Available via license: CC BY-NC 4.0
Content may be subject to copyright.
Highlights in Science, Engineering and Technology
ESETEP 2024
Volume 104 (2024)
207
Research on survey line arrangement of a multibeam
bathymetric system in ocean mapping
Hongtao Xu 1, *, #, Feiyu Zhang 2, #, Yuyang Wang 3, #
1 School of Electrical Engineering and Automation, Wuhan University, Wuhan, China, 430072
2 School of Remote Sensing and Information Engineering, Wuhan University, Wuhan, China,
430072
3 School of Computer Science, Wuhan University, Wuhan, China, 430072
* Corresponding author: 18150958955@163.com
#These authors contributed equally.
Abstract. Submarine topography measurement technology is an important technology for exploring
marine resources. Multi-beam bathymetry systems have high efficiency and important application
value in underwater resource surveys, marine delimitation, and other fields. They are currently one
of the most widely used measurement technologies. This study aims to optimize multi-beam
bathymetry technology and apply it to seabed topography measurement, achieving a transition from
point measurement to line measurement and minimizing measurement paths. A mathematical model
was established for the coverage width and overlap rate between adjacent bands of multi-beam
bathymetry at a given water depth based on planar geometric modeling and three-dimensional
geometric modeling. The model was applied to a rectangular sea area with a length of 2 nautical
miles (3704 meters) from north to south and a width of 4 nautical miles (7408 meters) from east to
west. The optimal survey line planning was obtained as follows: all survey lines are in the north-
south direction, with a total of 34 survey lines and a total length of 68 nautical miles. This model has
good solution results for optimizing the layout of survey lines under different seabed conditions and
can adjust important parameters of the system according to different conditions. The model has
broad practical significance and can provide a reference for ocean-sounding work and other fields
with high accuracy.
Keywords: Multi-beam sounding, geometric model, target planning model.
1. Introduction
With the gradual deepening of research on the structure of the Earth, ocean exploration has become
an important research direction, and related technologies have developed rapidly in recent years.
Among them, seabed topography measurement is a fundamental marine surveying work [1], which
mainly constructs seabed topography and landforms by measuring the three-dimensional coordinates
of seabed points. For underwater topography measurement, the measurement of water depth is
particularly important. Currently, the main depth measurement technologies in the industry include
single-beam depth measurement and multi-beam depth measurement. Compared to the limitations of
traditional single-beam detectors, multi-beam detection systems can achieve full coverage and precise
scanning of the seabed without dead angles, allowing users to obtain clear, comprehensive, and high-
precision underwater microtopography and landforms [2]. In the process of multi-beam depth
measurement, each measuring line will obtain a strip with a certain width, and the coverage width of
the strip varies with the change of the transducer opening angle and water depth. To prevent missing
measurements between bands, there is generally a certain degree of overlap between the bands [3].
To ensure the convenience of measurement and the integrity of data, the overlap rate between adjacent
bands should be maintained between 10% and 20%. Therefore, setting up a reasonable route is a
crucial aspect.
Ma et al. established a large-scale, high-resolution seabed DEM and implemented database
management based on multi-beam sounding data using ArcGIS and GeoDatabas technologies [4];
Tian et al. obtained accurate water depth of the navigation channel using multi-beam depth
Highlights in Science, Engineering and Technology
ESETEP 2024
Volume 104 (2024)
208
measurement technology [5]; Xia et al. used a multi-beam depth measurement system to finely
measure the bed terrain of a typical section of the Upper Jingjiang River for the first time. They used
an improved sand wave morphology quantification algorithm to statistically analyze various sand
wave morphology parameters and analyze the changing characteristics of sand wave morphology
under different water flow intensities [6]; Zhao et al. combined the multi-beam system with unmanned
ship technology and applied it in underwater terrain measurement, simplifying the installation and
calibration process of sounding equipment and improving operational efficiency [7].
All of the above studies have investigated the application of multibeam bathymetry in different
occasions, while the studies on the planning of survey lines when using multibeam bathymetry in
different situations are relatively lacking. To analyze the relationship between the coverage of
multibeam bathymetry and the routes in different situations, and to facilitate the application of
multibeam bathymetry to more scenarios, this paper uses the data provided by the website
https://cumcm.cnki.net to first analyze the coverage width of a single survey line along the direction
of constant water depth at a certain moment for a non-flat seabed, and further study the overlap rate
between equidistant routes. Then we take the center of a certain area size as the position of the survey
vessel and study the coverage width of the survey vessel at different angles and distances by building
a three-dimensional model. Finally, taking the length of the measuring line as the optimization
objective, an optimization model is built, and the length and orientation of each measuring line under
the shortest measuring line are finally obtained by analyzing the feasibility under different situations.
