¹University of Victoria, Department of Electrical and Computer Engineering

Victoria, B.C., CANADA

adam@ece.uvic.ca

　

²Pacific Biological Station

Nanaimo, B.C., CANADA

　

　

A typical echo sounder used in fisheries applications consists of a single, narrow beam transducer mounted on the hull of a vessel. Acoustic pulses (pings) are transmitted at a fixed rate and the echoes from various targets in the water column and from the bottom are conveniently displayed as an echogram. The horizontal axis of the echogram displays time or distance steamed while its vertical axis displays range or depth. Different colour indicates the intensity of the received echo after adjustments for absorption and spreading losses are made. The echogram provides information on single or multiple targets in the water column, such as individual fish or fish schools, and on the bottom. Vessel heave, roll, pitch and yaw have adverse effects on echograms. Heave will appear as a vertical offset on the features shown in the echogram and roll and pitch will affect both the intensity and the target traces. The degree of these distortions depends on vessel speed and motions, target structure and trajectory, ping rate and beam-pattern. We will evaluate these effects by synthesising echograms for different situations including simulated and actual vessel motion data. Methods to minimise these effects will be discussed.

　

　

Fisheries acoustics has received a good deal of attention over the past years. A variety of procedures have been developed for the use of acoustics in fisheries. Currently, research vessels are the primary platforms for acoustic surveys in fisheries. Vessel motion will affect the observations made with a vessel-mounted transducer. In heavy weather, observations may be impossible or severely distorted. Here, we distinguish between primary and secondary vessel motion. The former describes the steady movement of the vessel along its path while the latter describes wind and sea induced vessel translations (surge, sway and heave) and rotations (roll, pitch and yaw).

　

Split-beam measurements can provide accurate estimates of the location of a target or single fish in the beam (MacLennan and Simmonds, 1992; Stephens, 1970). Additional knowledge of primary and secondary vessel motion is required to determine target location in a fixed reference frame. The processing of received sonar echoes must, therefore, include compensation for transducer motion when meaningful and accurate estimates of target position are required. This paper presents a review and discussion of the effect of vessel motion on single fish echoes and provides a model to visualise and compensate for them.

　

　

Surveys and acoustic measurements that use hull mounted transducers will be affected by adverse weather conditions. The transducer will follow all vessel motions including surge, sway, heave, roll, pitch and yaw. When these motions are severe a transducer may transmit in one direction and look in another when the echo arrives. This misalignment results in errors in target strength estimates and has been well studied for fish biomass estimation from echo integration surveys (Furusawa and Sawada, 1991; Dunford, 2002; Stanton, 1982; Williamson, 2000). Vessel motions affect many other acoustic techniques. A list of acoustic techniques in order from least to most affected includes echo integration, echo counting, target strength (TS) measurement, near bottom detection, target tracking and, finally, calibration with a standard target. Adverse effects of vessel motion on the detection and tracking of single fish targets discussed here include not only the signal fluctuations mentioned above, but also the distortion of the target's trace on the echogram, the possible premature loss of the target from the acoustic detection volume and the difficulty of converting the observed target location in the beam to a fixed earth reference frame.

　

To analyse the effect of vessel motion on acoustic measurements, a model for single target detection and location with a downward-looking, single-beam echosounder has been developed. Generally, an object in space has six degrees of freedom which here are: surge, sway, heave, roll, pitch and yaw. Let us assume that vessel motion can be described by the primary and secondary vessel motions that were introduced above, that the transducer is rigidly mounted to the vessel, that its location may not coincide with the vessel's center of motion and that a single stationary target is observed. The acoustic size of the target is measured by its backscatter cross-section or TS. Accordingly, target tracks will be simulated and plotted for assumed echo sounder and vessel motion parameters, and for real vessel motion data. To generate echograms accurately, we make the following assumptions:

　

　

A single beam echo sounder provides amplitude and time (depth) information from each echo. The information from successive sound transmissions (pings) can be displayed in a depth versus ping count, time or distance diagram (echogram). A typical echogram from an acoustic survey is shown in Figure 1. Given a vertically aligned transducer and calm seas, single fish echoes (traces) will be displayed as inverted Vs. Irregularities in target trace shape and intensity reflect wind and wave induced vessel motion.

