Theoretical Modelling of Acoustical Measurement Accuracy for Swath Bathymetric Sonars
By Xavier Lurton, Ifremer - Service Acoustique et Sismique, France
Multibeam echosounders and bathy number of samples is considered; also metric side-scan sonars are nowadays the specificity of measurements close widely used for seafloor topographic to the vertical is discussed. An appli mapping. Depending on the measure cation example is finally presented. ment angle sector and on the sonar array structure, various methods are usable to estimate time-angle pairs Introduction needed to determine sounding point positions. Distinctions are to be made Most seafloor topographic mapping sur between methods based on either sig veys are carried out using specialised nal amplitude or phase; and between bathymetric sonars. Limited for a long measurements at either given time or time to vertical sounding carried out by angle; this leads to define four main single-beam sounders, bathymetric methods, covering most of bathymetry sonars used today mainly work in oblique systems available today (maximum incidence. Installed under the hull of a amplitude instant, phase difference ship or on an underwater vehicle, a swath direction, zero-phase difference in bathymetry sonar (Figure 1) ensonifies a stant, maximum amplitude direction). ground strip, narrow in the alongtrack In this paper, the principles of these direction and broad acrosstrack, thanks four approaches are presented, and to one (or two) transmit arrays of large their respective measurement accuracy longitudinal dimension. For Bathymetric is evaluated as a function of the signal- Side-Scan Sonars (BSSS), the receive to-noise ratio. The averaging over a arrays are identical to the transmit arrays,
Figure 1: Bathymetric measurement using a swath sonar: each sounding point along the across-track ensonified strip is defined by measurements of angle d and oblique range R given by the two-way travel time t and do not provide additional angular filtering. For Zeraphase Difference Instant (ZDI): estimation MultiBeam EchoSounders (MBES), echoes are re of the instant corresponding to null phase dif ceived inside a vertical fan of narrow beams, formed ference between two beams formed in a given using an ad hoc array. direction In all cases, the received backscattered echo is Phase Difference Direction (PDD): estimation of recorded as a function of time. After the complete the arrival angle at a given instant, from the reception of an echo, the sonar emits a new signal phase difference between the time signals on that covers a seafloor strip shifted due to vessel two sensors advance. The seafloor echoes are used on the one Maximum Amplitude Direction (MAD): estima hand to perform bathymetric measurements, and tion of the angle corresponding to the maximum on the other hand to build the sonar imagery from energy among a fan of beams considered at a the bottom reflectivity; only the first topic is con given instant sidered in this paper. Every sounding measurement by a bathymetric In all cases, spatial processing is necessary to per sonar is based on the joint estimate of two char form angle measurements, which are implemented acteristics (range and angle of arrival) of echoes; either starting from a beamforming array (MAI, these allow one to locate the impact point posi MAD), or starting from a dephasing measurement tions on the bottom relative to the sonar, taking between two simple receivers (PDD), or else by into consideration the propagation characteristics. mixing both approaches (ZDI). The systems consid These points are then positioned geographically ered here are MBES (carrying out the measure starting from measurements of navigation and ves ment' of bathymetry at the output of many formed sel attitude with respect to the sonar. This paper beams) and BSSS (working on the phase differ will examine only the first part of this series of ence between signals received on two, or more, operations, i.e. the processing of the acoustic sig receiving arrays). nals for the (range, angle) estimation. The detailed The fundamentals of these various methods of analysis of the other causes of errors (platform array and signal processing are classical (they may attitude, refraction due to sound speed, etc.) and be found e.g. in Burdic's textbook [Burdic, 1984]). their influence are detailed in [Hare et al., 1995], They have been applied progressively to the vari ous generations of swath bathymetric sonars (see Since the oblique range is given by the tw&way propa e.g. review papers [de Moustier, 1988] and [de gation time t (ideally R(t) = ct/2 for a medium with con Moustier, 1993]). For multibeam