An Investigation into Speed of Sound and Depth
Calculations for Subsea Navigation
Alberto Brines Corral
Supervisor: Dr. J.C. Iliffe
MSc in Hydrographic Surveying - Project
METHODOLOGY
INTRODUCTION
In this project a deep review of both speed of sound and depth equations
Literature review methodology approach:
Density. Good CTD data means
good density profile, therefore,
good depth data for LBL and
USBL applications
available for subsea navigation systems such as Long Base Line (LBL) and
“International one
atmosphere equation”
Ultrashort Base Line (USBL) is carried out. These equations (UNESCO, Del
Grosso, Coppen, Mackenzie, etc.) are used to obtain speed of sound and
Density calculations from
temperature and salinity
data
depth from Conductivity, Temperature and Pressure measurements from CTD.
“Millero et al, 1976
equation”
Density
pressure
effect. Millero
et al 1980
“Poisson et al, 1981
equation”
Even although high accuracy velocimeters based on “time of flight” approach
Different
temperature
and salinity
range. Density
results and
comparison.
“UNESCO formula”
Different latitude/
longitude and
pressure range
Density for
pressure to
depth
conversions
Matlab implementation
+
Different Gravity formulas:
•  Anon 1970
•  Helbert
•  Old international 1967
•  International 1980
Results and
comparison
are widely used to derive speed of sound in subsea navigation systems,
Matlab implementation
formulae conversions are still an usual practice in industry. There is a
“Mackenzie’s equation
1981”
remarkably lack of standardisation on procedures when it comes to use these
Different
temperature
and salinity and
pressure.
Speed of
sound results
and
comparison.
“Coppen’s equation,
1981”
Formulae to convert
Temperature, Salinity and
Pressure/Depth from CTD
data to speed of sound
formulae and also uncertainties in the value of the speed of sound depending
on the formula applied.
“UNESCO, Chen and
Millero equation, 1997”
“Del Grosso equation,
1974”
What happens if we are wrong in speed of sound?. Coordinate of unknown points
estimated by means of least squares under different scenarios of speed of sound
errors.
“EOS-80 equation”
Besides the literature review, real CTD data collected at field are investigated,
Matlab implementation
most of these data (speed of sound profiles and raw CTD data) show the
Speed of sound anomalies methodology approach:
presence of speed of sound anomalies in deep waters beyond 2.000 metres
Set of 40 profiles of real
data from CTD. Speed of
sound profiles and
temperature, pressure
and salinity raw data
depth. Anomalies can be a natural phenomenon but also can be a
consequence of the formula or procedure applied to derive speed of sound
Data and sound speed
anomaly description if
detected.
Spatial and temporal
relationship between
profiles
Correlation analysis.
The Pearson correlation
coefficient “r” allows to
establish the degree of
linear relationship
between two variables
from raw CTD data. Since these uncertainties can lead to errors in subsea
Whole data in a profile:
-Speed of sound versus
temperature
-Speed of sound versus
salinity
Speed of sound anomaly
range depths:
-Speed of sound versus
temperature
-Speed of sound versus
salinity
Can we find any differences when applying a
certain sampling rate or formula?.
“Mackenzie’s equation
1981”
“UNESCO, Chen and
Millero equation, 1997”
“Del Grosso equation,
1974”
“Regular and
irregular data
sampling”
“EOS-80 equation”
navigation that exceeds the requirements, it is important to clarify the role of
formulae or procedures as a possible origin of errors in speed of sound
calculations.
RESULTS
Literature review:
OBJECTIVES
Seawater density for different salinity values (the
line on the bottom is for 0 ppt and additional lines
above it represent a 5 ppt increasing step
salinity), temperature and authors (red squares
are Millero, blue lines are International, black
lines are Poisson formula). Source: own.
The first objective in this dissertation is try to answer different questions
relating to how is observed and calculated depth and sound speed offshore for
subsea navigation systems, covering an explanation about different
Del Grosso and UNESCO speed of
sound results comparison. Source:
Own.
Del Grosso and UNESCO speed of
sound results comparison. Differences
at 9 celsius temperature and 5000
dbar pressure. Source: Own.
Effect of pressure in seawater density.
Source: own. Y-axis Seawater density
kg/m3. X-axis Temperature in degrees
Celsius. Source: Own.
Speed of sound anomalies:
methodologies to acquire and process data for this technologies and the
actual industry practice. It will be also covered the magnitude of the errors that
Correlation matrices. Up, whole
profile and Del Grosso method.
Down, speed of sound anomaly
range depths and State80
method. Source: Own.
can be introduced through the different processing / measurement
methodologies.
In sound velocimeters each sound velocity
measurement is made using a single pulse of
sound travelling over a known distance, so is
independent of the inherent calculation errors
present in all CTDs. (http://swathe-services.com/).
CDT system from profiling from a ship, it has integrated
temperature and conductivity sensors. Source: http://
www.seabird.com/
Methodology/procedure:
Regular or irregular
sampling
+
Formulae:
UNESCO, Del Grosso,
Coppen, etc.
Summary processing results sound speed data from P7 to P12 profiles from H16 group.
Sound speed velocity from different
methods in depths below 1850
metres. Source: Own.
Accuracy:
Depth 0.1-0.01 m.
Speed of Sound
0.2-0.5 m/s
Methodology/procedure:
“Time of Flight”
Accuracy:
Speed of Sound
0.025-0.05 m/s=
Speed of sound and
depth
CONCLUSIONS
•  Additionally to the literature review it has been clarified the role of procedures and formulae
Speed of sound and
depth
applied as a possible triggering factor for speed of sound anomalies as well as the correlations
The second objective is to clarify the origin of deep water speed of sound
between temperature, salinity dynamics and speed of sound values at those depths in which
anomalies detected in real data gathered at field.
anomalies have appeared.
Speed of sound versus depth and some anomalies detected in
different depths. Source: Msc in Hydrographic Surveying own
project.
Possible sound speed anomalies origin ?
40 sound speed
profiles and raw data
derived from CTDs
measurements in Lo
Santos plateau
(Brazil).
Environmental
processes lead to
changes in temperature/
salinity at depth:
•  Shelf eddies and
associated filaments.
•  Meandering fronts.
•  Internal waves and
tides.
•  Spicy thermohaline
structure
Instrumental/processing
methodology:
•  Irregular/regular data
sampling
•  Processing
methodology
(differences between
formulae)
•  It has been found a clear correlation between temperature and sound speed anomalies that
yields the preliminary rejection of instrumental/methodology cause for this features. The origin of
temperature/salinity changes detected need further investigation to relate them with deep water
environmental processes such as internal waves, tides and the spicy thermohaline structure that
are known to drive the dynamic of these factors.
References: “An investigation into speed of sound and depth calculations for subsea navigation. MSc in Hydrographic
Surveying project, 2014”