HYBRID SEISMIC ACQUISITION WITH WIDE-TOWED

Abstract

The present invention concerns a system for marine seismographic data acquisition, in particular for use in survey design. The invention provides a method for marine seismographic acquisition whereby subsea data and information can be collected using sea floor receivers and suspended receivers simultaneously. This is achieved by aligning the geometries of the two acquisition techniques and utilizing a system of wide-towed seismic sources that produce seismic energy on all the source point locations required to fulfil both acquisition methods.

Claims

1-4. (canceled)

5. A method for acquiring marine seismic data comprising the steps of: defining a horizontal inline axis Y and a horizontal crossline axis X perpendicular to the inline axis; determining first and second distances along the X and Y-axes based on spatial sampling requirements for S-waves whereby the first and second distances determine a bin size for S-waves; determining third and fourth distances along the X and Y-axes based on spatial sampling requirements for P-waves whereby the first and second distances determine a bin size for P-waves; defining a sail line parallel to the Y-axis over a survey area, and for each sail line; arranging a set of N.sub.2 seafloor receiver lines parallel to the Y-axis; arranging a set of n equally spaced source lines parallel to the Y-axis with equal spacing x.sub.0 between the source lines, and at least one source line laying between adjacent seafloor receiver lines; moving the source lines along the X-axis such that the distance between a source line and an adjacent seafloor receiver line becomes equal to or less than twice the first distance; defining a crossline distance to a next sail line equal to n times the distance (x.sub.0) between adjacent source lines; determining a shot interval equal to or less than twice the second distance; arranging a set of N streamers over the source lines and seafloor receiver lines such that crossline distances between a source line and an adjacent seafloor receiver line or an adjacent streamer is equal to or less than twice the third distance; and if necessary, reducing the shot interval to twice the fourth distance.

6. The method according to claim 5, further comprising the step of deploying seafloor receivers along the seafloor receiver lines at inline distances computed from the second distance and a shot point.

7. The method according to claim 6, further comprising the step of towing a source array with n acoustic sources having equal spacing x.sub.0 between adjacent sources at a first depth below a sea surface with a centre of the source array along the sail line.

8. The method according to claim 7, further comprising the step of towing a streamer array at a second depth below the sea surface with a centre of the streamer array along the sail line.

9. The method according to claim 5, further comprising reducing the shot interval to twice the fourth distance

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The invention will be explained in the following detailed description with reference to the attached drawings, in which:

[0037] FIG. 1 illustrates a context for the invention and notation used in this document,

[0038] FIG. 2 is a top view illustrating a towing vessel and further details,

[0039] FIG. 3 is a front view illustrating the towing vessel sailing along adjacent sail lines,

[0040] FIG. 4 is a top view illustrating a configuration around one sail line shown in FIG. 3, and

[0041] FIGS. 5-8 illustrate shot patterns.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0042] The drawings illustrate example configurations and are not to scale. Several details known to those skilled in the art are omitted for clarity of illustration.

FIGS. 1-3

[0043] FIGS. 1-3 illustrate configurations, definitions and notation used in this is document.

[0044] FIG. 1 is a use diagram schematically illustrating a survey plan. A vessel 101 illustrates towing along a planned sail line 201. For completeness, we will describe common tackle 102-105 with reference to FIG. 2.

[0045] In this document, capital letters X, Y, Z denote global, right-handed Cartesian coordinates with the sail line 201 pointing in the direction of the X-axis and the Z-axis pointing downwards. Lower case letters x, y, z are vessel bound Cartesian coordinates with the x-axis mid-ship from stern to bow, y-axis mid-ship from port to starboard and z-axis pointing downwards. The x-axis point in the direction of the X-axis during a pass along a sail line 201, and in the opposite direction (−X) during a pass along an adjacent sail line 202.

[0046] We will use the term ‘inline’ for directions parallel to the X-axis and ‘crossline’ for directions parallel to the Y-axis. In reality, water currents etc. will cause ‘feathering’, e.g. curved streamers in the XYZ-system. That is, in this document ‘inline’ does not mean ‘along streamers’ and ‘crossline’ does not mean ‘perpendicular to the streamers’.

[0047] We adhere to the common convention of assigning traces from suspended receivers 152 to bins. The bins in a common midpoint (CMP) gather lie in a projection plane. This does not mean we assume a flat seafloor. Further, a rectangular grid of bins is equivalent to a rectangular grid of midpoints of the bins—these two regular grids are just displaced half a bin size from each other. For illustrative purposes, FIGS. 1-3 show acoustic sources 151, suspended receivers 152 and seafloor receivers 153 on a regular grid. This should be interpreted as ‘resampling on a regular grid’ rather than an unrealistic idealisation.

[0048] A dashed rectangle 10 illustrates the area of interest in the present invention. In this area, seafloor receivers 153 are deployed to detect S-waves. The sail lines 201, 202 extend past the rectangle 10 to illustrate that there may be a larger survey area in which traditional P-P acquisition suffices.

[0049] A dashed border 20 illustrates a region with an increased demand for resolution. We assume reduced bin-sizes within the border 20. Note that FIG. 1 shows the regions 10 and 20 small compared to a streamer array 120 for illustration. In real embodiments, the regions 10 and 20 are several times bigger than the streamer array 120 in both the X and Y-directions.

[0050] A source array 110 comprises N.sub.1 acoustic sources 151 at a regular crossline distance y.sub.1 between adjacent sources. When towed, each source 151 generates a shot line 119 parallel to the X-axis. The shot lines 119 are also known as ‘source lines’. Filled circles illustrate shot points 150, specifically points in space and time at which an acoustic source 151 should release an acoustic pulse according to the survey plan. The crossline distance between adjacent shot lines 119 equals the distance y.sub.1 between adjacent sources 151. A related inline distance x.sub.1 corresponds to the inline distance between consecutive shot points 150.