echosounders, stant sound velocity c), its estimation will be, in the fol MAI alone was used in the pioneer SeaBeam sys lowing, equivalently considered in the time domain. tem ([Renard & Allenou, 1979]). In order to get Two categories of (time, angle) measurement wider swath widths, MAI was later completed by methods may be distinguished: either ZDI ([Pohner, 1987]) or MAD ([Satriano et al., 1991]), depending on manufacturers. On the - Arrival time estimation, for fixed observation other hand, sidescan sonars began to be equipped angles with PDD interferometers in the early 1980s - Arrival angle estimation, as a function of time in ([Blackington, 1986], [Denbigh, 1989]). Theoreti reception cal elements and comparisons between these sonar processing methods (possibly outside the Each one of the two approaches above can be bathymetry measurement context) may also be applied to either amplitude or phase criteria of the found in [Quazi, 1981], [Billon, 1987] or [Leclerc, received signal; this leads therefore to four meth 1994], ods; every current bathymetric sonar uses one or In the present paper, after defining the geometrical two of these. We will refer to them in the remain configuration and limiting the scope of our study, der of this paper as: we examine in the main section the four methods of measurement. In each case, expressions of - Maximum Amplitude Instant (MAI): estimation angular and bathymetric errors are proposed of the instant corresponding to the maximum according to Signal to Noise Ratio (SNR) and sonar energy of the received temporal signal inside a characteristics. The variance reduction due to beam formed in a given direction averaging of successive samples is examined, as well as the particular problems raised by measure c _ (1) ments at incidence angles close to the vertical. An ------= -— + tan d.dd H t example of application to a typical sonar configura tion is also presented. Hypotheses on Signal and Noise In the following, a received signal of average power
is superimposed on a white Gaussian noise, in General Presentation the signal frequency band, spatially isotropic, with average power The bottom is assumed to be flat and horizontal, < n > with homogeneous characteristics; acoustical Considering that the estimation of parameters is backscatter is caused only by the z=0 interface. carried out after adapted filtering and receiver The sonar system is assumed to have a narrow array processing, the output SNR to consider directivity pattern in the y direction (normal to the becomes: measurement plane xz), so that propagation and (2) backscatter are confined to the vertical plane xz. d — Gpd q The receiving array, situated at altitude H above the where G0 is the array directivity index. In the ideal seafloor, is rectangular with dimensions L in the xz case of a rectangular array of dimensions (w, L), plane and w in the xy plane (not shown in Figure 2); consisting of omnidirectional sensors summed with the array is tilted at an angle y/ with respect to the out weighting, and forming a beam in the direction horizontal. At the time of measurement, the direc y, the array directivity index is approximated by: tion of the (supposed rectilinear) signal trajectory (3) makes an angle 0with the bottom, and y= Q -y with AtiLw cos y respect to the axis normal to the array length. D 1 Joint estimation, in reception, of the backscattered thus depending on the beam steering angle y . wave angle 6 together with the time of flight t The signal duration considered here may be, equiv allows computation of the impact point position. alently: For example, assuming propagation with constant sound speed c, the instantaneous oblique range is Either that T of the emitted signal envelope ct , and one obtains for the impact point coor- (possibly within -3 dB), in the case of a narrow R = — 2 band signal dinates n ct and TT ct „ Or the lobe width (roughly 1/6) of the autocor D = — sin i? H = — co$,0 2 2 relation function, in the case of a signal modu The depth relative error is therefore linked to the lated with spectral bandwidth 8, after a ‘pulse measurement errors in time and angle by: compression’ processed by an adapted filter Figure 2: Measurement configuration The signal received on the array has, in first approx fact that at any given instant the various points of imation, a plane wave structure. It is supposed of the array do not "see" exactly the same seafloor constant average amplitude (while its instantaneous part [Lurton, 2000]; thus the echo radiated by amplitude may be fluctuating); in other words, inside the non-common scatterers plays the role of dis a beam footprint the average backscatter index is turbing