Modellering, prediksjon og styring av slepte seismiske kabler · results from the commercial...

KART OG PLAN x–2017 1

Modellering, prediksjon og styring av slepte seismiske kablerJan Vidar Grindheim1,2,3,*, Inge Revhaug2, Egil Pedersen4 og Peder Solheim1

Vitenskapelig bedømt (refereed) artikkel

Jan Vidar Grindheim et al.: Modeling, prediction and control of towed marine seismic streamers

KART OG PLAN, Vol. 77, pp. 1–16, POB 5003, NO-1432 Ås, ISSN 0047-3278

A 3D numerical model for towed marine seismic streamers has been implemented. The solution isbased on the FDM box method, which is a proven method for cable dynamics simulation problems,and tolerates large cable movements. The model has presently been extended to include lifting de-vices (control birds) for lateral and depth steering, a tailbuoy, tail stretch section as well as instru-ments and weights externally mounted on the streamer. The solution is validated by comparing withresults from the commercial software Orcaflex, showing generally good agreement. Secondly, a sim-ulation has been conducted investigating the maximum streamer deflection range in vertical and lat-eral dimensions for a range of bird wing angles, and additionally comparing these results when usingbird force inputs instead of wing angles. The prime motivation is to develop a seismic streamer sim-ulator including control birds, with low computational cost yet high accuracy, for the development ofimproved streamer steering algorithms.

Key words: towed marine seismic streamers, control birds, prediction, steering algorithms

Jan Vidar Grindheim, PhD student, Faculty of Science and Technology, Norwegian University of LifeSciences, P.O.B. 5003, NO-1432 Ås. E-mail: [email protected]

IntroductionImproved operational efficiency has enhan-ced margins for marine seismic survey provi-ders and increased seismic data acquisitionaffordable to oil companies. This study in-tends to improve prediction and controlcapability of towed seismic sensor cables(streamers). Improved prediction of stream-er behavior is one aspect of improving thecontrol capability.

Increasing numbers and lengths ofstreamers deployed, combined with 4D seis-mic requiring the replication of historicstreamer positions, as well as non-traditio-nal streamer deployment configurationssuch as slanted and fanned streamers, haveincreased the control precision and capabi-

lity requirements significantly. The recentdecline in oil prices has increased the effici-ency requirements for offshore E&P evenfurther in order to compete with shale oilE&P. The seismic survey line-change is anexpensive operational maneuver moving thestreamer spread 180° to the next acquisitionline. This turn typically takes a few hours,accounting for a significant portion of thesurvey and accompanying costs, dependingon the length of survey lines. Improvedstreamer control has the potential of decrea-sing this time consumption (Ersdal, 2004).

Streamer entanglement can occur bothduring a survey line and in turn, especiallyin unfavorable current conditions, and canresult in damaged or destroyed streamers.

1. GEOGRAF AS, Strandgata 5, NO-4307 Sandnes, Norway.* Corresponding author. E-mail: [email protected] 2. Faculty of Science and Technology, Norwegian University of Life Sciences (NMBU), P.O.B. 5003, NO-1432 Ås,

Norway.3. Laboratório de Ondas e Correntes (LOC) at UFRJ/COPPE, Federal University of Rio de Janeiro, Rio de Janeiro

22241-160, Brazil.4. Department of Engineering Science and Safety, UiT - The Arctic University of Norway, Hansine Hansens veg 18,

NO-9037 Tromsø, Norway.

Bedømt (refereed) artikkel Grindheim, Revhaug, Pedersen og Solheim

2 KART OG PLAN x–2017

Optimal streamer steering is an importanttool for avoiding streamer tangles. Given thehigh cost of seismic streamers and surveydown-time, the relatively low cost of impro-vements to streamer steering algorithms area sensible investment.

Until approximately 2000, depth controlwas achieved with externally mountedstreamer devices where horizontal orientedwings (hydrofoils) provided the control forces(Fig. 1). By 2010, lateral steering was embra-ced industry wide with the development anddeployment of various types of lateral stee-ring devices. These devices, containing bet-ween two and four wings, give force in bothvertical and lateral directions, and are gene-rally referred to as “control birds” (Fig. 3).