[0051] If we assume equidistant shot lines 119 over the area 10, the distance between adjacent sail lines 201, 202 is N.sub.1y.sub.1 and the width of array 110 is (N.sub.1−1)y.sub.1. In FIG. 1, N.sub.1=6 so the width of array 110 is 5y.sub.1 and the distance between the sail lines 201 and 202 is 6y.sub.1. Numbered examples 1-3 below regard an overlap region where the distance between outermost shot lines during adjacent passes is not necessarily equal to y.sub.1.

[0052] A streamer array 120 has 8 streamers 121-128 in this example. FIG. 1 illustrates a fan-out in which each streamer 121-128 forms an angle θ≠0 with the X-axis. We distinguish between ‘fan-out’, which is intentional, and ‘feathering’ due to external forces such as sea currents. Either way, each suspended receiver 152 in the streamer array 120 generates a receiver line 129, and the number of receiver lines N.sub.2 quickly becomes greater than the number of streamers. The fan-out in FIG. 1 intentionally enables decreased bin sizes and increased resolution. This is relevant in the region 20.

[0053] An enlarged view of two adjacent suspended receivers 152 illustrates that x.sub.2=x.sub.2′ cos θ where x.sub.2′ is the distance between adjacent receivers measured along is streamer 121. For example, x.sub.2′=12.5 m is a typical distance in a modem streamer. An angle θ=37° yields x.sub.2 about 10 m, and an inline bin size reduced from 6.25 m to 5.0 m. Of course, crossline bin-sizes are simultaneously reduced by multiplication with sin θ.

[0054] In short, fan-out enables reduced bin sizes for P-waves within the border 20, and our definitions of ‘inline’ and ‘crossline’ differ from the definition ‘along’ and ‘across’ streamers.

[0055] In FIG. 1, each sail line 201 and 202 coincides with a seafloor receiver line, and there is one seafloor receiver line on either side of the sail line. The seafloor receiver line halfway between the sail lines 201, 202 is utilised during passes along the respective sail lines 201 and 202. In general, the crossline distance between adjacent seafloor receivers 153 in array 130 is y.sub.3, and the corresponding inline distance is x.sub.3. Recall that FIG. 1 illustrates a plan.

[0056] FIG. 2 is a schematic top view of the vessel 101 towing the source array 110 and the streamer array 120 over the seafloor array 130. We do not repeat the description of notation and reference numerals that were explained with reference to FIG. 1.

[0057] In FIG. 2, we assume that the vessel 101 travels with a constant speed v along a return path, i.e. in the −X direction. Vessel bound coordinates x, y, z are as in FIG. 1.

[0058] Winches on the vessel 101 and ropes 102 connected to paravanes 103 control the width of the streamer array 120. Birds (not shown) along each streamer 121-128 may provide additional control, for instance to compensate for feathering and/or create an intentional fan-out as shown in FIG. 1. Birds and streamers with near neutral buoyancy facilitate depth control. Online searches for keywords in the present paragraph will reveal further details. Streamer control as such is outside the scope of the present invention and need no further explanation herein.

[0059] There are numerous alternatives for providing towing forces, is communication and power to the arrays 110 and 120. Without loss of generality, we assume that the ropes 102 comprise steel wires and/or synthetic fibres able to exert a towing force. Further, we assume that cables 104 from the vessel 101 to the streamers 121-128 contain ropes 102 plus communication lines for transferring data. Finally, in this example umbilicals 105 are cables 104 with additional power supply lines for supplying pressurized air and/or electric power to the source array 110.

[0060] In FIG. 2 and later examples, acoustic sources 151 in the source array 110 have reference numerals 111-116 from port to starboard. At towing speed v, the inline distance between adjacent shot points 150 along a shot line 119 becomes x.sub.1=vT.sub.S, where T.sub.S is a shot interval measured in seconds. A minimum time interval is required to recharge an acoustic source 151. This affects shot patterns that will be described with reference to FIGS. 4-8.

[0061] In FIG. 2, the streamers 121-128 are parallel to the sailing direction x. Thus, the number of receiver lines 129 trailing behind suspended receivers 152 becomes N.sub.2=8 in this example. Further, the vessel 101 is sailing between seafloor lines 132 and 133, not directly above a seafloor receiver line as in FIG. 1. As noted, regular grids defining bins and mid-points of bins are equivalent. Three seafloor receivers 153 in the lower left of FIG. 2 are displaced from regular grid intersections to illustrate that real data may be resampled on a regular grid. Exact deployment of seafloor receivers 153 on grid intersections is of course unrealistic in practical surveys.

[0062] FIG. 3 is a schematic view of the vessel 101 on a sea surface 1 during two adjacent passes 201 and 202. In FIG. 3, the global X-axis would point out of the paper plane. The streamer array 120 is wider than the source array 110 and defines an overlap area 203 between sail lines, on the port side of vessel 101 in FIG. 3. The distance y.sub.1 between the outermost port sources during the two passes 201 and 202 is an example. We will describe other distances in numbered examples 1-3.

[0063] An irregular line illustrates a ‘realistic’ seafloor 2. We will only consider midpoints between shots and receivers projected onto horizontal projection planes 204-206, so the seafloor receivers 153 are shown at regular intervals along the global Y-axis.