noise. This affects the interferometric independent of angle, and the transmission loss measurement of phase difference between sep variations are neglected. In addition, one considers arate receivers; in this case the equivalent SNR here only the random fluctuations of measurement can be expressed roughly, in oblique incidence, related to the acoustical SNR, disregarding the other as the ratio between the lengths of the common measurement error causes rather leading to esti and non-common parts of the footprint: mation biases (array installation geometry, igno cT rance of the local sound speed profile, etc.). '■slf -1 (6) asm The noise disturbing measurements may be either additive noise, or degradations related to the struc where a is the interferometer spacing1. Implicitly, ture of the backscattered signal itself. dM tends towards a zero limiting value when the two footprints become completely disjointed. The Additive noise occurs from acoustical or electri footprint shift can be corrected if the signal arrival cal causes, and intervenes like a random com direction is known: in a MBES, each beam nominal ponent superimposed on the signal; the effect angle gives an estimate of y with a precision suffi of this noise upon SNR is reduced by the direc cient for neglecting this effect. On the other hand tivity index of the receiver array [Burdic, 1984], the phenomenon is very penalising for BSSS hav as expressed in (2) ing no a priori angular information; one solution, in - The effect of angular decorrelation is related to this case, is to take the first interferometric meas the radiation of the echo by a seafloor elemen urement of /and then, starting from this estimate, tary instantaneous target (delimited by the sig to carry out the preliminary compensation to the nal footprint): the array receivers do not per final interferometric measurement; another possi ceive this target as a point-like source, but as ble solution lies in the use of wide-band modulat a scattered sound field with a directivity pattern ed signals, in which case the cross-correlation due to the spatial extent of the signal footprint. function provides an estimate of time delay This effect can be expressed as a SNR degra between the two receivers giving access to a /esti dation [Jin & Tang, 1996] in: mate. It should be noted that, even if the footprint V (4) shift is compensated, a residual error may subsist, d-rng j related to the signal time sampling rate. In this case the relationship between common and non sin// kO- . 2 si with v = , and i} = — Ax cos #cos y common parts of the footprint becomes: 2 H , T (6a) where k is the acoustic wavenumber and a the d « " 7 ” 1 spacing between two points of the receiving where t is the standard deviation of the error array. The signal instantaneous spreading Ax due to time sampling period. on the bottom is: To synthesise these various effects, a resulting CT H A Û \ signal to noise ratio d combines these contri Ar = min butions, assumed independent: 2sin#’ cos2$ ^ 1 1 1 1 (7> given either by the signal duration T or by the d d., angular beam width AO inside which detection is *shf carried out. This decorrelation effect, also where d.dd is the additive SNR, dm and dsh, are known in radar as glint, corresponds to an angu the equivalent SNR for angular spreading and lar measurement spreading directly related to shifting footprint. The relative importance of the instantaneous target size [Lurton, 2000] the various terms depends on the system type The effect of footprint shift is caused by the and the configuration considered. 1 The corresponding formula in [Lurton, 2000] is erroneous by a factor 2 20 ______Beamforming and Array Weighting bottom. The range difference between the footprint In the MBES case, the receiving array forms narrow edges, for a beam with width A60 at -3 dB (always beams (typically 1° to 2° nominal width) in the xz considered in the beam vertical plane, and given by plane, by dephasing or delaying the signals (8)), is: received on its elementary sensors. Amplitude H sin 8 . weighting is applied to limit the effect of the A Rn =■ cos 9 unwanted echoes received by the beam pattern sidelobes, in particular the strong contribution from where the temporal spreading (Figure 3) is: coming from the normal to the bottom (specular 2H sin # A ^ echo). This method provides a level reduction of ccos2* 0 (1°) the directivity secondary lobes, but at the price of a broadening of the main lobe, and a correlative It should however be noted that, in the case of a degradation of the directivity index. For a flat array, beam close to the vertical (typically 0<2O°), this the main lobe width (at -3 