Abstract:
A seismic streamer system and associated methods for estimating the shape of a laterally steered seismic streamer. The streamer is divided into a series of contiguous streamer segments by lateral-steering devices. Heading sensors positioned in forward and aft portions of each segment produce heading readings. Each segment is modeled as having a linear shape in the forward portion and a curved shape in the aft portion. The shape of the segment is estimated according to the model from the heading readings on the segment.

Description:
BACKGROUND 
     The invention relates generally to marine seismic prospecting and more particularly to seismic streamer arrangements and methods for estimating the shapes of laterally steered streamers. 
     Seismic streamers towed by survey vessels and instrumented with hydrophones receiving seismic reflections are used in marine seismic surveys. The accuracy of the survey depends on an accurate estimate of the shape of each streamer. As the number of streamers towed behind survey vessels has increased, lateral-steering devices attached along the lengths of streamers are becoming a more common method of controlling streamer separations for more regular spatial sampling and for avoiding streamer entanglement. A known problem in estimating the shape of a laterally steered streamer is accounting for the local shape distortions caused by the lateral forces applied by the lateral-steering devices against the streamer. Typically, these devices kink the streamer, especially when applying a substantial lateral force to steer the streamer to port or starboard. The kink represents a discontinuity in the first derivative or the tangent to the streamer at the point on the streamer where the lateral force is applied. The magnitude of this local shape distortion increases as the tension in the streamer decreases toward its tail. 
     Thus, there is a need for better estimates of the shapes of laterally steered streamers. 
     SUMMARY 
     One version of a seismic streamer system embodying features of the invention comprises a seismic streamer that extends in length from a head end to a tail end. Lateral-steering devices attached to the streamer apply a lateral force at spaced apart steering positions along the length of the streamer. The lateral-steering devices divide the streamer into a series of contiguous streamer segments. Each segment extends from a fore end at a steering position to an aft end at the next consecutive steering position closer to the tail end of the streamer. A plurality of first and second heading sensors producing heading readings are disposed along the length of the streamer. Each of the first heading sensors is disposed in one of the streamer segments closer to the fore end than to aft end. Each of the second heading sensors is disposed in one of the streamer segments proximate the aft end of the segment. Means for estimating streamer shape computes a shape estimate of the streamer segments as a function of the heading readings of the first and second heading sensors in the streamer segment. 
     In another aspect of the invention, a method for estimating the shape of a seismic streamer comprises: (a) attaching lateral-steering devices at spaced apart steering positions along the length of the seismic streamer to divide the streamer into a series of contiguous streamer segments between the steering positions of consecutive lateral-steering devices; (b) positioning first heading sensors providing first heading readings along a forward portion of each streamer segment; (c) positioning second heading sensors providing second heading readings along an aft portion of each segment proximate a lateral-steering device; and (d) computing an estimated shape of each streamer segment as a function of the first and second heading readings from the heading sensors in the streamer segment. 
     In yet another aspect of the invention, a method for estimating the shape of a seismic streamer steered laterally by lateral-steering devices disposed along the streamer&#39;s length comprises: (a) defining a series of contiguous streamer segments between the positions of consecutive lateral-steering devices; and (b) modeling the shape of each streamer segment as linear along a forward portion of the segment and as curved along an aft portion of the segment. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These aspects and features of the invention, as well as its advantages, are better understood by referring to the following description, appended claims, and accompanying drawings, in which: 
         FIG. 1  is a top plan schematic view of a survey vessel towing laterally steered streamers in a streamer system embodying features of the invention; and 
         FIG. 2  is a top plan enlarged schematic view of a portion of one of the streamers of  FIG. 1 . 
     
    
    