[0064] For later reference, we assume that sail line 201 is at a constant C.sub.Y in global coordinates. That is, vessel bound coordinates y=Y−C.sub.Y. A crossline midpoint (y.sub.1+y.sub.2)/2=(Y.sub.1+Y.sub.2−2C.sub.Y)/2=(Y.sub.1+Y.sub.2)/2−C.sub.Y. In words, a midpoint between global coordinates Y.sub.1 and Y.sub.2 is the constant C.sub.Y plus the midpoint between corresponding vessel bound coordinates y.sub.1 and y.sub.2. Next, we assume that the sail line 201 is displaced ΔC.sub.Y from the nearest line of seafloor receivers 153, and that the crossline distance between seafloor receivers is y.sub.3. Since the sources 151 is symmetric about sail line 201 and seafloor receivers 153 are displaced ΔC.sub.Y+ny.sub.3 from the sail line, the midpoints are displaced by ΔC.sub.Y/2.

[0065] Ellipses near the sea surface 1 represent the acoustic sources 151. Unfilled ellipses illustrate sources along sail line 201 and filled ellipses illustrate sources along sail line 202. Each source 111-116 is connected to the vessel 101 by an umbilical 105. Ropes 102, paravanes 103, cables 104 and several umbilicals 105 are omitted in FIG. 3 for clarity.

[0066] Large circles near the sea surface 1 represent suspended receivers 152 in streamers 121-128. Unfilled circles illustrate receivers along sail line 201, and circles with crosses illustrate receivers along sail line 202. As noted, each streamer 121-128 contains receivers 152 at regular intervals.

[0067] The horizontal projection plane 204 illustrates a cross section of a common mid-point (CMP) gather acquired by the sources 111-116 and the streamers 121-128. In this particular configuration, midpoints may be grouped into groups of four. Near the outermost sources 111, 116 and streamers 121, 128, the outermost groups lack 3, 2, and 1 midpoints, respectively. We will return to this in numbered examples 1-3.

[0068] The horizontal projection plane 205 shows a subset of a CMP-gather is acquired by the source 111 and three seafloor receivers 153.

[0069] The horizontal projection plane 206 illustrates a combination of midpoints between sources in array 110 and suspended receivers 152, and between sources in array 110 and seafloor receivers 153. The ‘x’-symbols relate to suspended receivers 152 and the ‘+’-symbols relate to seafloor receivers 153.

[0070] In the following, a ‘grid cell’ has dimensions x.sub.0×y.sub.0 and a ‘bin’ has dimensions mx.sub.0×ny.sub.0 where m and n are integers >1. For example, traces from suspended receivers 152 in a 3D survey may define a ‘natural grid’ with P-wave bins x.sub.P×y.sub.P=x.sub.0×y.sub.0=6.25×6.25 m.sup.2. In a later example, S-wave bins are x.sub.S×y.sub.S=4x.sub.0=6y.sub.0=25.0×37.5 m.sup.2. During later processing, traces may be assigned to even larger bins.

[0071] For example, P-SV data may be assigned to bins in a common conversion point (CCP) gather, in which optimal bin sizes depend on formation properties and the bins must be neither too small nor too large for optimal imaging. The sides in a CCP bin might be in the range 45-60 m rather than the ˜5 to 10 m of a CMP bin for P-P acquisition. Alternatively, traces from all S-wave bins with centres within an optimal radius may be assigned to a round CCP-bin for use in the later processing of P-SV data. The present invention concerns seismic data acquisition, which account for later processing by means of a suitable grid.

[0072] In the following, we assume cell sizes x.sub.0×y.sub.0 equal to the bin size in a CMP-gather during P-P acquisition. Recall that fan-out reduces x.sub.0 and y.sub.0, e.g. from 6.25 m determined by streamer design. With the definitions above, x.sub.0 is the distance between midpoints along the X-axis and y.sub.0 is the distance between midpoints along the Y-axis. Further, x.sub.1 to x.sub.3 and y.sub.1 to y.sub.3 are multiples of x.sub.0 and y.sub.0, respectively We will use the following notation:

[0073] x.sub.1=m.sub.1x.sub.0, y.sub.1=n.sub.1y.sub.0,

[0074] x.sub.2=m.sub.2x.sub.0, y.sub.2=n.sub.2y.sub.0,

[0075] x.sub.3=m.sub.3x.sub.0 and y.sub.3=n.sub.3y.sub.0, where m.sub.1 to m.sub.3 and n.sub.1 to n.sub.3 are integers.

[0076] A midpoint M.sub.ij=(S.sub.i+Rj)/2 where bold letters indicate (X, Y)-coordinates, S.sub.i is a source position and Rj is a receiver position. We will use lower case m.sub.ij for decompositions in vessel bound coordinates.

Crossline Configuration of Sources and Suspended Receivers

[0077] We assume that the vessel 101 will tow the source array 110 approximately 100 m in front of the streamer array 120, and that both arrays 110 and 120 are symmetric about a sail line 201, 202. In the crossline direction and vessel bound coordinates, the midpoint becomes

[00001]$\begin{array}{cc}{m}_{ij}=c+i{y}_1\text{/}2+j{y}_2\text{/}2& \left(1\right)\end{array}$

where i and j are integers and c is a constant.

Example 1: Crossline Midpoints on Plane 204

[0078] Assume N.sub.1=6 sources 111-116 and N.sub.2=8 parallel streamers 121-128 as in FIGS. 2 and 3. Further, n.sub.1=8, n.sub.2=10 and y.sub.0=6.25 m give y.sub.1=50 m between sources 151 and y.sub.2=62.5 m between suspended receivers 152 in parallel streamers.