dB) depends on the time spreading is usually small. The final time array length L and steering angle y by the approxi spreading is approximately given by the quadratic mate relation: summation of the emitted signal duration and the lengthening by angular sweeping, all values con A#0 O') K 0.88-— — — (8) Lco s/' sidered within -3 dB. where X is the wavelength, and a is a corrective coefficient (>1) depending on the particular weight The depth measurement thus corresponds to the ing law. This law differs between sounders, so no arrival time estimate for a fluctuating and noise- general approach will be given here. In the follow added signal of duration © = iJ t 2 + A/02 , whose ing, the performance of a weighted array will be average envelope is a function of the beam pat parameterised by: tern, emitted signal shape, and local seafloor roughness; note that at this stage, the sediment - The factor a-widening of the principal lobe (typ interface is considered horizontal, homogeneous ically 1.2 to 1.4) and impenetrable to sound waves. - The factor /3 - degradation of the directivity The estimation error for the maximum amplitude index (typically 0.6 to 0.8) instant depends on the actual processing details. A frequently used processing consists in seeking Note that, for a rectangular array,a ~ \ t (for a the gravity centre of the echo envelope: the rms weighting applied to one rectangle side). Refer to error then decreases approximately in proportion e.g. [Harris, 1978] for the detailed definitions and with ...e , where N is the number of samples used the precise numerical values of these degradation ■Jn factors. in the barycentre computation, and hence depends For a cylindrical array, the beamwidth depends on on the algorithm details. From numerical simula the active array length considered; it is independ tions of a signal envelope fluctuating according to ent of the steering angle. a Rayleigh’s law around the average shape of a sine function main lobe (the lobe width being 0 at -3 dB) it may be found (see [Lurton, 2001]) that, if Performance of Bathymetric one uses all N signal samples of the average lobe Measurement Methods digitised with sampling period Ts, the standard deviation is around ^ * o,10-^L= O.1OJ07T- Maximum Amplitude Instant For slightly tilted beams, the MAI method (presum This general formulation of a time measurement ably used in every MBES) basically consists in rms error proportional to the signal duration j -. seeking the maximum amplitude in the temporal leads to: ■Jn signal envelope collected in each formed beam. It —il / 2 is thus a measurement of time of arrival along the 2 H sin Û *MAI A0O I +TZ beam axis angular direction. -Jn c cos2 0 (11) The time signal inside a beam is generated by the emitted signal sweeping the beam footprint on the The depth measurement relative error is then: Figure 3: Geometry of two oblique beams of different angles (left) and corresponding signal envelopes used for the estimation of arrival times tand t2 (right) 1/2 interface will cause a time spreading propor S i \2 (tan Û.AÛ0 f + [ cos 9 (12) tional to its peak-to-trough maximum amplitude 2H H h (projected at angle 8), hence in __— __ to The measurement error given by (12) is expected c. cos 6 to be too optimistic, since time spreading, here be added quadratically inside the brackets of (11) defined for an ideal flat seafloor, is clearly under The signal penetration inside the seafloor and estimated. To be more realistic, the echo envelope sediment volume backscattering will create a model should account for the variations of the trail depending upon the frequency and the sed seafloor features inside the beam footprint: slope iment characteristics (absorption and hetero (both alongtrack and acrosstrack), large-scale geneity). Since the absorption coefficient inside roughness (hence at a different scale from inter soft sediments may be roughly comprised face microroughness causing backscattering), pen between 0.1 and 0.2 dB/X [Hamilton & Bach etration inside the sediment volume (echoes raised man, 1982] (or, equivalently, about 0.8 to 1.6 by buried interfaces and scatterers mixed with the dB/m at 12 kHz), it is readily seen that layers water-sediment interface contribution) and patchi buried at depths of several meters may raise ness (horizontal changes of the seafloor type and significant echoes blurring the sediment inter characteristics). All of these effects cause an face detection. This order of magnitude for extra-spreading related to the relief and sediment bathymetry errors makes problematic (along variability inside the beam footprint, with a huge with other causes) the use of low-frequency variety in configurations making it impossible to multibeam echosounders for shallow-water model globally. As a first approach, four basic geo bathymetry applications. metrical effects are evoked here (see Figure 4): The acrosstrack average slope Çt will modify the effective incident angle 9 into & ±Çt inside - The roughness of an average flat horizontal eq.