2. Two-dimensional geometric model
2.1. Width analysis
For a non-flat seabed, the coverage width of the strip is the horizontal distance between the
intersection of the outermost beam and the seabed [8]. In this section, the construction process of the
width model is analyzed using the example of the survey vessel on the left side of Figure 1.
Figure 1. Schematic diagram of the calculation of the overlap rate between neighboring bands
(1) Relationship between angles and edges
If the angle of the multi-beam transducer is θ, the seabed slope is α, it can be obtained from the
formula for the inner angle of a triangle
(1)
By the sine theorem
Highlights in Science, Engineering and Technology
ESETEP 2024
Volume 104 (2024)
209
(2)
(2) Construction of the width model
According to the integration of formulas (1) and (2), the strip coverage width model is
(3)
2.2. Analysis of overlap rates
The calculation of the overlap rate needs to take the coverage width of the two sides of the survey
line as a reference respectively, so the coverage width of the two strips needs to be calculated.
According to the width model, the overlap rate model can be constructed as:[9]
(4)
Where denotes the overlap rate when takes and denotes the overlap rate when
takes .
3. Three-dimensional model
Since the coverage width of the survey vessel at any point along any direction in the sea area to
be measured is different, here in this paper, only the survey line through the center point of the sea
area is considered, and the schematic diagram is shown in Figure. 2.
Figure 2. Three-dimensional model of the work of the survey ship
Assume that at a certain moment, the measuring ship reaches the position of point S. At this time,
the intersection point of point S vertically downward with the seabed is set as O, and the intersection
points of the outermost beam and the seabed are A and B, respectively, that is, the measuring line is
perpendicular to the plane SAB. Extend SO, set the intersection of the extension line of SO and the
dashed horizontal plane as O′, extend AB, set the intersection of the extension line of AB and the
dashed horizontal plane as B′.
Take point C on the line of intersection of the submarine slope and the dashed horizontal so that
the line B′C is perpendicular to the plane OO′C. It is easy to obtain that <OO′C = <OO′B′ = <O′CB′
=
Let the dip of the seafloor slope, <OCO′ = α, <OB′O′ = β, <O′B′C = ψ, and <OB′O′ = γ. If the
magnitude of γ can be found, the previous width model can be used.
(1) Analysis of the three-dimensional dimension
Highlights in Science, Engineering and Technology
ESETEP 2024
Volume 104 (2024)
210
Analyzing Rt∆OO′C, Rt∆O′CB′ and Rt∆OO′B′ we get:
(5)
Joining the three equations in formula (5), we get.
(2) Analysis of the two-dimensional dimension
So to find out the magnitude of γ, we must first solve for the magnitude of ψ. The horizontal plane
given in the question is analyzed, and the relationship between the vectors and the auxiliary lines is
shown in Figure 3 (a). analysis, the relationship between the vectors and the auxiliary lines is shown
in Figure 3 (a). Since the direction of vector
is the same as the projection of the normal direction
of the slope on the horizontal plane, MN ⊥ NC, and similarly, the direction of vector
is the
same as the projection of the direction of the survey line on the horizontal plane, so MO′ is
perpendicular to the plane SAB, and so MO′ ⊥ O′B′.
Combining these analyses, the angles in quadrilateral MNCO′ and triangle O′CB′ satisfy the
following relations respectively:
(6)
Since MO′⊥ O′B′, it follows that:
(7)
Substituting formula (7) into formula (6) yields:.
Assuming that the depth of seawater at the center of the sea area is, the depth of seawater here
is set to be when the angle between the direction of the line of measurement and the normal
direction of the seafloor slope is in the horizontal plane and the distance of point S from the center
of the sea area is s. The top view of the sea level is shown in Figure 3 (b).
Figure 3. (a) Schematic of sea floor level; (b) Top view
The above figure shows that the displacement of S relative to the center point of the sea area in the
direction of the projection of the normal direction of the slope along the bottom of the sea on the
horizontal plane is: (8)
Where, if , denotes the direction of displacement in the opposite direction of the
projection of the normal direction of the bottom slope along the horizontal plane.
Since the magnitude of the slope of the seabed slope is α, the depth of water at point S is:
Highlights in Science, Engineering and Technology
ESETEP 2024
Volume 104 (2024)
211
(9)
Combined with the previously established width model, the three-dimensional model can be
obtained as:
(10)
4. Line planning model
In the actual planning process of the survey line, it is necessary to always ensure that the overlap
rate between neighboring strips is between 10% and 20%, so it is necessary to plan the navigation
route of each survey line in turn according to the size of the overlap rate [10].
Assuming that the length of the ith measuring line is, the total length of the measuring line is
, and the spacing of the measuring line between the th measuring line and the th measuring
line is . Take the southwest corner of the rectangular area to be measured as the origin of
coordinates, and take the direction of due east as the positive direction of the -axis, and the direction
of due north as the positive direction of the -axis to set up the planar right-angle coordinate system.