Lateral steering enables narrow intra-streamer separations by reducing the likeli-hood of streamer entanglement. Less lateralstreamer separation increases crosslinesampling resolution. Additionally, monitor-ing of existing reservoirs using 4D-seismichas become increasingly important (Polyd-orides et al., 2008). The intention is to incre-ase the oil reservoir recovery rates. In 4Dseismic, the aim is to replicate streamer po-sitions from historic surveys to detect chan-ges in the reservoir caused by production.Therefore, accurate lateral control is increa-singly important. Thirdly, as more complica-ted streamer configurations are employed,efficient real time 3D streamer control is im-perative (Polydorides et al., 2008). One

example of newly employed survey strategi-es is coil shooting, where covering of the sur-vey area is achieved by steering the vessel inlarge circular paths (Buia et al., 2008). Pre-diction of future streamer state is one impor-tant aspect of improved streamer steering al-gorithms (Solheim, 2013).

As prescribed by International seagoing la-ws, the tail end of each streamer is identifiedto non-survey vessel traffic by a tailbuoy to-wed from each streamer. This tailbuoy ensu-res tail-end tension and provides a platformfor navigation instruments such as acousticpingers, compasses and satellite navigationsystems. A stretch section is installed betwe-en the last streamer section and the tailbuoy,to dampen tugging noise on the streamer.Streamer positions are determined with theuse of streamer mounted instruments thatdetermine distances (acoustically), magneticdirections (compasses) and Global Navigati-on Satellite Systems (GNSS) navigation con-trol points installed at the tailbuoys, stream-er front buoys and at the vessel.

Ballasting to bring the streamer to thedesired depth is achieved by attachingweights along the streamer. Lead weightsare installed to balance the streamer secti-ons as salinity may vary at the survey pro-spect. Hence, ballasting reduces the worklo-ad on depth keeping birds and gives consis-tent cable depth between depth control birdlocations. All streamer add-ons, whether in-struments inserted between streamer secti-

Fig. 1: Illustration of seismicspread with installed devicesfrom Pedersen (2001).

Modellering, prediksjon og styring av slepte seismiske kabler


ons or attached to streamer coils, or weightsclamped onto the streamer body, typicallyhave densities much larger than the stream-er, thus affecting the vertical shape of thestreamer significantly (Grant, 2015). Theirdrag properties also differ from the streamer,affecting the lateral streamer shape.

Within the seismic industry, various stream-er control devices have been developed.Kongsberg Seatex has developed the eBird®streamer steering device for combined roll,depth and lateral control, which is an in-linecontrol unit with 3 wings (Seatex, 2013a)(Fig. 3).

In the present article, a novel seismic si-mulator is described. The model is in threedimensions and includes cable stretch andtension. It is solved using a Finite DifferenceMethod (FDM). Control birds are included inthe simulator, as well as a tailbuoy which isconstrained to the surface using a PID con-troller. It is custom-tailored to simulate seis-mic streamers, hence implementation of aspecific seismic design is straight-forwardfor the user. As the code is implemented inMatlab® (Matlab), it can easily be combinedwith other codes or technologies, for instancethe Ensemble Kalman Filter (Grindheim etal., 2017). It can also be customized furtheraccording to user specifications.

Towed underwater 3D cable modelFor studying the behavior of a buoyantstreamer, a three-dimensional cable dyna-mics model is required (Grant, 2015). Ersdal(2004) concluded that for simulation of ”ma-neuvering and special operation” of thecomplete seismic spread, “an effective threedimensional model of a cable that allowshigh deformation” would be necessary. Sucha model has been implemented.

The streamer’s dynamics can be adequate-ly described by six coupled nonlinear partialdifferential equations (Burgess, 1991, Grind-heim et al., 2017):

(1)

where

(2)

and

(3)

Fig. 2: Example of seismic streamer towingconfiguration (courtesy of Petroleum Geo-Services).

Fig. 3: Kongsberg Seatex eBird® for lateralsteering and depth control of seismic stream-ers (Seatex, 2013b).

s ty y

M N q

t n bT v v vy

1 0 0 0 0 00 1 0 0 cos0 0 1 0 sin0 0 0 1 sin cos 00 0 0 0 cos 00 0 0 0 0

b n

b t

n t

v vv v

v vT

T

M



(4)

and q is a 6x1 vector accounting for hydrodynamic and buoyancy forces:

(5)

T is tension, v is velocity, and t, n and b aretangential, normal (nadir) and bi-normalvectors, respectively (Fig. 4). θ and φ are hor-izontal and vertical angles, respectively, be-tween tangent t and the x-vector (Fig. 4). E iscable elasticity, A is cable cross-sectional ar-ea, EA = EA , V is velocity relative to sur-rounding fluid, i.e. Vt = vt – Ut, Vn = vn – Unand Vb = vb – Ub. m is cable mass per unitlength, m1 is cable mass including addedmass, per unit length, ρ is fluid density, g isgravity constant, Ct is tangential drag coeffi-cient, Cn is drag coefficient for both n- and b-directions, and d is cable diameter.