(9) to (12), the +/- sign depending upon the Figure 4: Geometrical approach of echo time spreading for steep beams; effects of roughness (a), sediment penetration (b), acrosstrack slope (c) and alongtrack slope (d) slope orientation; Phase Difference Direction The alongtrack relative angle Çi between the The Phase Difference Direction (PDD) method is seafloor and the beam fan (due to the average often used in sonar and radar to locate a target; it slope and/or non-compensated ship’s pitch) will consists in measuring, at a given instant, the cause a time spreading in 2//tan^tan^z. be phase difference between two receiving points, giv cos# ing a precise estimate of angular direction. In the added quadratically inside the brackets of (11)). case of topographic measurement, the cell resolu Practically, the relative influence of these effects may tion of the signal on the ground delimits the instan be strongly dependent upon the seafloor type and the taneous target; a large number of independent geometrical configuration, precluding the definition of measurements can thus be obtained along the a generic model usable in the present framework. swath swept by the signal. This method is em Moreover, a paramount problem encountered in ployed in BSSS but also in satellite-borne radars measuring central beams lies in the elimination of for topographic mapping [Maitre, 2001]. the specular reflected contribution (arriving at Considering the configuration of Figure 5, the phase difference between the signals emanating 2 H t = ___ whatever the beam), which may be very from M and measured at points A and 6, separat c ed by a, is: dominant especially at low frequencies. An inaccu A 0AB = kJR = ka sin y rate compensation of the specular echo may bias the depth estimates: due to its synchronicity, it. where k = — is the wave number, S i = MA - MB À tends to circularise the seafloor profile around the central sounding. Its suppression is made very dif the range difference, and y is the angle between ficult by its proximity in time and angle to the use the target direction and the interferometer axis. ful backscattered echo. The estimate of y is obtained from the A 0 ab Away from the vertical, the depth relative error measurement: deteriorates according to the tan0 term in (12), (14) although the number N of available samples : arcsin ka increases with angle 9. Moreover, the above accu V racy is obtainable only if the envelope shape of This process can be easily implemented on a BSSS: the backscattered pulse is sufficiently short and the phase measurement is then taken between two smooth; thus it is necessary that the bottom struc identical receiving arrays, whose sections correspond ture is flat and homogeneous on the scale of the to points A and B of Figure 5. The synchronous time beam footprint, which may be too strong an series received on the two sensors are processed for assumption at oblique incidences. Note that in a computation of their instantaneous phase differ actual systems, at oblique and grazing incidences, ence (giving the arrival angle); together with the cor MAI detection is always replaced by another responding oblique distance given by the measure method. ment time, this constitutes the raw bathymetric data. — f'i = 1 —o ~ N = 3 - m - N = 10 Figure 6: Phase difference N = 30 standard deviation (in degrees) N = 100 for a Rayleigh-fiuctuating signal, as a function of signal-to-noise ratio (in dB), according to formulae (16) and (17). The curves are parameterised by the number N of samples used in d (dB) the processing The PDD method offers the advantage of not requir Considering that practically the phase difference ing a complex array structure In the vertical plane, has to obtained from processing a set of N sam and is often used for providing an auxiliary bathy ples (N>2), it may be shown [Lurton, 2001] that its metric function to sidescan sonars initially designed standard deviation 8A¢ is given by: -11/2 ,, „ for imagery. As a counterpart to its simplicity it suf 1 N I (17) fers from some disadvantages: ambiguity in the (N-l)d 1(N-\){N-2)d2 phase difference determination (13) leading to non unique solutions to equation (14) and requiring spe valid in the range of small phase fluctuations (8A f 12 ■Q .1 d 1-0.05 hi d (16) resolution is then degraded proportionally to