Since each measuring line is a straight line, let the function corresponding to the th measuring line
be (11)
Let the region that can be probed by the th line be the set and the region to be measured by
the set .
Consider a rectangular sea area with a north-south length of 2 nautical miles (3704 m) and an east-
west width of 4 nautical miles (7408 m), with a seawater depth of 110 m at the center point of the sea
area, deep in the west and shallow in the east, with a slope of 120°, a gradient of 1.5°, and a multi-
beam transducer opening angle of 120°. In summary, the survey line planning model is established
as follows:
The objective function is: (12)
The constraints are:
① Overlap between neighboring bands is between 10 and 20 percent:
(13)
② Survey ships can only work within the sea area to be surveyed:
(14)
③ Complete coverage of the entire sea area to be measured:
(15)
In summary, the survey line planning model is:
Highlights in Science, Engineering and Technology
ESETEP 2024
Volume 104 (2024)
212
(16)
5. Solving the line-planning model
The opening angle of the multibeam transducer is set to 120◦, the slope is set to be 15◦, and the
depth of seawater at the center point of the sea area is set to 70 m. Using the geometrical model, the
depth of seawater under different positions is obtained, and the coverage width of the survey line and
the overlap rate with the previous survey line are shown in Table 1.
Table 1. Arithmetic example results for geometric model solving
Distance of the line from the center point
/m
depth of sea
/m
Coverage width
/m
Overlap with previous
line/%
-800
90.95
315.71
-
-600
85.71
297.53
32.78
-400
80.47
279.35
28.40
-200
75.24
261.17
23.42
0
70
242.99
17.69
200
64.76
224.81
11.04
400
59.53
206.63
3.21
600
54.29
188.45
-6.13
800
49.05
170.27
-17.46
The original setting is unchanged, now based on the original data, the three-dimensional model is
utilized to solve the coverage width of the survey line under different survey line inclinations and
different positions, and the calculation results are shown in Table 2.
Table 2. Arithmetic example results of the three-dimensional model solution
Coverage width /m
Measurement of the distance of the ship from the center point of the sea
area mile
0
0.3
0.6
0.9
1.2
1.5
1.8
2.1
Measuring line direction
angle /°
0
415.69
466.09
516.49
566.89
617.29
667.69
718.09
768.48
45
416.12
451.79
487.47
523.14
558.82
594.49
630.16
665.84
90
416.55
416.55
416.55
416.55
416.55
416.55
416.55
416.55
135
416.22
380.45
344.77
309.10
273.42
237.75
202.08
166.40
180
415.69
365.29
314.89
264.50
214.10
163.70
113.30
62.90
225
416.12
380.45
344.77
309.10
273.42
237.75
202.08
166.40
270
416.55
416.55
416.55
416.55
416.55
416.55
416.55
416.55
315
416.12
451.79
487.47
523.14
558.82
594.49
630.16
665.84
In the rectangular sea area considered in 4, it is necessary to determine the direction of the survey
line, which is broadly categorized into the following three cases:
① The measured line is in the north-south direction
When the direction of the survey line is north-south, the vertical distance from the same survey
line to the seabed remains constant when the survey vessel works along each line, and then the first
survey line needs to be planned from the easternmost or westernmost. Then plan the second line
according to the probe range and overlap rate of the first line, and so on, as shown in Figure 4(a).
Highlights in Science, Engineering and Technology
ESETEP 2024
Volume 104 (2024)
213
Figure 4. (a) Schematic of north-south alignment (b): Schematic of east-west alignment
To ensure that the final total length of the measurement line is the shortest, so set the overlap rate
between the measurement lines is 10%, the results are shown in Table 3 and Table 4.
Table 3. Plot of lines where the first line is located in the westernmost part of the line
line
number
The x-coordinate of
the measurement line
x-coordinate corresponding to
the western boundary of the
coverage area
x-coordinate corresponding to
the eastern boundary of the
coverage area
Coverage
width (m)
1
358.52
0.00
685.93
685.93
2
947.86
617.34
1249.70
632.36
…
…
…
…
…
33
7345.43
7318.85
7369.69
50.84
34
7389.11
7364.61
7411.48
46.87
Table 4. Line plan with the first line in the easternmost part of the line
line
number
The x-coordinate of
the measurement line
x-coordinate corresponding to
the western boundary of the
coverage area
x-coordinate corresponding to
the eastern boundary of the
coverage area
Coverage
width（m）
1
7385.47
7360.80
7408.00
47.20
2
7341.48
7314.72
7365.92
51.20
…
…
…
…
…
33
898.81
565.96
1202.78
636.82
34
305.32
-55.73
635.04
690.77
The corresponding line planning diagrams are shown in Figure 5 and Figure 6 respectively.
