The shape of a marine streamer in a cross current

Abstract

A serious problem in marine data collection (particularly 3‐D) is the necessity to assign to each hydrophone a precise location on the surface of the earth. The data available for this purpose can come from the vessel’s navigation system, a radio beacon (at the tail buoy), an acoustic transponder (at the head of the streamer and occasionally elsewhere), and magnetic compasses distributed over the length of the cable. The shape of the streamer is commonly reconstructed by fitting a curve’s tangents to the compass readings. The shape deduced in this fashion is highly sensitive to compass errors. As an alternative to the ad hoc numerical fit, we have derived the shape of the streamer in a cross current from physical principles. The mechanical equilibrium of tension and drag forces leads to differential equations which we integrate analytically to obtain a formal solution for the tension. A further analytic integration yields an equation (containing two integration constants) that relates arc length along the cable to the tangent angle. This equation can be matched to compass readings (for stability and minimum error) by a least‐squares estimation of the integration constants. A satisfactory fit is obtained with a representative data set. Parametric equations are also obtained for x and y along the cable (with the x-axis in the fluid flow direction), as functions of the tangent angle; they contain the same integration constants (evaluated by the previous procedure). Elimination of the angle between the two parametric equations yields the equation of the cable shape in Cartesian coordinates.