N. i d + 1 The SNR d considered here should account for the Zero-phase Difference Instant three causes of noise discussed above and syn For this method which is a derivative of the previ thesised in (7). ous one, a MBES receive array is partitioned into sub-arrays (left), envelope amplitudes of the temporal signals resulting from the two half-beams and measurement of the phase difference for determination of the instant to of A(j)=0 (right) two sub-arrays. For a given receive direction, each When reported in the depth measurement relative sub-array forms a beam in the chosen direction. error (1), this expression (21) becomes equivalent The phase difference is measured between the to equation (15) for the PDD angular measurement outputs of the two beams thus formed. The phase error along the interferometer axis (>=0). The corresponding to the nominal direction of beams phase error term 8A In L{\-/l)cosy The performance of this measurement may be studied similarly to PDD, with some modifications. where 8A The time measurement relative error around to is Practically, as in the case of PDD, a number of time then connected to the phase difference measure samples have to be processed in order to estimate ment error 8A Maximum Amplitude Direction Based on the hypothesis that an instantaneous This measurement method consists in estimating, at signal footprint may be considered as a point a given moment, the direction corresponding to the like target, the MAD method is practically usable maximum energy received among a great number of in configurations where the signal angular beams formed with a small angular step (Figure 8). spreading at a given moment is not too penalis ing; this condition is well fulfilled in oblique inci The measurement quality is related to the actual dence, but is not adequately satisfied close to processing used in angle estimation. Basically, it the vertical. consists in searching for the angle with maximum amplitude in a series of fluctuating sample values corresponding to the outputs of the consecutive D is c u s s io n beams. So the performance will rather be, in the angle domain, similar to the one presented above Variance Reduction Due to Averaging for MAI in the time domain. At a given time the A measurement corresponding to one single tem angle measurement error should be in: poral sample is usually too disturbed and vague to (25) be effectively usable; moreover the bathymetric KAi. n profile thus carried out from a very dense set of temporal samples (typically the output sampling where Q. is the lobe width considered in the esti period is close to the signal duration itself) may be mation, and N is the number of angular points of little practical interest. A common practice is instantaneously available (Figure 8). The lobe width then to reduce the variance of individual measure to consider is a combination of the array beamwidth ments by taking into account N independent occur Adfrom (8), and the angle spreading due to the sig rences of each. The typical variation 5X/y of a nal length (10): bathymetry measurement is given, at first approxi 11 / 2 mation, by the standard deviation 8X of each ele \2 cT. cos 6 (26) mentary measurement divided by *J~N ; however n = Aé?„ + 2H sin 6 this improvement may be formally more complex, as it appears e.g. in eq.(17). The depth measurement relative error is then for As a counterpart, increasing the number N of mally identical to (12): processed samples will cause a degradation in the resolution obtained: a given angle measurement f cT . cos 9 V (27) will be not be associated any more with a footprint (tan 0 A 0 aŸ + on the bottom given by the only local and instanta H 4 n { 2 H ) neous resolution of the signal, but rather with a Note that this accuracy corresponds to one given whole range extent defined by consecutive sam measurement instant; it may be Improved further ples. Thus the final quality of measurement will by averaging the angle estimation over a number of depend on the number of points being used for successive time samples (see below). averaging; this number will be limited by the homo- geneity of the bottom characteristics over the sum 2Ax . . ; this process imperfectly N* = — sind? mation interval, and by the required resolution: a c a gain -J n in precision, obtained by summing N sam compensates for the degradation of precision ples, has to be balanced against a degradation of in z, but can prove to be the most relevant strat the horizontal resolution, approximately in^/sin^- egy compared to the requirements of bathymet The number of samples used in the averaging filter ric mapping in order to try to maintain a con can be selected