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A Post-Processing Method for theRemoval of Refraction Artifacts inMultibeam Bathymetry DataFanlin Yang a b c , Jiabiao Li a b , Ziyin Wu a b , Xianglong Jin a b ,Fengyou Chu a b & Zhongzhi Kang ca Key Laboratory of Submarine Geosciences, State OceanicAdministration, Hangzhou, Chinab State Oceanic Administration, Second Institute of Oceanography,Hangzhou, Chinac Key Laboratory of Foundational Geo-information and Digitization,Shandong University of Science & Technology, Qingdao, China

Version of record first published: 22 Jan 2008.

To cite this article: Fanlin Yang, Jiabiao Li, Ziyin Wu, Xianglong Jin, Fengyou Chu & Zhongzhi Kang(2007): A Post-Processing Method for the Removal of Refraction Artifacts in Multibeam BathymetryData, Marine Geodesy, 30:3, 235-247

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Marine Geodesy, 30: 235–247, 2007Copyright © Taylor & Francis Group, LLCISSN: 0149-0419 print / 1521-060X onlineDOI: 10.1080/01490410701438380

A Post-Processing Method for the Removal ofRefraction Artifacts in Multibeam Bathymetry Data

FANLIN YANG,1,2,3 JIABIAO LI,1,2 ZIYIN WU,1,2 XIANGLONGJIN,1,2 FENGYOU CHU,1,2 AND ZHONGZHI KANG3

1Key Laboratory of Submarine Geosciences, State Oceanic Administration,Hangzhou, China2Second Institute of Oceanography, State Oceanic Administration,Hangzhou, China3Key Laboratory of Foundational Geo-information and Digitization, ShandongUniversity of Science & Technology, Qingdao, China

Sound refraction artifacts are often present in multibeam swath bathymetry data. For aflat array, the artifacts are usually more serious in outer beams than in inner beams. Ina 3D topographical mapping they appear as ridges that parallel the tracks of the vessel.To shorten the survey time, the outer beams should be utilized as often as possible.Therefore, the refraction errors should be removed. In this paper, we present a model ofreduced sound speed profile that consists of three water layers. The sound speed of thetwo upper layers has a constant gradient, and the third layer has the same sound speedas the most bottom measured layer. The model parameters can be searched based on theprinciple of the minimum difference of depth between the overlap of two neighboringswaths. The horizontal position and depth of each beam can be accordingly recalculatedusing the model parameters. To avoid being trapped in local optimum, the initial searchscope is limited according to assumed lunch angle and travel time in each subregion.The method is verified by comparing the simulated and real data.

Keywords Multibeam sonar, SSP, refraction, artifact

Sound refraction artifacts are usually present in a multibeam survey and are more obviousfor the flat seafloor (Kammerer 2000; Sui et al. 2004). They are usually serious for the edgebeams of swath and trivial at nadir. If the Sound Speed Profiles (SSPs) for a survey regionare accurate, the spatial positions for all beams can be precisely computed using ray tracingalgorithm. However, SSPs normally change in some situations (especially in the estuary)and cannot be accurately obtained during the surveying. Otherwise, they usually cannot beimproved by interpolating among successive SSPs (Cartwright and Hughes Clarke 2002;Cartwright 2003). Consequently, the refraction artifacts seriously degrade the quality ofthe final survey result. In some extreme situations, the precision of water depth cannotmeet the requirement of the International Hydrographic Organization (IHO). Therefore, a

Received 20 November 2006; accepted 20 March 2007.This work was supported by the project of National Nature Science Foundation of China,

Contract 40506023 and 40506017.Address correspondence to Fanlin Yang, Associate Professor, Key Laboratory of Submarine

Geosciences, State Oceanic Administration, 36 N. Baochu Rd., Hangzhou, Zhejiang, China, 310012.E-mail: flygps@sina.com

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236 F. Yang et al.

post-processing method for the removal of multibeam sound refraction artifacts is neededto improve the quality of bathymetry.