The model uses a local coordinate systemfollowing the cable tangent t (Fig. 4), as thissimplifies the equations. v (ms–1) is velocity,T is cable tension (N), and θ and φ are anglesas given in Fig. 4.

There are three equations resulting fromthe cable kinematics, essentially starting

from the equation for cable strain (Eqn. (6))and the rotation matrix from absolute to lo-cal (t,n,b) coordinate system.

(6)

where p and s are stretched and unstretchedcable lengths, respectively. (T / EA) equals ca-ble strain, with EA = E · A, where E is elas-ticity, and A is the cross sectional cable area(m2): A = π (d / 2)2. d is cable diameter (m).

Secondly, there are three equations resul-ting from the equilibrium of forces, where ca-ble tension distance derivative equ-als the sum of inertial ( ), hydrodynamic( ) and buoyancy ( ) forces:

(7)

1 1

11 1

11 1

0 0 cos

10 0 0 0 0

0 0 0 0 0 1

0 0 0 0 1 cos 0

0 0 sin cos 0

0 0 sin

tb n

A

A

A

A

bn t

A

nb t

A

mvm m v m v

E T

E

TE

TE

m vm m v mv

E T

m vm m v mv

E T

N

12

12 1

2

12 1

2

12

2 212

2 212

1 sin

000

1

1 cos

t t tA

n b n bA

n n n bA

Td C V V m A g

E

TdC V V V

E

TdC V V V m A g

E

q

1A

p Ts E

/T siF

hF

wF

i h w

TF F F

s



Variations of the model have been utilized bynumerous authors (Gobat and Grosenbaugh,2006). The model includes cable tension, ca-ble stretch and ocean current which can varyalong the cable, and it tolerates large cabledeflections.

The boundary conditions are:

– Known velocity at front– Known tension at tail and assuming

straight cable at tail point.

Solving the equationsThe equations (1) are solved using the boxmethod, which is a Finite Difference Method(FDM). The solution was introduced byAblow and Schechter (1983) and improved byMilinazzo et al. (1987) and Burgess (1991).Newton-Raphson iteration is used for solv-ing the next timestep. The box method givessecond order accuracy and allows for arbi-trary, i.e. non-uniform, spacing in time andspace, and allows for rapid variations in timestep size (Cebeci et al., 2005). The discretiza-tion is centered in time and space. The meth-od has proven close match with full-scaledata and low computational cost (Burgess,1991). Further details of the method are pre-sented in Grindheim et al. (2017).

The solution is stable for long time steps,typically in the order of 20 seconds, resulting infast integration time. For seismic surveys, typ-ically update timesteps is in the order of 10 sec-onds, which is well within the stability time-step size. Nodes or control birds could be placed

at any point along the cable. Implementationhas been performed in Matlab® (Matlab).

For realistic simulations of seismic stream-ers, several additional features have beenadded to the model:

– Control birds have been added. The hydro-dynamic bird forces are added as an extracurrent vector [Ut_bird Un_bird Ub_bird] at thetwo cable elements adjacent to each bird.This extra current is calculated to give theforce corresponding to the bird force giventhe state, including velocity and currentvectors, at present time. The reason forthis choice and the details of the procedurewill be explained.

– A tailbuoy has been added. Using bounda-ry condition at tail vz = 0 was attempted,but instability issues occurred. Instead, atailbuoy vertical buoyancy force is addedat the tail, with a PID-controller con-trolling this vertical force for keepingdepth = 0. In addition, a short cable sec-tion of large diameter following the tail isadded to account for the tailbuoy drag.

– Components with specified weight in wa-ter and diameter can be installed at userdefined locations. Nominal componentlength is 1 meter.

– A stretch section of user defined length isinstalled prior to the tailbuoy, connectingthe tailbuoy and streamer.

Example of a simulation plot is presented inFigs. 5–6. Control birds are marked withgreen dots, and the red dot is the tailbuoy.