Figure 5. Plot of the first line in the westernmost part of the line
Highlights in Science, Engineering and Technology
ESETEP 2024
Volume 104 (2024)
214
Figure 6. Line plan with the first line in the Far East
② The measured line is in an east-west direction
The survey line is planned as shown in Figure (4) b. The width of coverage of the strip is calculated
to be 717.04 m in the westernmost part and 45.06 m in the easternmost part.
(1) If the overlap rate of neighboring lines in the easternmost part is 10%, the distance d between
two neighboring lines is 40.55m. At this time, the overlap rate of neighboring lines in the westernmost
part is 94.34%>20%, which does not meet the meaning of the question, so it is discarded.
(2) If the overlap rate of neighboring lines in the easternmost part is 20%, the distance d between
two neighboring lines is 36.05m. At this time, the overlap rate of neighboring lines in the westernmost
part is 94.97%>20%, which is not in line with the meaning of the question, so it is discarded.
(3) If the overlap rate of neighboring lines in the westernmost part is 10%, the spacing d between
two neighboring lines is 645.34 m. Since the coverage width of the strip in the easternmost part is
45.06 m < the spacing between two neighboring lines, η < 0, the omission occurs, which does not
conform to the meaning of the question, and it is discarded.
(4) If the overlap rate of adjacent lines in the westernmost part of the strip is 20%, then the spacing
d between two adjacent lines is 573.63 m. Since the width of the strip in the easternmost part of the
strip is 45.06 m < the spacing between two adjacent lines, η < 0, there is a leakage of measurements,
which is not in line with the meaning of the question, so it is discarded.
Therefore, the requirement is not satisfied when the survey line is in the east-west direction.
The line of sighting is in the other direction
When the direction of the measuring line is neither parallel nor coincident with the x-axis nor with
the y-axis, as shown in Figure 7.
Where the hexagon is the coverage of the measurement line (beyond the
rectangular to-be-measured area is ignored). In order not to have a missed measurement, the coverage
of the next measurement line must include the point , which is the boundary line at the
lower right of the coverage of , and the point coincides with the point . At this point, the
overlap rate =50%>20% between the strips corresponding to the survey line and the survey
line is not in line with the meaning of the question rounded off.
Highlights in Science, Engineering and Technology
ESETEP 2024
Volume 104 (2024)
215
Figure 7. Schematic diagram of line measurement in other directions
In summary, the optimal line plan is: all lines are in a north-south direction, with a total of 34 lines
and a total line length of 68 nautical miles (125,936 m).
6. Conclusion
In this paper, by analyzing the multibeam transducer opening angle, seabed slope line direction,
the model of line coverage width and line planning model is established, according to the
characteristics of the seabed in the sea area, analyzing the situation corresponding to different line
directions, and designing the shortest line program, which provides a reference program for a certain
range of multibeam surveying. In real life, this paper can not only bring help to the seabed topographic
survey but also provide a certain degree of reference when using UAVs to photograph unknown areas,
even mountainous areas.
References
[1] LIN Haiwen, AN Qunchuan, FANG Jie. Application of several detection methods in marine topographic
mapping [J]. Mapping and Spatial Geographic Information, 2023, 46 (06): 188 - 190+194.
[2] Guan Xiaohan. Advantages of multibeam bathymetry technology and new ideas of ocean mapping [J].
China Water Transportation, 2019 (05): 51 - 52.
[3] Xu D, Lv B, Cui X. A study on the buried depth test of bridge enlarged foundation based on multibeam
detection. Urban Roads and Bridges and Flood Control, 2021 (10): 196 - 198.
[4] Ma Jianlin. Research on digital seabed topography based on multibeam and ArcGIS and its realization
[D]. Zhejiang University, 2005.
[5] Tian Peixian, Chen Weijian, Lin Qihui, et al. Application of geophysical survey techniques for offshore
waterways. Physical and Chemical Exploration, 2023, 47 (06): 1450 - 1455.
[6] Xia Junqiang, Cao Yuqin, Zhou Meirong, et al. Characterization of sand wave patterns in a typical section
of the Upper Jing River based on a multibeam topographic survey. Lake Science, 2023, 35 (06): 214 4 -
2154.
[7] Zhao Baocheng, Xu Jian, Xu Jian, et al. Application of multibeam system for underwater topographic
survey based on unmanned vessel. Geospatial Information, 2023, 21 (09): 65 - 68.
[8] Ning Jinsheng. Introduction to Surveying and Mapping: Wuhan University Press., 2004.
[9] WANG Ning, JING Huang, SWEET Rao. Line optimization model under multibeam bathymetric system
[J]. Electroacoustic Technology,2023,47 (06): 61 - 64.
[10] WANG Nan, YU Zhicheng, WANG Jingxian. Multibeam line placement model based on dynamic
planning [J]. Journal of Nantong Vocational University, 2023, 37 (04): 64 - 69+97.