The Ocean Mapping Group (OMG) at the University of New Brunswick has studiedthe problem of sound refraction artifacts. The OMG developed a two-layer SSP modelto evaluate the refraction coefficients according to two neighboring parallel lines andcrossing check lines (Kammerer 2000). The method is not accurate for the steep terrain.Researchers also presented a geometric rotating method to correct the artifacts through thestatistic average angle (Hughes Clarke 1996). Although it is simple, it is merely suitablefor the flat seafloor. Ding, Zhou, and Tang (2004) used MB-VelocityTool from MB-Systemsoftware to edit SSPs and then corrected the raw data with the edited SSP, but this methodis a preliminary research and only suitable for the flat seafloor. More researchers areinterested in inversing SSPs (Zhou, Zhang, and Zhou 1999; He 2000; Zhou, Zhao, andZhou 2001; Zhao 2002; Qi and Tian 2003; Wu et al. 2005). However, these kinds ofmethods may be inaccurate in some regions, especially in the estuary with sharply changedsound speed. Some methods need be further verified by the real multibeam data. Normallythe measurement of SSPs is difficult in such regions (Batton 2004); therefore, we need todevelop a post-processing method to improve the quality of bathymetry.

This paper presents a new post-processing method based on the equivalent SSP theory.The structure of an actual SSP normally is very complex and sometimes even unknown, sowe want a simple SSP to replace it. The spatial position of each beam will be recalculatedaccording to the equivalent SSP.

Systematic Error Correction Before Removing Refraction Artifacts

If SSPs are inaccurate in a survey region, the real sound rays will diverge from their correctpositions. Therefore, the overlap between the two neighboring swaths will be inconsistent.The systemic errors are obvious from their sun-illuminated swath terrain. These errors willparallel the tracks of the vessel and look like ridges. Roll mount angle bias, imperfect tidecorrection, and incorrect beam steering can also cause such artifacts in 3D terrain image.To correct refraction artifacts through the equivalent SSPs, such effects must be removedfirstly. If the tide is not perfectly corrected in the multibeam swath data, there will be avertical offset between adjacent lines and for several swaths in a vertical projection plane.The method for calculating tide should be checked before refraction artifacts are removed.As we know, tide gauge is very accurate in inshore areas. However, for continental shelf,tide prediction is a good way to get accurate tide data. Sometimes, satellite tide remotesensing is an optional way to obtain tide information where the tide gauge is very distantand cannot control the survey area effectively. Incorrect beam steering will have systematicbiases on the projection plane, caused by either wrong hardware or inaccurate surfacesound speed. We will have a detailed analysis on the influence of surface sound speed inthe next section. If hardware is wrong, the best way is to tell the manufactory. Next, wewill emphasize on how to correct roll mount angle bias.

A patch test is usually used to obtain roll mount angle parameter in a flat seafloor.However, it’s difficult to find an absolutely flat seafloor during this test. Sometimes, thetransducer has a subtle motion for a long time. In these situations, the roll parameterwill have some bias. If some swath data in a flat seafloor are projected along orthogonaldirection, the shape of data on projection plane is similar to the letter V (Figure 1). Whenwe change the roll mount angle, the shape of artifacts will vary accordingly. When theV-shape disappears, the current roll mount angle bias parameter is what we need.

Other factors, such as pitch, heave, and yaw, have little influence on the track-parallelridge artifacts; therefore, we will not discuss them in this paper.

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A Post-Processing Method for the Removal of Refraction Artifacts 237

Figure 1. The artifact caused by inaccurate roll parameter.

Influences of Inaccurate Sound Speed on Multibeam Systems

The influences of inaccurate sound speed on a multibeam echo sounding system (MBES)include inaccurate surface sound speed and sound traveling in water column (Dinn,Loncarevic, and Costello 1995; Kammerer 2000). These influences cause refractionartifacts. The post-processing corrections will be fulfilled according to the characteristicsof the two aspects.

The Snell’s Law can be expressed as

sin θ0

C0= sin θ1

C1= · · · = sin θi

Ci

= · · · = sin θn

Cn

= p, (1)

where, θi is the incidence angle in water layer i, Ci is the sound speed in water layer i. i =0,1, . . . ,n, and p is a constant. The surface sound speed errors can only have an impact onsteering beams. For a flat array, all beams except the center beam are steered. Thereforedeparture angle of outer beams will have errors �θ (Dinn et al. 1995):

�θ = �ca0

ca0tan (θ − β − ρ) , (2)

where, ca0 is the real sound speed, �ca0 is the difference between measured sound speedand real sound speed, θ is the steered angle, β is the array roll mount angle, and ρ is themeasured roll angle.

