer system  406  can operate in conjunction with sources  404  and sensors  402  having any structure, configuration, or function described above with respect to  FIGS. 1A-1C  and  2 A- 2 E. In some embodiments, sources  404  can be any suitable seismic energy sources. For example, sources  404  may be marine airguns, which generate a omnidirectional pressure wave. Any appropriate number of sources  404  may be used. Furthermore, sources  404  may be arranged in any appropriate geometry, such as an array, and positioned at any appropriate depth, according to the design of the seismic survey. For example, sources  404  may be coupled to a streamer line, a towing line, or maintained in a selected position or location using any other suitable positioning system. 
     Determination of a far field signature of a source by computer system  406  may use signals received by sensors  402 . In some embodiments, sensors  402  detect pressure fluctuations in the surrounding water. Each sensor  402  detects reflected seismic waves received from sources  404  and transforms the reflected seismic waves into a seismic signals. A seismic signal may be digital sample data, an analog electrical signal, or any other appropriate representation of the seismic waves detected by the sensor. In some embodiments, sensors  402  may include geophones, hydrophones, accelerometers, fiber optic sensors (such as, for example, a distributed acoustic sensor (DAS)), or any suitable device. Such devices may be configured to detect and record energy waves propagating through subsurface geology with any suitable, direction, frequency, phase, or amplitude. For example, in some embodiments, sensors  402  are vertical, horizontal, or multicomponent sensors. As particular examples, sensors  402  may comprise three component (3C) hydrophones, 3C accelerometers, or 3C Digital Sensor Units (DSUs). System  400  may utilize any suitable number, type, arrangement, and configuration of sensors  402 . For example, system  400  may include one, dozens, hundreds, thousands, or any suitable number of sensors  402 . As another example, sensors  402  may have any suitable arrangement, such as linear, grid, array, or any other suitable arrangements, and spacing between sensors  402  may be uniform or non-uniform. Furthermore, sensors  402  may be located at any suitable depth. 
     Computer system  406  may include any suitable devices operable to process seismic data recorded by sensors  402 . Computer system  406  is operable to process multiple sets of seismic data to determine far field signatures of sources and utilize the signatures in processing seismic data. Computer system  406  may be a single device or multiple devices. For example, computer system  406  may be one or more mainframe servers, desktop computers, laptops, cloud computing systems, or any suitable devices. Computer system  406  receives data recorded by sensors  402  and processes it to determine a far field signature for a source  404 . Computer system  406  may be operable to perform the steps described above with respect to  FIG. 3 . Computer system  406  may also be operable to control certain sources  404 . Computer system  406  may be communicatively coupled to sensors  402  via network  414  during the recording process, or it may receive the recorded data after the collection is complete. In the illustrated embodiment, computer system  406  includes network interface  408 , processor  410 , and memory  412 . 
     Network interface  408  represents any suitable device operable to receive information from network  414 , transmit information through network  414 , perform suitable processing of information, communicate with other devices, or any combination thereof. Network interface  408  may be any port or connection, real or virtual, including any suitable hardware and/or software (including protocol conversion and data processing capabilities) to communicate through a LAN, WAN, or other communication system that allows computer system  406  to exchange information with network  414 , other computer systems  406 , sources  402 , sensors  402 , and/or other components of system  400 . Computer system  406  may have any suitable number, type, and/or configuration of network interface  408 . 
     Processor  410  communicatively couples to network interface  408  and memory  412  and controls the operation and administration of computer system  406  by processing information received from network interface  408  and memory  412 . Processor  410  includes any hardware and/or software that operates to control and process information. In some embodiments, processor  410  may be a programmable logic device, a microcontroller, a microprocessor, any suitable processing device, or any suitable combination of the preceding. Computer system  406  may have any suitable number, type, and/or configuration of processor  410 . Processor  410  may execute one or more sets of instructions to determine far field signatures, including the steps described above with respect to  FIG. 3 . Processor  410  may also execute any other suitable programs to facilitate the data stabilization such as, for example, user interface software to present one or more GUIs to a user. 