[0079] In this example, the width of source array 110 is 5.Math.50=250 m. With y=0 on a sail line 201 or 202, the sources 111-116 are located at 50 m intervals from −125 to +125 m. The middle sources 113, 114 are located at −25 and +25 m. Similarly, the width of streamer array 120 is 7.Math.62.5=437.5 m and the receivers are located at 62.5 m intervals from −218.75 to +218.75 m. The middle receivers are located at −31.25 and +31.25 m. Thus, when y=0 on the sail line, the outermost midpoints ±M.sub.0 are ±(125+218.75)/2=±171.88 m from the sail line, and the middle midpoints are ±(−25+31.25)/2=±3.125 m from the sail line.

[0080] The width of source array 110 is (N.sub.1−1)y.sub.1/2 and the distance between sources is y.sub.1=n.sub.1y.sub.0. Similarly, the width of streamer array 120 is (N.sub.2−1)y.sub.2/2 and the distance between suspended receivers is y.sub.2=n.sub.2y.sub.0. According to equation (1), we may obtain midpoints simply by adding multiples of y.sub.1/2 and y.sub.2/2 to a constant c. In order to get positive indices i=0 to (N.sub.1−1) and j=0 to (N.sub.2−1), we change origin to the outermost port midpoint. That is:

[00002]$\begin{array}{cc}{m}_{ij}=\left[-\left(N_1-1\right)y_1\text{/}2+i{y}_1-\left(N_2-1\right)y_1\text{/}2+j{y}_2\right]\text{/}2=\left[-M_0+i{n}_1\text{/}2+j{n}_2\text{/}2\right]y_0\mathrm{where}& \left(2\right)\\ i=0\mathrm{to}\left(N_1-1\right),j=0\mathrm{to}\left(N_2-1\right)\mathrm{and}{M}_0=\left[\left(N_1-1\right)n_1+\left(N_2-1\right)n_2\right]\text{/}4.& \left(3\right)\end{array}$

[0081] Note that changing origin from y=0 on the sail line to y=0 at −M.sub.0y.sub.0 corresponds to changing the constant c in (1) from c=0 to c=−M.sub.0y.sub.0.

[0082] It is practical to ‘factor out’ y.sub.0 to simplify changing grid sizes, e.g. from 6.25 m to 5.0 m. Inserting N.sub.1=6, N.sub.2=8, n.sub.1=8 and n.sub.2=10 in (2) yields m.sub.ij=[−27.5+4i+5j]y.sub.0 where i=0-5 and j=0-7. Table 1 contains the values of [−27.5+4i+5j] arranged in N.sub.1=6 rows and N.sub.2=8 columns:

TABLE-US-00001 TABLE 1 Values of (−27.5 + 4i + 5j) j i 0 1 2 3 4 5 6 7 0 −27.5 −22.5 −17.5 −12.5 −7.5 −2.5  2.5 7.5 1 −23.5 −18.5 −13.5 −8.5 −3.5 1.5  6.5 11.5 2 −19.5 −14.5 −9.5 −4.5 0.5 5.5 10.5 15.5 3 −15.5 −10.5 −5.5 −0.5 4.5 9.5 14.5 19.5 4 −11.5 −6.5 −1.5 3.5 8.5 13.5 18.5 23.5 5 −7.5 −2.5 2.5 7.5 12.5 17.5 .22.5  27.5

[0083] Equation (2) and Table 1 are essentially convenient ways to illustrate crossline midpoints independent of y.sub.0. For example, y.sub.0=6.25 m yields outermost midpoints at ±M.sub.0y.sub.0=±27.5.Math.6.25=±171.88 m. The midpoints closest to the sail line are at ±0.5.Math.6.25=±3.125 m, etc. These are equal to the values computed using y=0 on the sail line above and illustrate that the effect of moving origin from the sail line is to add a constant, here −M.sub.0y.sub.0.

[0084] Of course, a different y.sub.0 yields different distances in metres. For example, y.sub.0=5.0 m in the region 20 yields y.sub.1=40 m between sources and y.sub.2=50 m between streamers. Table 1 remain unchanged provided N.sub.1, N.sub.2, n.sub.1 and n.sub.2 remain unchanged, so we obtain new midpoints by multiplying the values in Table 1 by y.sub.0=5.0 m rather than by y.sub.0=6.25 m.

[0085] In Table 1, it is easily seen that the midpoint values increase by n.sub.1/2=4 from one row to the next and by n.sub.2/2=5 from one column to the next as expected from equation (2). This causes midpoint values separated by 1 in diagonals upwards to the right in Table 1. In general, the distance between adjacent midpoint values along such a diagonal may be found from equation (1):

[00003]$\begin{array}{cc}\begin{array}{c}{m}_{ij}-m_{\left(i+1\right)\left(j-1\right)}=\left[c+i{y}_1+j{y}_2\right]\text{/}2\\ -\left[c+\left(i+1\right)y_1+\left(j-1\right)y_2\right]\text{/}2\\ =\left(y_2-y_1\right)\text{/}2\end{array}& \left(4\right)\end{array}$

[0086] Equation (4) shows that the distance between neighbours in a table diagonal is independent of c, i and j so we may set (y.sub.2−y.sub.1)/2=y.sub.x where y.sub.x is the crossline bin size y.sub.P or y.sub.S for P-waves or S-waves, respectively. Substituting y.sub.1=n.sub.1y.sub.x and y.sub.2=n.sub.2y.sub.x in equation (4) shows that nd.sub.2=n+2 gives the desired distance 1 between crossline midpoints that are neighbours along a ‘table diagonal’ upwards to the right.

[0087] Following diagonals in Table 1, it is easy to verify that the table contains midpoints at every unit step from −15.5 to 15.5. With y.sub.P=y.sub.0=6.25 m, this corresponds to crossline midpoints every 6.25 m from −96.88 to 96.88 m. Near the upper left and lower right corners, Table 1 ‘runs out of sources and streamers’, so the diagonals become incomplete.