in various ways. The relation stant horizontal resolution between the time-sampling step ( Averaging over a number of samples N constant Close to the vertical, in the absence of angular with range neither improves the resolution filtering by the directivity pattern, the instanta degradation at short distances, nor compen neous footprint of the signal is maximum in x, sates in a sufficient way the precision degrada and is worth roughly: tion at long distances; the effect of this method c T \1/2 is thus only to reduce by a global factor the A x * H 6 1 + -1 (29) total variance of the bathymetry measurement Averaging over a constant angular opening AQ The corresponding angular spreading (the angle leads to a number of points increasing with sector covered instantaneously by the signal) is range ^ sinff ^ ; this method also maximum: Ae c d cos2 6 tends to compensate for the bathymetry error cT cT A 0=6 1 + -1 cos2 0 « 6 -1 which increases with range, at the price how H02 H Û1 (30) ever of a degraded resolution. This second solution is employed quite naturally in MBES, This instantaneous angular spreading effect is irre which usually provide only one sounding depth ducible for systems without angular filtering (PDD) per beam, the footprint width of which (and or carrying out an angular scanning at a given therefore the number of available points) instant (MAD). On the other hand, for the two other increases with the incidence angle. Practically, modes of detection, processing data inside one things are more complicated because of the formed beam, the angular spreading effect can be necessary trade-off between the measurement limited by the directivity lobe width, which fixes the precision (using as many samples as possible) upper limit of the AQ value and resolution (keeping N at a reasonable - The footprint shift effect is also at its maxi value). For instance in MAI measurement for mum; it is shown that its amplitude, depending steep-angle beams, with few samples avail on array mounting \//, is then: able, the trend is to use the whole beam foot a i------(31) print data; at the other end, in actual ZDI pro ck ~ — cos y f- H 8 i- y]H 1 &1 + a H s in ^ cessing, averaging is not to be made over the whole phase ramp, but rather over a restricted The corresponding SNR is given roughly by the ratio sector (smaller than the beam footprint) A x _ expressed from (29) and (31). around the zero-phase crossing Figure 9: Relative depth error along a swath half-width (given by x/H, with H=50 m), for a 100-kHz multibeam echosounder using MAI and ZDI methods. See text for details /j=0.5; one half of the footprint points are used for hand the parameters of the emitted signal and its ZDI estimation. processing. They have been defined for an ideally The model results are given in Figure 8. Most of flat homogeneous seafloor; specific effects such the estimated depth error is smaller than 0.1 per as seafloor type patchiness or sediment penetra cent, which is quite small but in good agreement tion have not been accounted for, despite their with commonly observed performances of modern dominant influence in particular cases. multibeam echosounders. This example makes clear the two regimes corresponding to the two bathymetry measurement methods. Close to the R e fe r e n c e s vertical the MAI error is low (around 0.04 per cent) and gently increases with incident angle; the ZDI is D. Billon (1987) Bearing estimation of a single then unusable, but its accuracy improves as inci monochromatic plane wave with a linear receiving dent angle increases. The two methods give equal array in Progress in Underwater Acoustics, ed. errors around 35° {x/H~0.7), beyond which the H.M.Merklinger, Plenum Publishing Corporation, phase detection gives better results; the ZDI error 1987 comes to a minimum around 45° (x/H=l), and increases regularly until a value of 0.1 per cent at W.S. Burdic (1984), Underwater Sound System 75° incidence (x/H~3.5). Analysis, Prentice-Hall, Englewood Cliff, 1984 J.G.BIackington (1986) Bathymetric mapping with Conclusions SeaMARC II: an elevation angle measuring side- scan sonar system, PhD dissertation, University of The acoustic measurement errors are often the Hawaii, 1989 less-well documented points in the various error- budget models available for sonar bathymetry per C. de Moustier (1988), State of the art in swath formances ([Hare, 2002]). This is due on one hand bathymetry survey systems, Int. Hydr. Rev., vol. to the fact that such analyses imply a thorough 65, pp. 25-54, 1988 knowledge of the sonar characteristics, which may be difficult to obtain from the manufacturers; and C. de Moustier (1993), Signal processing