Fig. 4: Local coordinate systemfollowing the cable tangent t.



Fig. 5: Example of simulation plot. The red dot is the tailbuoy, the green dots are control birdsand components are marked with magenta dots. Note the large variations in axis scales.

0 5 10 15 20 25 30 35 40 45

10000

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y coordinates (m)

xco

ordi

nate

s (m

)Local x y coord (m) and depth (m). Time: 470 (s). t: 10 (s) Iterations: 4. # of nodes: 1198. T

front|Tailbuoy: 30869 | 619 (N). v

front: 2.315 m/s

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0

2

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8

Cumulative straight distance in horizontal plane from node to node (m)

dept

h (=

z)

rela

tive

to to

wpo

int (

m)

Fig. 6: Close-up of the x-y coordinate plot in Fig. 5, showing three steering birds. Note the largedifference in scale between x- and y-axis.

43.5 44 44.5 45 45.5 46 46.5

10000

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)



Implementing control birdsThe control birds have been added to theoriginal model (Eqn. (1)). For each bird, twocable segments, each of equal unstretchedlength (default value 5 m), are included adja-cent to the bird. The bird inputs could be giv-en as wing deflections (degrees) and wingorientation (degrees), or directly as force (N)in n- and b-direction. For the bird wing de-flection option, the force calculation proce-dure is given in the following.

Hydrofoil force calculationHydrofoil forces are calculated based on theactual wing angle of attack with respect towing deflection, local bird velocity and seacurrent.

Lift- and drag curves are implemented fora basic symmetric wing profile. It is assumeda maximum lift coefficient ∂CL(α)/∂α|α = 15° =0.7, where α is the angle between incomingfluid stream and hydrofoil chord line. The co-efficient is linear with angle of attack untilclose to stall angle, where the lift decreases(Fig. 7). For simplicity, a rate of decrease inCL is assumed after stall that is equal to therate of CL increase before stall (Fig. 7). Thehydrofoil is symmetric, giving equal lift- anddrag coefficients for both positive and nega-tive angles of attack.

The drag coefficient CD is the sum of thefriction coefficient and the pressure drag co-efficient, where the friction coefficient is con-stant, and the pressure drag coefficient is as-sumed to depend on α only (Newman, 1977,p. 23). At α = 0°, CD approximately equals thefriction coefficient, whereas the assumptionis that the remaining drag, i.e. the pressuredrag, depends only on angle of attack (New-man, 1977, p. 23). Friction drag could be ap-proximated by friction drag CF of a flat plateat zero angle of attack (Newman, 1977, p.23). Assuming wing chord length of 0.3 mand towing speed 2.4 ms–1, typical for seis-mic operations, this gives friction coefficientCF = 0.0055 (Newman, 1977, p. 17).

Based on these notions, idealized Fourierseries curves have been developed for both CLand CD as functions of angle of attack α(James et al., 2011, pp. 571-575). The curveswith their derivatives are shown in Fig. 7. Forcalculating CL, NFourier (Fourier series length)

has been set to 20, while for CD, NFourier = 6has been utilized. One advantage of usingFourier series is that its derivative is continu-ous, which would not be the case if a piecewisefunction was utilized. The described Fourierseries lift- and drag coefficient calculationroutines are utilized in the function calculat-ing hydrodynamic force for bird wings.

The code calculates hydrodynamic forcesfor each hydrofoil based on relative fluidvelocity, deflection and orientation of wing,wing area, fluid density and stall angle(Newman, 1977). The results are L (lift) andD (drag).

Subsequently, the force vector is rotatedby angle (β–α) to generate Ft (force in cabletangent direction) and Fbn (force in b–n-plane, i.e. 90° to cable tangent) (Fig. 8). Thisis because by definition, the drag componentis in the direction of the fluid velocity, andthe lift is perpendicular to the drag (New-man, 1977, p. 21).From Fbn, the Fb and Fn components are cal-culated based on orientation angle of thebird. The calculated forces are then imple-mented as additional forces in the q-vector,Eqn. (5), at the two cable elements adjacentto the birds.

The bird forces are represented by addi-tional currents added only at the two cable el-ements adjacent to the bird. The additionalcurrents are calculated to give the correct re-sultant q-vector force at the bird elements, i.e.the resultant force of hydrodynamic, gravita-tional and buoyancy, and bird force. The rea-son for this choice is issues with stability andconvergence experienced when attempting toimplement the bird forces explicitly in the q-vector, Eqn. (5). One reason for stability is-sues may be the high sensitivity of the birdforce with respect to wing angle of attack.