[0088] Specifically, the last diagonal with n.sub.1/2=4 consecutive values within is Table 1 contains values 12.5 to 15.5 and starts at i=5, j=4. An extension of the column j=4 with 3 elements in steps of n.sub.1/2=4 would contain the values 16.5, 20.5 and 24.5. Starting from these values, there are three incomplete diagonals directed upward to the right:

[0089] d1 lacks 16.5 and contains 17.5, 18.5 and 19.5;

[0090] d2 lacks 20.5 and 21.5 and contains 22.5 and 23.5; and

[0091] d3 lacks 24.5, 25.5 and 26.5 and contains 27.5.

[0092] For later reference, d1 lacks 1 value, d2 lacks 2 values and d3 lacks 3 values, cf. the small circles on projection plane 204 in FIG. 3 and comments above.

[0093] A fourth diagonal to the right would lie entirely outside Table 1. It follows that the number of incomplete diagonals generally equals (n.sub.1/2−1). In this example, (n.sub.1/2−1)=3 and the starting column is at j=7−3=4. By symmetry, there are similar incomplete diagonals in the upper left part of Table 1 with negative values.

[0094] Recall that N.sub.2 is the number of receiver lines 129, not necessarily the number of streamers. In the present coordinates, incomplete diagonals on the port side start at j=N.sub.2−n.sub.1/2 for any N.sub.2. Since the starting column correspond to an integer, n.sub.1 must be even.

[0095] Table 2 illustrates passes along adjacent sail lines.

TABLE-US-00002 TABLE 2 Midpoints in the overlap region 203 m.sub.n 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5 24.5 25.5 26.5 27.5 44 − m.sub.n 27.5 26.5 25.5 24.5 23.5 22.5 21.5 20.5 19.5 18.5 17.5 16.5 48 − m.sub.n 27.5 26.5 25.5 24.5 23.5 22.5 21.5 20.5 Combo 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5 24.5 25.5 26.5 27.5

[0096] Row ‘m.sub.n’ represents the pass along sail line 201 and contains the values 16.5 to 27.5 from the incomplete diagonals d1 to d3. Values in bold typeface are present in Table 1, and values in normal typeface belong to the incomplete diagonals d1 to d3 outside Table 1.

[0097] During a return pass along an adjacent sail line, the outermost midpoint might fit into the first gap. Here, this would yield a distance between sail lines (16.5+27.5)y.sub.0=44y.sub.0. With y.sub.0=6.25 m, 44y.sub.0=275 m.

[0098] Row ‘44−m.sub.n’ is obtained by subtracting values of m.sub.n from 44. Since (44−16.5)=27.5, (44−17.5)=26.5 etc., row ‘44−m.sub.n’ contains the values in row ‘m.sub.n’ in reverse order. Bold typeface indicate values within Table 1 as in row ‘m.sub.n’. Every column has a value in bold typeface either in row ‘m.sub.n’ or in row ‘44−m.sub.n’, so all midpoints 16.5 to 27.5 would be covered by two passes along adjacent sail lines Y.sub.1=44y.sub.0 apart.

[0099] As noted, an equal distance y.sub.1 between shot lines 119 implies Y.sub.1=N.sub.1y.sub.1 between adjacent sail lines 201 and 202. In the present example, N.sub.1y.sub.1=6.Math.8y.sub.0=48y.sub.0.

[0100] Row ‘48−m.sub.n’ contains cells from row ‘44−m.sub.n,’ shifted 48−44=4 columns to the right. With y.sub.0=6.25 m, the displacement of columns corresponds to ‘moving’ the next sail line 202 to Y.sub.1=48y.sub.0=300 m from the sail line 201.

[0101] Row ‘Combo’ represents the combined passes along sail lines 201 and 202 separated by 48y.sub.0. The columns contains the values 16.5 to 27.5 in ascending order from sail line 201. The gap at 20.5 associated with sail line 201 is filled by the value 27.5 from Table 1 for line 202 because 48−27.5=20.5, etc. Graphically, a value in a column's row ‘Combo’ is bold if there is a bold value in the column's row ‘m.sub.n,’ and/or row ‘48−m.sub.n,’. The values 16.5, 21.5 and 26.5 in normal typeface represent gaps called ‘remaining gaps’ in the following. In the CMP-gather, remaining gaps correspond to rows of empty bins parallel to the shot lines.

[0102] Shifting cells, here by 4 columns, will always leave a remaining gap in the first column, here at 16.5. Further, 21.5+26.5=48, so these remaining gaps appear in both rows ‘m.sub.n,’ and ‘48−m.sub.n’.

[0103] Table 2 assumes the overlap region 203 on the port side of vessel 101 and contains port to starboard coordinates. By symmetry, an overlap region 203 on the starboard side of vessel 101 and starboard to port coordinates would yield a similar table.

Example 2: A Different Configuration of Source and Streamer Arrays

[0104] In this example, we change N.sub.1 from 6 to 7 and n.sub.1 from 8 to 6. In order to keep the distance between values in a diagonal (n.sub.2−n.sub.1)/2=1, we set n.sub.2=6+2=8. We keep N.sub.2=8 parallel streamers as in Example 1. With y.sub.0=6.25 m, we get y.sub.1=6.Math.6.25=37.5 m between sources and y.sub.2=8.Math.6.25=50 m between streamers. The distance N.sub.1n.sub.1y.sub.0 becomes 7.Math.6.Math.6.25=262.5 m. A reduced CMP-bin size y.sub.0=5.0 m would yield y.sub.1=30 m between sources and y.sub.2=40 m between streamers. Equidistant shot lines 119 would yield 7.Math.6y.sub.0=42.Math.5.0=210 m between adjacent sail lines.