For a flat array, the errors of steered angle for outer beams are larger than those forinner beams. However, for a curved or barrel array, if it has no steering for inner beam, theerrors of surface sound speed will not have any impact on these inner beams. For example,EM1000 has no steering between −60 and 60, and therefore it only has subtle impact onouter beams that have little steered angle errors.

Total water column is usually divided into many layers. The position of each beam canbe calculated by the sound ray tracing method, the basic principle of which is the Snell’sLaw. In each water layer, the sound speed is assumed as a constant or it has a constantgradient. When real SSPs are unknown, the constant gradient is usually more intuitive andconvenient for the calculation of position than the former.

In each layer, the actual track of ray is an arc if the sound speed has a constant gradient.The radius R of the arc is (Zhao 2002; Cartwright 2003)

R = −1/(pgi), (3)

where, gi is the sound speed gradient. Subscript i denotes the number of layer.The horizontal distance xi in layer i is (Zhao 2002; Cartwright 2003)

xi = (1 − (pCi)2)1/2 − [1 − p(Ci + gi�zi)2]1/2

pgi

, (4)

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238 F. Yang et al.

where, Ci is the sound speed at the initial position of the layer and �zi is the depth of thelayer.

The length of the arc is (Zhao 2002; Cartwright 2003)

Si = Ri(θi − θi+1), (5)

where, θi is the incidence angle, and θi+1 is the departure angle. So the travel time in thelayer is (Zhao 2002; Cartwright 2003)

ti = Si

CH

= arcsin[p(Ci + gi�zi)] − arcsin(pCi)

pg2i �zi

ln

[1 + gi�zi

Ci

], (6)

where, CH is the harmonic sound speed.For a flat array, even though the steered angle predicted is wrong, the Snell’s constant

is still correct. In the last layer, the ray will usually refract back to a direction parallel tothe intended ray path. For this special case, the refraction errors will be constant and haveno relation to depth. Refraction errors will be minimal in deep water. However, the originalSnell’s constant is not correct for a curved or barrel array. The ray path in the majority ofthe water column is not parallel to the intended path. Refraction errors become larger at theenvironment of deep water (Hughes Clarke 2003).

Method of Removing Refraction Artifacts

The equivalent SSP was presented by Geng and Zielinski (1999). If a sound ray is tracedin two different SSPs using the same travel time and initial steering angle, and the twoSSPs have the same surface sound speed and the same area between ray and depth axis(the polygon 0-c1-c3-z3–0 in Figure 2), the calculated position of this footprint will also bethe same. Thus, a simple SSP can be obtained to replace the actual complicated SSP. This

Figure 2. The model of SSP.

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A Post-Processing Method for the Removal of Refraction Artifacts 239

simple SSP has a constant gradient in each layer, such as in the model described in thispaper.

In order to fully cover the seafloor, an overlap is required between two neighboringswaths. If a roll parameter bias, imperfect tide correction, incorrect beam steering, andrefraction artifacts do not exist, the depths of two neighboring swaths in the overlap shouldbe consistent. However, the differences usually exist because of these errors. After the threeformer errors have been corrected, the only main factor for differences is the influence ofthe sound refraction errors.

In this paper, an equivalent SSP model is presented, which has three water layers(Figure 2). This model includes five parameters: surface sound speed c0, the sound speedc1 and c2 in the bottom of the first and second layer, and depths z1 and z2 of the firstand second layer. The sound speeds of the upper two layers have a constant gradient. Thesound speed c2, depth z2 and sound speed gradient of the third layer are the same as oneof the most bottom layer of measured SSP. Therefore, the sound speed c2 and the depth z2