     DETAILED DESCRIPTION 
     A seismic streamer system embodying features of the invention is shown in  FIG. 1 . A survey vessel  10  tows the plurality of streamer cables  12  whose tail ends  14  are tethered to tail buoys  16 . Head ends  15  of the streamers  12  are attached to a system of tow cables and tethers  18  attached to the rear deck of the vessel  10 . Paravanes  20  are used to maintain a wide spread of the deployed streamer network. Lateral-steering devices  22 —disposed at spaced apart steering positions  24 , or steering nodes, e.g., every 300 m, along the length of each streamer—exert lateral forces  26  to drive the streamer to starboard or port. The lateral-steering devices  22  divide each streamer  12  into a series of contiguous streamer segments  28 . Each segment extends rearward from a fore end  30  at a forward steering position  24  to an aft end  31  at the next consecutive steering position. The last, or rearmost, streamer segment  29 , unlike the other segments, does not terminate at its aft end in a cable-steering device. Instead, its aft end is tethered to its tail buoy  16  on the sea surface. Heading sensors  32  are also attached to the streamer in each segment. The heading sensors may reside within the streamer itself, be housed in inline streamer control devices, or be housed in external streamer control devices, such as depth-control or lateral steering devices rotatably attached to the streamer. Each streamer segment has a heading sensor positioned closer to its fore end than to its aft end. 
     A controller  34  aboard the survey vessel  10  is connected to the heading sensors, lateral steering devices, and depth-control devices by a communications link such as a hardwired link running along the tow cables  18  and through the streamers  12 . The controller receives readings from the heading sensors and other data from devices on the streamer and sends control commands to the lateral-steering devices and depth-control devices over the link as required. 
     As shown in the enlarged view of  FIG. 2 , the streamer  12  tends to distort, or kink, at the steering positions  24  because of the lateral force exerted by the lateral-steering device  22  against the streamer at these positions. Because of the tension in the streamer resulting from being towed through the water, the shape of each streamer segment  28  of length L between the steering position  24  of consecutive lateral-steering devices  22  is generally straight for the first 25%-50% of the segment and then curves gently in the direction of lateral movement in the rest of the segment. The curvature increases rearward along the segment to the aft steering position. The magnitude of the curvature depends on the amount of lateral force applied by the lateral-steering device at the aft end of the segment. Consequently, the shape of the streamer segments may be approximated by a linear portion  36  that extends from the fore end  30  to an intermediate point  38 , which may coincide with the position of a heading sensor  32  at the rear end of the linear portion, and by a contiguous curved region  40  that extends from the intermediate point to the aft end  31  of the segment. 
     The heading sensor  32  attached to the forward, linear portion  36  of the streamer segment may be a self-contained device within the streamer or be housed in a depth-control device  42  as shown or other kind of streamer control device. A second heading sensor  32 ′ is disposed proximate the steering position  24  at the aft end of the segment. The second heading sensor  32 ′ may be self-contained or housed in the lateral-steering device or in another streamer control device in front of the steering position, i.e., just ahead of the kink in the streamer. 
     Each segment is modeled from fore end to aft end as a linear portion  36  whose tangent equals the heading reading θ 1  of the heading sensor  32  in the forward portion of the segment and a contiguous curved portion  40  whose tangent is approximated by an exponential function that depends on the heading reading θ 1  of the forward heading sensor  32  and the heading reading θ 2  of the heading sensor  32 ′ at the aft end. In the model, the tangent to the linear portion and to the curved portion are equal at their junction at the intermediate point  38 . Thus, the model produces an estimated shape of the streamer section by computing tangents T to the forward, linear portion and to the aft, curved portion from the heading readings. The tangent T L  at each point on the linear portion is given by T L =θ 1 . The tangent T C  to the curved portion at each point is given by T C =θ 1 +(θ 2 −θ 1 )·(d/s) p , where s is the length of the curved portion, d is the distance of the point along the streamer segment measured rearward from the intermediate point, and p is an empirically determined exponent, e.g., 2.5. The ratio d/s is the percentage distance along the curved portion of each point on the curved portion. Because the last streamer segment  29  attached to the tail buoy does not terminate in a lateral-steering device, it is modeled as a linear segment whose tangent T L =θ 1 . 
     The shipboard controller  34 , which receives all the heading readings from the heading sensors, can compute a more or less real-time shape estimate of the streamers in a streamer-shape estimating software routine that implements the mathematical model. The shape of each of the streamers is a piecewise connection of the shapes of the individual streamer segments. The streamer shape may also be estimated off-line by data-processing computers using the model on stored heading readings or later-refined heading readings. Either of these means for estimating streamer shape may be used. 
     Although the invention has been described in detail with respect to a few preferred versions, other versions are possible. For example, a heading sensor was shown in  FIG. 2  as coincident with the intermediate point at the junction of the linear and curved portions of the streamer segment. But the heading sensor can be attached forward of the intermediate point anywhere in the forward, linear portion. So, as this example suggests, the versions described in detail are meant to exemplify features of the invention.