[0105] Next, we define starboard to port coordinates by changing sign on equation (2):

[00004]$\begin{array}{cc}{m}_{ij}=\left[M_0-i{n}_1\text{/}2-j{n}_2\text{/}2\right]y_0& \left(5\right)\end{array}$

where M.sub.0=[(N.sub.1−1)n.sub.1+(N.sub.2−1)n.sub.2]/4, i=0 to (N.sub.1−1) and j=0 to (N.sub.2−1) as before.

[0106] With values in Example 2, m.sub.ij=(6.Math.6/4+7˜8/4−3i−4j)y.sub.0=(23−3i−4j)y.sub.0. Table 3 contains values of (23−3i−4j) for i=0 to 6 and j=0 to 7.

TABLE-US-00003 TABLE 3 Values of (23 − 3i − 4j) j i 0 1 2 3 4 5 6 7 0 23 19 15 11 7 3 −1 −5 1 20 16 12 8 4 0 −4 −8 2 17 13 9 5 1 −3 −7 −11 3 14 10 6 2 −2 −6 −10 −14 4 11 7 3 −1 −5 −9 −13 −17 5 8 4 0 −4 −8 −12 −16 −20 6 5 1 −3 −7 −11 −15 −19 −23

[0107] In Table 3, the first diagonal with n.sub.1/2=3 consecutive elements contains the values 17, 16 and 15 when listed upwards to the right. In port to starboard coordinates, the values would be −17, −16 and −15, i.e. in ascending order simply due to the change of sign. Following diagonals, it is easy to verify that Table 3 contains all integers from −17 to 17.

[0108] On the left of Table 3, there are (n.sub.1/2−1)=2 incomplete diagonals. When listed upwards to the right:

[0109] d2 from i=0 contains the value 23 and lacks the values 22 and 21, and

[0110] d1 from i=1 contains the values 20 and 19 and lacks the value 18.

[0111] Consistent with the naming in Example 1, d1 lacks 1 value and d2 lacks 2 values.

[0112] Table 4 is constructed in the same manner as Table 2, however with (18 10+23)=41 in the second row and N.sub.1n.sub.1=42 in the third row.

TABLE-US-00004 TABLE 4 Alternative midpoints in the overlap region 203 m.sub.n 18 19 20 21 22 23 41 − m.sub.n 23 22 21 20 19 18 42 − m.sub.n 23 22 21 20 19 Combo 18 19 20 21 22 23

[0113] In this example, the remaining gaps in row ‘Combo’ become 18 and 21. Similar to Example 1, the first remaining gap, here at 18, is due to the shift of columns, here by (42−41)=1. In this example, the only other remaining gap is at 21 because (42−21)=21. This concludes Example 2.

[0114] The first lacking value L.sub.1 in a table such as Table 1 or 3, that is 16.5 in Example 1 and 18 in Example 2, is found by extending the column which is (n.sub.1/2−1) from the edge of the table with n.sub.1/2 from the last value in the column. After algebraic simplification:

[00005]$\begin{array}{cc}{L}_1=\left[\left(N_1+1\right)n_1+\left(N_2+1\right)n_2-n_1{n}_2\right]\text{/}4& \left(5\right)\end{array}$

[0115] For an optimal distance between adjacent sail lines, we add equations (5) and (3):

[00006]$\begin{array}{cc}{L}_1+M_0=\left[2N_1{n}_1+2N_2{n}_2-n_1{n}_2\right]\text{/}4=N_1{h}_1+N_2{h}_2-h_1{h}_2& \left(6\right)\end{array}$

where h.sub.1=n.sub.1/2 and h.sub.2=n.sub.2/2.

[0116] With numbers from Example 1, equation (6) yields L.sub.1+M.sub.0=(6.Math.4+8.Math.5−4.Math.5)=44. With numbers from Example 2, we obtain L.sub.1+M.sub.0=(7.Math.3+8.Math.4−3.Math.4)=41.

Example 3: Yet Another Configuration of Source and Streamer Arrays

[0117] In this example, we reduce N.sub.1 to 5 and increase n.sub.1 to 10. We keep N.sub.2=8 as in Examples 1 and 2, and set n.sub.2=12 for the desired distance 1 between values is in diagonals. From (3), M.sub.0=(4.Math.10+7.Math.12)/4=31. Rather than creating a table similar to Tables 1 and 3 from ±(31−5i−6j), we use (5) to obtain L.sub.1=12. L.sub.1+M.sub.0=12+31=43 may be obtained directly from (6). Since the number of incomplete diagonals is n.sub.1/2−1 and the number of values in each incomplete diagonal is n.sub.1/2=h.sub.1 in all Examples 1-3, we may arrange the incomplete diagonals in blocks as illustrated in Table 5.

TABLE-US-00005 TABLE 5 Incomplete diagonals from Examples 1 to 3 Example 2 Example 1 Example 3 h.sub.1 = 3, N.sub.1 = 7 h.sub.1 = 4, N.sub.1 = 6 h.sub.1 = 5, N.sub.1 = 5 d1 18 19 20 16.5 17.5 18.5 19.5 12 13 14 15 16 d2 21 22 23 20.5 21.5 22.5 23.5 17 18 19 20 21 d3 24.5 25.5 26.5 27.5 22 23 24 25 26 d4 27 28 29 30 31

[0118] In each Example 1 to 3, n.sub.2=n.sub.1+2 and N.sub.2=8. In each non-zero block in Table 5, the upper left and lower right values are L.sub.1 from equation (5) and M.sub.0 from equation (3). As before, values in bold typeface appear in a table similar to Table 1 or 3, whereas values in normal typeface belong to incomplete diagonals outside the table. The remaining gaps between two adjacent passes are underlined.