The bird force currents are updated eachshotpoint given the present state. The birdforce calculations are decoupled from theNewton iteration, leading to a time lag. How-ever, the time lag should be reasonable smallas the forces are updated each shotpoint. Ifhigher accuracy is desired, the timestep sizecould be reduced by user. The non-linear in-teraction between the cable velocity, sea cur-rent and control forces will still be accountedfor, but with a time lag and approximation.



The added bird force currents are calculatedbased on the hydrodynamic force equations

given in the q-vector (Eqn. (5), elements 1, 6and 5, respectively).

Fig. 7: Idealized Fourier series curves for both CL and CD (as functions of angle of attack α), aswell as their derivatives.

Fig. 8: Hydrofoil with angles, vectors and explanations.

Angle of attack

Hydrofoil deflection

t (cable tangent)

Hydrofoil chord line

Drag

-( - )

Fluid

velocity

Lift



For calculating the bird force currents, tangen-tial force current Ut_bird is calculated based on:

(8)

Bi-normal and normal force currents Ub_birdand Un_bird are calculated from Eqn. (9) and

Eqn. (10), respectively, using least squaresmethod.

(9)

(10)

The extra current [Ut_bird Un_bird Ub_bird] rep-resenting the bird force is added to the seacurrent at the two short cable elements adja-cent to the bird.

Validation of implementationThe streamer simulation implementation hasbeen verified against a simulation performedwith Orcaflex®, a commercial software for hy-drodynamic simulations (Orcina, 2016).

The development of the present simulatorwas justified by the following requirementsthat are not met by Orcaflex:

1. Generic initialization customized for seis-mic streamer simulation.

2. Optimized cycle time for seismic streamerproblem.

3. In-house control of all aspects of the simu-lator and underlying model, and furtherdevelopment of any desired extensions,modifications or improvements.

In the Orcaflex verification run, the simulat-ed cable is a seismic streamer of unstretchedlength 7800 m, diameter d = 6 cm and neu-tral weight in water, resulting in constantdepth of the cable. The complete cable hasuniform cable properties. Towpoint tension(total drag including cable, wings and tail-

buoy) is 20.9 kN at 4.5 knots (2.315 m/s) withwings not activated. The cable has 25 birdswith 300 m spacing between each. 25 simula-tions are run, where for each simulation,only one of the birds are activated, givingconstant lateral force of 270 N. Timestep sizeis 10 seconds. The resulting cable shape fromone of the simulations (activating bird num-ber 5) is given in Fig. 9.

The accuracy of the FDM method is depen-dent on number of cable nodes; hence there isa tradeoff between accuracy and computatio-nal cost. Computational cost of the algorithmincreases in a linear fashion with number ofnodes. With distance between cable nodes at10 meters, each 200 second simulation takesca. 1.3 seconds on a standard laptop, decrea-sing to ca. 0.5 seconds for 50 meters betweenthe cable nodes. The simulation results fordistance between nodes at 10, 25, 50 and 100meters, as well as the Orcaflex simulation re-sults, are presented in Fig. 10. Generally,good agreement with the Orcaflex result isachieved, but towards the end of the cable,the agreement decreases for the larger dis-tance between cable nodes (Fig. 10). The de-flection trend shows that the closer to thetowpoint, the less the deflection will be (Fig.10). Close to the tailbuoy, the tailbuoy dragwill constrain the cable.

Ft d CtT

EAvt Ut bird vt Ut bird

12

1

12

_ _

Fb dCbT

EAvb Ub bird vn Un bird vb Ub bi

12

1

12 2

_ _ _ rrd

212

Fn dCnT

EAvn Un bird vn Un bird vb Ub bi

12

1

12 2

_ _ _ rrd

212



Fig. 10: Results of the 25 simulations, comparing FDM code results for different number of ca-ble nodes, with the Orcaflex result. For each simulation only one of the control birds is activa-ted, and the cable deflection at the bird after 200 s is given in the figure. Bird number 1 is clo-sest to the front, and bird number 25 is closest to the tail. Upper plot shows absolute results, lo-wer plot shows relative results in relation to the Orcaflex results.