　

　

　

　

The roll, pitch and yaw part of the vessel's secondary motion is observed in the right handed level vessel co-ordinate system (LVCS) shown in Figure 2. Its origin is at the vessel's centre of motion and its x and y-axes are in a horizontal plane. The x-axis points in the direction of the vessel's forward motion. Vessel roll, pitch and yaw correspond to rotations about the x, y and z-axes, respectively. The direction of positive rotation is given by the curved arrows and is defined by the right hand rule. In calm weather, the LVCS coincides with the vessel co-ordinate system (VCS) which has its axes aligned with the vessel's stern to bow, port to starboard and vertical axes, respectively.

　

The level transducer co-ordinate system (LTCS) is obtained by translating the origin of the LVCS to the rotated transducer location. In calm weather, the LTCS coincides with the transducer co-ordinate system (TCS).

　

　

For a single target, the target range function (TRF) is observed on the echogram as target range or depth versus time or distance. Given target position P(x, y, z) (Fig.2) and assuming that the transducer is at the origin, the TRF is given by the range r between the transducer and the target:

　

　

The TRF for arbitrary transducer location is given in the Appendix.

　

　

The echo level from a single target is a function of its TS and position in the transducer beam. The echo sounder output level EL is given by:

　

　

where SL is the source level, RG and TVG are fixed and time varied receiver gains, BP_t and BP_r are the transmit and receive beam pattern at the respective angular directions, TS is target strength and the two negative terms account for the spreading and absorption loss. The range between transducer and target is r and α is the absorption coefficient. The target location in the beam is given by the spherical co-ordinates θ and φ. Subscripts t and r refer to transmit and receive, respectively. All quantities except r, θ and φ are in dB. SL and RG are determined by calibration with a reference hydrophone or a standard target. The TVG compensates for the spreading and absorption loss and range r is determined from the time between transmit and echo reception (Traynor and Ehrenberg, 1990). Combining known terms into a constant, CO, and cancelling the TVG terms against the spreading and absorption loss yields:

　

　

To eliminate the constant, we introduce the target strength error TSE. It is given by -(BP_t + BP_r). The axis of the beam pattern may change between transmit and receive instances particularly if the target is at a large range (long echo travel time) and when vessel angular motion is rapid. For split-beam measurements that provide target position as seen by the receive beam and hence estimates of BP_r it would be appropriate to define a split-beam TS error TSE_split as: TSEsplit = -(BP_t-BP_r). However, in this paper we have chosen to illustrate the target strength error, TSE that occurs when no beam pattern corrections are made. We also assume that BP_t is equal to BP_r, as our simulation will be for moderate target range and vessel motion.

　

　

The rotation of a point in a fixed co-ordinate system or the rotation of a co-ordinate system is described by well-known rotation matrices and matrix equations (Hare et al., 1995; Harrington, 1987; Hearn and Baker, 1986; Wolfram, 2002). A brief account is given below and further details appear in the Appendix. The effect of these motions on target position in the beam is readily described when we assume that the transducer location coincides with the co-ordinate origin or equivalently with the vessel's centre of motion. In this case, the target position seen by the rotated transducer is given by:

　

　

where P₁₁ and P₃₁ are column vectors that give the target position as seen from a level and from a rotated transducer, respectively. The inverse rotation matrices R_x^-1 , R_y^-1 and R_z^-1 are given in the Appendix. The Appendix also describes the general situation for a transducer that is not located at the origin and the transformation from Cartesian to spherical coordinates required for beam-pattern calculations (Clay and Medwin, 1987).