[0119] In Example 3, the distance N.sub.1n.sub.1y.sub.0 between sail lines becomes 50y.sub.0, and L.sub.1+M.sub.0=12+31=43. In a table similar to Tables 2 and 4, the remaining gaps may be found by shifting a row ‘43−M.sub.n’ (50−43)=7 columns to obtain a row ‘50−m.sub.n’. As noted in Example 1, such a shift always leave a gap. These are the remaining gaps at L.sub.1 in all three blocks in Table 5.

[0120] Further, in the block for Example 3, we observe that (22+28)=(23+27)=50. Thus, in a table similar to Tables 2 and 4, the remaining gaps in parentheses is would appear in the same column in rows ‘m.sub.n’ and ‘50−m.sub.n’.

[0121] Lastly in Example 3, we note that, in addition to the remaining gaps at L.sub.1,

[0122] h.sub.1=3 and N.sub.1=7 leads to a single remaining gap at 21,

[0123] h.sub.1=4 and N.sub.1=6 leads to one pair of remaining gaps 21.5 and 26.5, and

[0124] h.sub.1=5 and N.sub.1=5 leads to two pairs of remaining gaps (22, 28) and (23, 27) where

23−22=28−27=1.

Example 4: Crossline Configuration of Sources and Seafloor Receivers

[0125] In this example, we assume a sail line 201 directly over a row of seafloor receivers as in FIG. 1. Further, we assume an S-bin size y.sub.S=25 m, distance between sources 50 m=2y.sub.S and vessel bound coordinates. Analogous to previous results, we set n.sub.3=n.sub.1+2=4 such that y.sub.3=4y.sub.S=100 m. In Table 6, the first column contains source positions at 50 m intervals from −125 m and the first row contains seafloor receiver positions at 100 m intervals from −300 m.

TABLE-US-00006 TABLE 6 Values of (s + r)/2/25 r s −300 −200 −100 0 100 200 300 −125 −8.5 −6.5 −4.5 −2.5 −0.5 1.5 3.5 −75 −7.5 −5.5 −3.5 −1.5 0.5 2.5 4.5 −25 −6.5 −4.5 −2.5 −0.5 1.5 3.5 5.5 25 −5.5 −3.5 −1.5 0.5 2.5 4.5 6.5 75 −4.5 −2.5 −0.5 1.5 3.5 5.5 7.5 125 −3.5 −1.5 0.5 2.5 4.5 6.5 8.5

[0126] The table values are computed as (s+r)/2/y.sub.S where y.sub.S=25 m. Similar to previous results, the distance between values in adjacent rows is h.sub.1=n.sub.1/2=1 and the distance between values in adjacent columns is h.sub.3=n.sub.3/2=2. We selected n.sub.3=n.sub.1+2 to obtain 1 between adjacent diagonal values. Consistent with previous results, there are n.sub.1/2−1=0 ‘lacking’ midpoint values in Table 6. Following diagonals, it is easy to verify that Table 6 indeed contains all values from −8.5 to +8.5 in integer steps. Values ±8.5 and ±7.5 appear once, ±6.5 and ±5.5 appear twice, and all values from −4.5 to +4.5 appear three times.

[0127] Similar to equation (2) and Tables 1 and 3, the values in Table 6 depend on N.sub.1, N.sub.2, n.sub.1 and n.sub.2. The values after the first row and column do not depend on the bin size y.sub.S.

Example 5: Crossline Configuration of Sources and Seafloor Receivers—II

[0128] Equation (6) describes a distance between sail lines that leaves no remaining gaps in the coverage parallel to the source lines 119. Replacing N.sub.2 and h.sub.2, with N.sub.3 and h.sub.3 yields:

[00007]$\begin{array}{cc}{N}_3=\left(N_S-N_1{h}_1+h_1{h}_3\right)\text{/}{h}_3& \left(7\right)\end{array}$

where N.sub.Sy.sub.S is the distance between adjacent sail lines. Other parameters are explained above.

[0129] Inserting N.sub.S=300 m/25 m=12, N.sub.1=6 sources, h.sub.1=1 and h.sub.3=2 from Examples 1 and 4 in equation (7) gives N.sub.3=4. This means that sail lines 201, 202 halfway between seafloor receiver lines minimise the number of systematic remaining gaps in the crossline coverage, and corresponds to ΔC.sub.Y=y.sub.3/2 in FIG. 3. Note that the values at ±8.5 and ±7.5 in example 4 are covered at both adjacent passes providing a ‘crossline fold’ of at least 2. This concludes Example 5.

[0130] Of course, different values for N.sub.S, N.sub.1, h.sub.1 and h.sub.3 in equation (7) yield different values for N.sub.3. In particular, we finds that N.sub.1=6 sources provides a reasonable balance between few remaining gaps and wide coverage per pass with adjacent sail lines 300 m apart. Recall that in Example 1, Y.sub.1=300 m=48.Math.6.25 m is as opposed to 44.Math.6.25=275 m between sail lines required to avoid remaining gaps parallel to the source lines 119.

[0131] So far, we have considered midpoints between sources and receivers, i.e. consequences of equation (2). Next, we increase the distance between seafloor receiver lines to 150 m.

Inline Configuration of Sources and Suspended Receivers

[0132] FIGS. 5-8 illustrate shot patterns where circles illustrate sources and filled circles illustrate fired sources. A Y-axis represents the crossline distance between acoustic sources in terms of the fixed distance y.sub.1 between sources. An x-axis represents the inline distance between shots. We assume a constant vessel speed v, so equal distances x.sub.0 correspond to equal time intervals.