for swath on the other hand, the influence of other error bathymetry and concurrent seafloor acoustic imag cases (the main ones being the carrier's attitude ing, in Acoustic signal processing for Ocean measurement accuracy, and the compensation of Exploration, J. M. F. Moura and I. M. G. Lourtie, the sound speed profile refraction) [Hare et al., Eds.: NATO Advance Study Institute, pp. 329-354, 1995] can appear to be dominant in a number of 1993 cases. However, the need for estimating this cate gory of acoustical measurement errors does exist, Ph. Denbigh (1989) Swath bathymetry: principles and will increase together with the system per of operation and an analysis of errors, IEEE Journal formance improvements and the users require of Oceanic Engineering, vol.14, No 4, pp 289-298, ments. This paper aims at filling the lack in avail 1989 ability, for sonar users, of practical formulae mod elling these effects. E. L. Hamilton and R. T. Bachman (1982), Sound We have proposed here accuracy models for the velocity and related properties of marine sedi various methods of acoustic measurement used in ments, Journal of the Acoustical Society of bathymetric sonars, the purpose being to define America, vol. 72, pp 1891-1904, 1982 formulations easily usable for performance predic tion and experimental results analysis. This was R. Hare, A. Godin & L. Mayer (1995), Accuracy esti done for the four methods currently used in mod mation of Canadian swath (multibeam) and sweep ern bathymetry sonars. The proposed models (multi-transducer) sounding systems, Canadian explicitly feature on the one hand the geometrical Hydrographic Service Internal Report, 1995 parameters for the measurement configuration (water depths, incident angles) and the sonar R. Hare (2002), Bathymetry error modelling: arrays (dimensions, tilt angle), and on the other approaches, improvements and applications, Canadian Hydrographic Conference CHC 2002, tion, évaluation et premiers résultats, Int. Hydr. Toronto, 2002 Rev., vol. 51, n° 1, pp 35-67, 1979 F.J. Harris (1978), On the use of windows for har J.H. Satriano, L.C. Smith & J.T. Ambrose (1991), monic analysis with the Discrete Fourier Transform, Signal processing for wide swath bathymetric Proc.lEEE, vol.66, N°l, pp51-83, 1978 sonars, Proc. IEEE 0ceans'91, 1, pp 558-561, 1991 G. Jin & D. Tang (1996), Uncertainties of differen tial phase estimation associated with interfero- C. Sintes (2002), Déconvolution bathymétrique metric sonars, IEEE Journal of Oceanic d'images sonar latéral par des méthodes inter- Engineering, vol.21, No 1, pp 53-63, 1996 férométriques et de traitement de l'image, Ph.D dissertation, Université de Rennes 1, France, F. Le Clerc (1994), Performance of angle estimation 2002 methods applied to multibeam swath bathymetry, Proc. IEEE Oceans’94, Brest, pp III 231-236, 1994 B io g r a p h y X. Lurton (2000), Swath bathymetry using phase difference: theoretical analysis of acoustical Xavier Lurton (born in Bordeaux, France, 1955; measurement precision, IEEE Journal of Oceanic PhD of Applied Acoustics, 1979). He was for eight Engineering 25(3), pp 351-363, 2000 years (1981-89) with Thomson-Sintra ASM, mainly specialising in underwater sound propagation mod X. Lurton (2001), Précision de mesure des sonars elling for naval applications. In 1989 he joined bathymétriques en fonction du rapport IFREMER (the French oceanic research agency) in signal/bruit, Traitement du Signal, vol.18, n°3, pp Brest as a R&D engineer. He worked on various 179-194, 2001 acoustical oceanography applications (ocean tomography, telemetry, fisheries sonar) and man H. Maître (2001), Traitement des images de RSO aged the IFREMER acoustics laboratory for five (SAR image processing), Hermes, Paris, 2001 years. He is now in charge of a technological research programme on advanced acoustical meth F. Pohner (1987), The Simrad EM100 multibeam ods for seafloor characterisation, his current inter echosounder, a new seabed mapping tool for the ests being both in physics of seabed backscatter- hydrographer, 13th Int. Hydrographic Conf., ing, sonar signal processing and multibeam Monaco, 1987 echosounder engineering. He has also been teach ing underwater acoustics in engineering schools A.H. Quazi (1981), An Overview of the Time Delay for several years, and he is the author of An intro Estimate in Active and Passive systems for Target duction to Underwater Acoustics (Springer-Praxis, Localization, IEEE Trans.Acoustics, Speech and 2002). See review in this issue. Signal Processing, Vol.ASSP-29 N°3, pp527-533, 1981 V.Renard & J.P.AIIenou (1979), Le SeaBeam , son deur multifaisceau du N/0 Jean Charcot: descrip E-mail: [email protected]