of the second layer are known. But the parameters of the first layer seem to be unknown,which include surface sound speed c0, sound speed c1, and depth z1. Surface sound speedhas much influence on sound ray tracing for linear array (Beaudoin, Hughes Clarke, andBartlett 2004). At first, we use Eq. (2) to correct surface sound speed errors according to theinterpolation of measured SSPs. Then new positions of beam footprints can be recalculatedafter the correction of surface sound speed errors. Next, we assume that the original watercolumn only has one layer and the sound speed is 1500 m/s. Then the travel time and launchangle of each beam can be recalculated using the across-track distance and depth, insteadof using raw records. The surface sound speed c0 in our model can be also considered as1500 m/s. If we assume that the two upper layers have the same thickness, the depth z1 willbe half of the depth z2 of the second layer. There will be only one unknown parameter left,i.e. sound speed c1. The variance of c1 will continuously change the area between SSP anddepth axis, causing the 3D positions of beam footprints to continuously move. Because weonly want to seek an equivalent SSP to displace unknown real SSP, we can make abovesuppositions. Then a Fibonacci search algorithm is adopted to obtain the sound speed c1.The sound speed c1 will be acquired if it becomes minimal for the squared sum of differencebetween the same positions of overlapping beams. Finally, an equivalent SSP is obtained.The spatial position of each beam will be recalculated according to the equivalent SSP. Tolimit the impact of terrain and avoid seeking an equivalent SSP where a single SSP cannotcontrol the real scope, multibeam data must be divided into many subregions. Each pingin subregions is projected along track direction. However, a discontinuity will occur at theedges of subregions. To solve this problem, the model parameters of each subregion willbe only represented by the central ping. The specific parameters of all other pings will becalculated through the interpolation of the c1 estimates between subregions.

The stop criterion of the search can be expressed as

d2min = min

∑ (z1i − z2

i

)2, (7)

where subscript i denotes the number of point, and superscripts denote the number of swath.To avoid being trapped in a local minimum, we need to limit an initial search scope.

The initial average value cin of speed c1 can be calculated based on the assumed lunch angleand travel time in each subregion. The search scope of sound speed c1 is [cin, 1600] or [cin,1400] according to whether the refraction artifacts are like a “smile” or a “frown.” It is solarge a scope that can cover any actual area under the profile.

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240 F. Yang et al.

Figure 3. Refraction artifacts in flat seafloor caused by inaccurate SSPs.

Data Analysis and Discussion

At first, a flat seafloor with the depth of 100 m is simulated. There are eight layers havingconstant sound speed gradient (Figure 3). The sound speeds of those layers are, respectively,1534.5 m/s, 1545.5 m/s, 1536.0 m/s, 1523.1 m/s, 1509.0 m/s, 1517.6 m/s, 1535.8 m/s, and1543.5 m/s from the surface layer to bottom layer. The bottom depth of those layers are,respectively, 6.3 m, 26.0 m, 43.7 m, 45.5 m, 50.0 m, 52.6 m, 64.2 m, and 100.0 m. It isassumed that the measured sound speed is 1534.5 m/s and only one layer exists. There are127 beams for the equidistant MBES. The distance between neighboring beam footprintsis about 4 m on the seafloor. Each swath has 15 beams in the overlap. The inaccurate soundspeed causes a concave artifact.

Our algorithm obtained good results after the removal of the sound refraction artifactsaccording to the simulated data (Table 1). In Table 1, although the refraction artifactsare serious, the maximal error of depth is only 0.02% after the data are corrected. Thedepth standard of IHO is

√(0.52 + (0.013 ∗ 100)2 = 1.4 m with a probability of 95%

(S-44 publication (v.4), Order 1). The simulated result easily meets the requirement. Themaximal error of horizontal position is only ±0.06 m (Table 1). It also easily meets therequirement of IHO in positional precision. The similar oblique seafloor is also simulated(Figure 4a). A good corrected result is also obtained (Figure 4b). Therefore, this methodcan be applied in both flat and oblique seafloor.

Figure 4. Refraction artifacts in oblique seafloor caused by inaccurate SSPs (a) and the result afterremoving artifacts (b).

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241

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242 F. Yang et al.

Figure 5. The raw sun-illuminated swath terrain (a) and the corrected result (b).

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A Post-Processing Method for the Removal of Refraction Artifacts 243