[0133] We assume a setup as in Example 1 and a desired inline bin size x.sub.0=6.25 m for P-waves. Since S-waves do not travel through fluids, the x.sub.0×y.sub.0=6.25×6.25 m.sup.2 cells pertain to P-waves. Similar to Example 1, x.sub.1=m.sub.1x.sub.0 where m.sub.1 is an integer. In general, m.sub.1 is sufficiently large to permit recharging between shots. In FIG. 5, m.sub.1=N.sub.1=6. This yields an inline distance x.sub.1=6.Math.6.25=37.5 m between adjacent shot points along a source line 119. At vessel speed v=2.5 m/s, about 4.9 knots, x.sub.1=37.5 m corresponds to a shot interval T.sub.S=15 s.

[0134] For P-waves, the streamers 121-128 determine the inline bin size. In this example, each streamer is 6 000 m long and has suspended receivers every 12.5 m. The streamers are parallel to the y-axis, so cos θ=1, and x.sub.2=12.5 m. Further, cells with sides equal to the distance between midpoints, here x.sub.2/2=6.25 m, form a natural bin grid.

[0135] FIG. 5 is a 6×6 diagram illustrating a shot pattern with six sources along the y-axis, and one shot per time interval or inline distance x.sub.0 along the x-axis. The pattern is repeatable from x=6x.sub.0. When v=2.5 m/s and 6x.sub.0=37.5 m, T.sub.S=s is available for recharging each acoustic source.

[0136] FIG. 6 illustrates a shot pattern in which two sources are fired at each interval ix.sub.0. With all other parameters equal to those in Example 1, each source is now fired at intervals of length 3x.sub.0. With x.sub.0=6.25 m and v=2.5 m/s, 3x.sub.0=18,75 m and T.sub.S=7.5 s. While the denser shot pattern in FIG. 6 provides a denser bin grid on the projection planes 204-206, T.sub.S=7.5 s may be too short to recharge a source 111-116. This illustrates one design parameter that must be left to the actual designer.

[0137] FIG. 7 is a 5×5 diagram corresponding to 5 source lines 119 spaced y.sub.1 apart. In general, the number of sources N.sub.1, streamers N.sub.2 and seafloor lines N.sub.3 can be different from 6, 8 and 3 as in previous examples. Further, x.sub.0=50 m as in previous examples would yield 250 m between the sail lines 201 and 202 and correspondingly larger fuel expenses for the towing vessel 101. Alternatively, the distance between sail lines might be retained. This would lead to a larger x.sub.0 and larger bin sizes in the crossline direction.

[0138] Specifically, FIG. 7 shows a pattern in which three sources are fired at each inline interval y.sub.0. With parameters from Example 1, each source is now fired every 12.5 m or every 5.0 s. As in the pattern in FIG. 5, the time T.sub.S=5.0 s between shots may be too short for practical applications.

[0139] FIG. 8 illustrate a pattern with 5 source lines in which two sources are fired at each y.sub.0. This may lead to inline shot intervals similar to those in FIG. 6.

Optimum Bin Size for Converted-Wave 3-D Asymptotic Mapping

[0140] A program has been developed to generate fold maps for converted waves recorded in multicomponent 3-D seismic surveys. The asymptotic conversion point is assumed for computing subsurface multiplicity. When a conventional common-midpoint bin size of half the receiver interval (Ar/2) is used, the fold distribution is highly variable and empty rows of bins parallel to the shot lines may result for the case when Vp/Vs=2 and the shot line spacing is an even integer multiple of Δr. Overlapping adjacent bins removes the empty bin problem but does not necessarily result in a smooth fold distribution. The optimum bin size for 3-D converted wave data is Δr/(1+Vs/Vp). Asymptotic binning using this bin dimension was found to produce a smooth fold distribution which is relatively insensitive to Vp/Vs.

[0141] In general, numerous combinations are possible. Further, increasing the amount of equipment associated with n, N and N.sub.2 and/or improving parameters x.sub.0 to x.sub.2, y.sub.0 to y.sub.2 obviously increase investment and operational costs. A cost-benefit analysis generally balances the increased costs against benefits such as reduced bin sizes and better resolution. These are design decisions that must be left to the skilled person designing the survey.

[0142] While the invention has been explained by means of examples, the scope of the invention is defined by the following claims.

TABLE-US-00007 APPENDIX Notation x, X Vessel bound and global inline directions y, Y Vessel bound and global crossline directions x.sub.0, y.sub.0 Bin sizes. In examples herein, P-waves have bins x.sub.0 × y.sub.0 = 6.25 × 6.25 m.sup.2 x.sub.1, y.sub.1 Separations of sources 151 x.sub.2, y.sub.2 Separations of suspended receivers 152 x.sub.3, y.sub.3 Separations of seafloor receivers 153 i, j, k Running integers N.sub.1 Number of sources. In examples herein, N.sub.1 = 6 N.sub.2 Number of streamer lines. In examples herein, N.sub.2 = 8 N.sub.3 Number of seafloor receiver lines. In examples herein, N.sub.3 = 3 to 5 m.sub.1, n.sub.1 Integer multipliers for sources: x.sub.1 = m.sub.1x.sub.0 and y.sub.1 = n.sub.1y.sub.0 m.sub.2, n.sub.2 Integer multipliers for suspended receivers: x.sub.2 = m.sub.2x.sub.0 and y.sub.2 = n.sub.2y.sub.0 m.sub.3, n.sub.3 Integer multipliers for seafloor receivers: x.sub.3 = m.sub.3x.sub.0 and y.sub.3 = n.sub.3y.sub.0