     Memory  412  stores, either permanently or temporarily, data, operational software, or other information for processor  410 , other components of computer system  406 , or other components of system  400 . Memory  412  includes any one or a combination of volatile or nonvolatile local or remote devices suitable for storing information. For example, memory  412  may include random access memory (RAM), read only memory (ROM), flash memory, magnetic storage devices, optical storage devices, network storage devices, cloud storage devices, solid state devices, external storage devices, or any other suitable information storage device or a combination of these devices. Memory  412  may store information in one or more databases, file systems, tree structures, any other suitable storage system, or any combination thereof. Furthermore, different types of information stored in memory  412  may use any of these storage systems. Moreover, any information stored in memory may be encrypted or unencrypted, compressed or uncompressed, and static or editable. Computer system  406  may have any suitable number, type, and/or configuration of memory  412 . Memory  412  may include any suitable information for use in the operation of computer system  406 . For example, memory may store computer-executable instructions operable, when executed by processor  410 , to perform the steps discussed above with respect to  FIG. 3 . Memory  412  may also store any seismic data or related data such as, for example, raw seismic data, 3D images, 4D images, weighting functions, or any other suitable information. 
     Herein, “or” is inclusive and not exclusive, unless expressly indicated otherwise or indicated otherwise by context. Therefore, herein, “A or B” means “A, B, or both,” unless expressly indicated otherwise or indicated otherwise by context. Moreover, “and” is both joint and several, unless expressly indicated otherwise or indicated otherwise by context. Therefore, “A and B” means “A and B, jointly or severally,” unless expressly indicated otherwise or indicated otherwise by context. 
     Particular embodiments may be implemented as hardware, software, or a combination of hardware and software. As an example and not by way of limitation, one or more computer systems may execute particular logic or software to perform one or more steps of one or more processes described or illustrated herein. Software implementing particular embodiments may be written in any suitable programming language (which may be procedural or object oriented) or combination of programming languages, where appropriate. In various embodiments, software may be stored in computer-readable storage media. Any suitable type of computer system (such as a single- or multiple-processor computer system) or systems may execute software implementing particular embodiments, where appropriate. A general-purpose computer system may execute software implementing particular embodiments, where appropriate. In certain embodiments, portions of logic may be transmitted and or received by a component during the implementation of one or more functions. 
     Herein, reference to a computer-readable storage medium encompasses one or more non-transitory, tangible, computer-readable storage medium possessing structures. As an example and not by way of limitation, a computer-readable storage medium may include a semiconductor-based or other integrated circuit (IC) (such as, for example, an FPGA or an application-specific IC (ASIC)), a hard disk, an HDD, a hybrid hard drive (HHD), an optical disc, an optical disc drive (ODD), a magneto-optical disc, a magneto-medium, a solid-state drive (SSD), a RAM-drive, or another suitable computer-readable storage medium or a combination of two or more of these, where appropriate. A computer-readable non-transitory storage medium may be volatile, non-volatile, or a combination of volatile and non-volatile, where appropriate. 
     This disclosure contemplates one or more computer-readable storage media implementing any suitable storage. In particular embodiments, a computer-readable storage medium implements one or more portions of interface  408 , one or more portions of processor  410 , one or more portions of memory  412 , or a combination of these, where appropriate. In particular embodiments, a computer-readable storage medium implements RAM or ROM. In particular embodiments, a computer-readable storage medium implements volatile or persistent memory. 
     This disclosure encompasses all changes, substitutions, variations, alterations, and modifications to the example embodiments herein that a person having ordinary skill in the art would comprehend. For example, while the embodiments of  FIGS. 1A-1C  and  2 A- 2 E illustrate particular configurations of sources  106  and  206  and sensors  110  and  210 , any suitable number, type, and configuration may be used. As yet another example, while this disclosure describes certain data processing operations that may be performed using the components of system  400 , any suitable data processing operations may be performed where appropriate. Furthermore, certain embodiments may alternate between or combine one or more data processing operations described herein. 
     Moreover, although this disclosure describes and illustrates respective embodiments herein as including particular components, elements, functions, operations, or steps, any of these embodiments may include any combination or permutation of any of the components, elements, functions, operations, or steps described or illustrated anywhere herein that a person having ordinary skill in the art would comprehend. Furthermore, reference in the appended claims to an apparatus or system or a component of an apparatus or system being adapted to, arranged to, capable of, configured to, enabled to, operable to, or operative to perform a particular function encompasses that apparatus, system, component, whether or not it or that particular function is activated, turned on, or unlocked, as long as that apparatus, system, or component is so adapted, arranged, capable, configured, enabled, operable, or operative.