In 2005, The Second Institute of Oceanography of State Oceanic Administration carriedout a multibeam survey project in the South China Sea. The multibeam system used wasthe Seabeam2100. The real data presented in this paper are a part of investigating data. Thescope of our example is from (EL112.50◦, NB13.00◦) to (EL115.31◦, NB15.24◦). Data areshown as a sun-illuminated terrain image (Figure 5a). It includes 42 swaths, with a fewswaths complementary and irregular. The maximal depth is about 6500 m and the minimaldepth is about 350 m. To explain the problem clearer, we extracted 7 swaths to expatiatethe algorithm (the polygon region in northeast corner of Figure 5a). The extracted dataare also illustrated in a sun-illuminated terrain image (Figure 6a). Then we transform allbeam footprints from geographical coordinates to Cartesian coordinates. A narrow andflat seafloor (thick line positions in Figure 6a) is selected to check roll mount angle bias.Figure 7a is the profile of the selected seafloor. The scale of depth axis is bigger than that ofthe abscissa axis. An obvious roll mount angle bias can be found in Figure 7a. Accordingto the manual adjustment, a bias of 23’ is obtained. Afterwards, all data are correctedaccording to this bias (Figure 7b). Because many swaths are longer than 100 km, a singleSSP cannot perfectly represent such large areas. Furthermore, to avoid the influence ofterrain, every two swaths should be divided into several subregions according to the scopeof depth. Otherwise, the equivalent SSP model will not represent the real SSP. Figure 8shows how to subdivide the left two swaths in Figure 6 into 7 subregions. Although the wayof dividing may be a little random, we should follow the principles. First, each subregionshould not be too long and should have almost depth; second, flat and slope seafloorsshould be divided into different subregions. Then the parameter c1 of each subregion canbe computed using our algorithm. If we suppose that the equivalent SSP model parameterscorrespond to the center of the subregion, each ping will have different parameters through

Figure 6. The raw sun-illuminated swath terrain (a) and the corrected result (b) of extracted 7 swathsfrom Figure 5(a).

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244 F. Yang et al.

Figure 7. The correcting processes: (a) raw 7 swaths, (b) after roll mount angle bias is removed,(c) after sound refraction artifacts are removed, (d) after redundant edge beams are automaticallydeleted.

interpolating. From Figure 7b we see that there is a minor “smile” in each swath. It canbe inferred that there are the refraction errors in survey data. A result can be obtained afterthe artifact is removed according to our algorithm (Figure 7c). After that, some redundantedge beams are automatically deleted according to their positions in the overlap, becausethey usually have big errors due to the flaw of device (Figure 7d). Finally, a mosaic terrainimage is obtained (Figure 5b and Figure 6b).

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A Post-Processing Method for the Removal of Refraction Artifacts 245

Figure 8. Region segmentation of the left two swaths in Figure 6.

By comparing Figure 5b with Figure 5a, it can be seen that a good result is obtained forreal data after roll mount angle bias and the refraction artifact are removed. Otherwise, theneighboring swaths can not be mosaiced. Division into subregions improves the accuracyof equivalent SSP model parameters. Interpolating on model parameters eliminates thediscontinuity among the edges of subregions. After the model parameters are obtained, i.e.,an equivalent SSP is formed, each beam footprint is recalculated by the equivalent SSP. Webelieve the equivalent SSP should be the replacement of unknown real SSP.

Conclusions

The qualities of edge beams are usually poor in multibeam systems. Sound refractionartifacts are one of the main factors. To improve the quality and increase the efficiency, amethod of removing refraction artifacts is studied in this paper. We presented an equivalentSSP model with three layers. The model has only one unknown parameter, i.e., sound speedc1, after we have made some reasonable assumptions. Then it can be obtained by a Fibonaccisearch algorithm. In other words, an equivalent SSP has been acquired. The positions of all

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246 F. Yang et al.

beams will be recalculated according to the equivalent SSP. We have developed the MbPPP(Multibeam Precise Post-processing) tool using these algorithms. From the analysis ofsimulated and real data, we draw the following conclusions.

1. Roll parameter offset, imperfect tide correction, and the incorrect beam steeringmust be checked to improve the calculation of refraction parameters. If these biasesexist, they must be removed at first.

2. To avoid the influence of terrain and long distances involving different SSP, eachtwo neighboring swaths must be divided into several subregions according to thescope of the depth.

3. To avoid the discontinuity between the neighboring subregions, the modelparameters of each ping should be interpolated according to that of each subregion.The searched parameters are considered as the parameters of central ping in thesub-region.

4. The method is based on equivalent sound speed profile. It is effective for improvingthe qualities of edge beams, especially in an estuary.

However, it should be known that it is not the best method for improving the qualitiesof multibeam data. A detailed SSP should be measured under real survey as accurateas possible. When SSP is accurate, there are no refraction artifacts. The post-processingmethod should be applied to the situation where accurate SSP cannot be obtained duringthe surveying. The future works will further research how to inverse precise sound speedfield according to the measured SSP. This sound speed field has four variables, i.e., 3Dposition and time. Any footprint can be precisely traced if the field is known.

References

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A Post-Processing Method for the Removal of Refraction Artifacts 247

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