0 5 10 15 20 250

5

10

15

20

Simulation number = activated bird (1~25)

Max

imum

late

ral c

able

def

lect

ion

(m) Maximum lateral cable deflection (m) after 200 s for activated bird.

FDM, distance between nodes = 10 mFDM, distance between nodes = 30 mFDM, distance between nodes = 40 mFDM, distance between nodes = 50 mOrcaflex

0 5 10 15 20 250.6

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eren

ce to

Orc

afle

x re

sults

(m

)

Simulation number = activated bird (1~25)

Fig. 9: Sample plot – bird number 5 is activated; cable deflection after 200 seconds is shown.Distance between nodes is 10 m. Note the difference in scale between x- and y-axis for the late-ral (upper) plot. Note the differences in axis scales.

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front: 2.315 m/s

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dept

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Exploring control ranges and correlation between lateral and vertical steeringA simulation study has been developed to de-termine the possible ranges of lateral anddepth control, as well as their correlations,when controlling both simultaneously. Esti-mating this is not straight-forward, as manyfactors contribute to the results. For in-stance, as the cable is moved out in the later-al, the wing angles of attack will change, andas the wings’ angle of attack approaches thestall angle, the stall effects will influence theresults. Secondly, steering in the verticalcould influence the steering in the horizon-tal, and vice versa.

The streamer has length 7800 m, diameter6 cm, weight in water of 0 N/m, and each birdhas a weight in water of 2.5 N. 24 birds areinstalled with spacing 300 m. Each bird hastwo wings of surface 0.208 m2, one orientedhorizontally (giving force in the verticalwhen activated) and one oriented vertically(giving horizontal force when activated).Wing area is set to give a lift force at stall an-gle of 400 N at nominal speed 2.315 ms–1. Astretch section with length 100 m is installed

500 m after the last bird. The stretch sectionconnects the streamer to the tailbuoy.

Prior to the front bird, 11 weights of 100 Neach are installed with equal spacing. This isa standard operational practice to make thefront section of the streamer stay closer tothe target depth. Nominal towpoint tensionwith birds not activated is 21.47 kN. Stream-er shape at simulation time zero is a steadystate solution with zero bird forces, as pre-sented in Fig. 11.

A number of 20 minute simulations havebeen run. The towpoint is running straightahead at 2.315 m/s. For each simulation run,wing deflections are constant for all 24 birds.The extreme cable deflection (i.e. the largestdeflection, positive or negative, at any node)after 20 minutes is recorded for both verticaland lateral dimensions.

One simulation example is given in Fig.12, where vertical force wing has deflection 4degrees, and horizontal force wing has de-flection –12 degrees.

All simulation results are presented inFigs. 13–14. Lateral force wing deflection isvaried between –20 and 20 degrees, and ver-tical force wing between 0 and 20 degrees,

Fig. 11: Simulation streamer shape at simulation time = 0. This is the steady-state solutionwith no bird forces. Green dots are birds and magenta dots the installed weights. The red dotis the tailbuoy.



with 1 degree resolution. Fig. 13 gives the re-sulting maximum vertical cable deflection,and Fig. 14 the resulting maximum lateralcable deflection, for all simulations run wit-hin the wing angles span.

Secondly, the results indicate that lateraland vertical steering are only slightly de-pendent on each other (Figs. 13–14). Thismay indicate that vertical and lateral controlcould be considered separately for simplicity.

Independent of the correlation betweenvertical and horizontal steering, since thesame birds are typically utilized for bothdepth and lateral steering, it could be benefi-

cial to develop a single control algorithm con-sidering both the vertical and the lateral di-mensions at the same time. 3D simulationswill certainly be beneficial in the control al-gorithm development for buoyant streamers(Ersdal, 2004). There is a limited amount oftotal control force available, and the algo-rithm needs to determine optimal distribu-tion of force in vertical and lateral dimen-sions. Further, in the field the streamershave varying buoyancy, thus requiring 3Dsimulations for accurate modeling (Grant,2015).

Fig. 12: Result plot for one of the 20 minute simulations. The green dots are the control birds.Magenta dots are installed weights. Note the differences in scale between x- and y-axis for bothof the two plots. In this simulation, vertical force wing has deflection 4 degrees, and horizontalforce wing has deflection –12 degrees.

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front: 2.315 m/

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Fig. 13: Extreme vertical cable deflection after 20 minutes. For each simulation, all 25 birds aregiven the same wing deflections for the lateral and the vertical force wing, respectively, and theextreme (i.e the largest, positive or negative) lateral cable deflection after 20 minutes is recorded.

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Fig. 14: Extreme lateral cable deflection after 20 minutes. For each simulation, all 25 birds aregiven the same wing deflections for the lateral and the vertical force wing, respectively, and theextreme (i.e the largest, positive or negative) lateral cable deflection after 20 minutes is recorded.



The same simulation has been run usingknown bird force input instead of control an-gles. In this case, maximum control force iscalculated by assuming maximum availableforce at Vt = 2.315 ms–1 (4.5 knots) is equal to400 N, which is equal to nominal force for thecontrol wings at stall angle at nominal speed(15 deg). This gives maximum force (100 %):

(11)

where Vt is tangential bird velocity relative tofluid. Note that this is a simplification as forceis also dependent on Vn and Vb, and since max-imum force in one direction is dependent onthe force in the other as there is a total maxi-mum force available for the bird. Secondly, in-creased streamer deflections will affect thewing angles, thus affecting available steeringforce. The results for the set bird force inputare presented in Fig. 15–16. The results showclose similarity to the results when using wingangles (Figs. 13–14), thus giving credit to thebird wing angle implementation.

ConclusionPresent motivations for modeling and pre-diction of seismic streamers are related tothe problem of improved streamer steering.

A 3D Partial Differential Equations (PDE)cable model for simulating towed underwa-ter cable dynamics has been extended to in-

clude typical seismic streamer devices suchas control birds, tailbuoy, tail stretch section,and weights and instruments externallymounted on the streamer. The implementa-tions are presented. The equations aresolved using the box method, a Finite Differ-ence Method (FDM). Validation shows good

22

4002.315 tMaxforce V

Fig. 15: Same simulation as in Fig. 13, but using known bird force input instead of wing an-gles. Extreme vertical cable deflection after 20 minutes. For each simulation, all 25 birds aregiven the same force in Fb and Fn, respectively, and extreme cable deflection after 20 minutesis recorded. (Fb is in the horizontal plane perpendicular to the cable tangent, while Fn is nadirvector perpendicular to cable tangent (Fig. 4)).



correspondence with simulation results fromthe commercial software Orcaflex. The im-plementation has low computational cost.

Secondly, the possible amounts of lateraland vertical steering for both a range of birdwing angles and a range of bird forces, aswell as their correlations, have been exploredthrough simulations. The results for wingangle variations generally compare well tothe result for known bird force, giving a vali-dation of the wing angle force implementa-tion. The simulations indicate that lateraland vertical steering are only slightly affect-ed by each other. However, typically thesame birds are utilized for both depth andlateral control, and the total control forceavailable is limited. Thus a single control al-gorithm considering both lateral and verticaldimensions simultaneously may be neces-sary for determining optimal force distribu-tion. Utilizing 3D simulations in the develop-ment should be beneficial, especially whenconsidering streamers that are not complete-ly neutrally buoyant, as is normally the case.

Recommendations for further workA simulation study comparing the control ef-ficiency of a 2-wing and a 3-wing bird designcould be of interest for the seismic industry,where both of these designs are widely uti-lized. However, when giving forces simulta-neously in vertical and horizontal directions,a choice must be regarding bird orientation.Algorithms must be developed to calculateoptimal bird orientations for combinations ofhorizontal and vertical bird force require-ments. Industry bird designs could be imple-mented in the simulation; however, thisshould ideally include the actual algorithmsfor bird orientation decision.

AcknowledgmentsThis work is part of an ongoing Industrial PhDat NMBU (Ås, Norway) for Geograf AS(Sandnes, Norway), by the corresponding au-thor. It is funded by Geograf AS and the Re-search Council of Norway through their Indus-trial PhD program, project number 234875.

Fig. 16: Same simulation as in Fig. 14, but using known bird force input instead of wing an-gles. Extreme lateral cable deflection after 20 minutes. For each simulation, all 25 birds aregiven the same force in Fb and Fn, respectively, and the extreme (i.e the largest, positive or neg-ative) lateral cable deflection after 20 minutes is recorded.



Corresponding author is presently on leave toLaboratório de Ondas e Correntes (LOC) atUFRJ/COPPE (Rio de Janeiro, Brazil).

Mr. Ken Welker of Geograf AS has contrib-uted with helpful discussions and manu-script improvements.

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