Part A | 8.2
178 Part A Fundamentals
present a brief description of the science behind electromagnetic fields and their interaction with an ocean
environment.
Pure water is a very good dielectric. Its permittivity is given by " D " 0 " w , where " 0 is the free-space
permittivity ( 8:8541878176 10
12 F=m), and " w is
the water’s dielectric constant equal to approximately
80:1 at 20
ı C. Due to the strong covalent bonds of
the hydrogen and oxygen atoms in the water molecule,
there are no electrons in the conduction band until
they are pumped up to that energy level by applying high amplitude electric fields. If the field reaches
a few megavolts=cm, pure water will undergo a dielectric breakdown forming an electric arc in the process.
Although pure water is a very good insulator, seawater
is a good electric conductor.
The disassociated salt ions in seawater cause it to be
a good electric conductor at all field levels. Although
electrons are the primary charge carriers in metallic conductors, the positively charged salt ions, called
cations and negatively charged anions, are both charge
carriers in seawater. If a source of electric potential gradient is introduced into the seawater, the cations will
migrate toward the source’s cathode (negative pole),
while the anions travel toward the anode (positive pole).
Electrochemical reactions occur at the anode, releasing
electrons in the process that then flow in the source’s
metallic conductor to the cathode where they recombine
with the cations.
The mobility of seawater ions is hampered by their
interaction with water molecules as they migrate, resulting in loss of energy in the form of heat. At the
engineering level, seawater can be treated as a simple
conductor with an electric conductivity ranging from
about 2:5 S=m in cold deep waters, and approaches
6 S=m in very warm waters. (A value of 4 S=m is
typically used for open ocean seawater.) This finite
conductivity attenuates electromagnetic energy as it
propagates through seawater, which is categorized as
a lossy medium.
Fortunately, seawater is nonmagnetic. Its magnetic
permeability is the same as free-space given by 0 D
410
7 H=m. This means the only way that seawater
can be a source of a static magnetic field is by electric
current flowing through it.
This chapter will focus on the science of electromagnetic field propagation and attenuation in seawater,
and the reflection and transmission of the fields at the
sea’s surface. Emphasis will be placed on electromagnetic field theory in the ultralow frequency (ULF) band
of 0 to 3 Hz, and the extremely low frequency (ELF)
band from 3 Hz to 3 kHz. Since the attenuation of electromagnetic waves increases rapidly with frequency,
radio frequency bands will not be covered here. Although remote observations of the sea surface from
airborne and satellite-based microwave radiometers and
radars are important tools for oceanographic research,
they are beyond the scope of this discussion. (The interested reader should consult [8.1, pp. 405–510] on this
topic.) A brief cursory discussion of ocean electromagnetics at optical wavelengths will be given at the end of
this chapter.
8.2 Electromagnetic Field Theory
It is not possible to give an in-depth description of general electromagnetic field theory here. A comprehensive
treatment of engineering electromagnetics is presented
in [8.2]. In order to introduce some basic principles for
electromagnetic fields in a lossy media such as seawater, the formulations for magnetic and electric fields in
an unbounded ocean will be presented first.
All electromagnetic field theories are based on
Maxwell’s equations. In differential form, they are
r r E D D
@B
@t
;
(8.1)
r r H D J C
@D
@t
;
(8.2)
r r D D q e ;
(8.3)
r r B D 0 ;
(8.4)
where E (v=m) and H (A=m) are the electric and magnetic field intensity vectors, D (c=m
2 ) and B (wb=m
2
or T) are the electric and magnetic flux density vectors,
J (A=m
2 ) is the electric current density, q e (c=m
3 ) represents the electric charge density, and t stands for time
(seconds). Maxwell’s equations by themselves are sufficient to solve any problem in electromagnetics.
Although magnetic charge and magnetic current
densities are not realizable, they can be included in
Maxwell’s equations through the generalized current
concept to aid mathematically in the solutions of certain problems. For example, a magnet can be represented mathematically as two opposite polarity magnetic charges at its ends. Adding the virtual magnetic
sources to Maxwell’s equations, and separating the
current density into its impressed and conduction components, allows (8.1) through (8.4) to be written in
a more symmetrical form as
r r E D DM i
@B
@t
;
(8.5)
178 Part A Fundamentals
present a brief description of the science behind electromagnetic fields and their interaction with an ocean
environment.
Pure water is a very good dielectric. Its permittivity is given by " D " 0 " w , where " 0 is the free-space
permittivity ( 8:8541878176 10
12 F=m), and " w is
the water’s dielectric constant equal to approximately
80:1 at 20
ı C. Due to the strong covalent bonds of
the hydrogen and oxygen atoms in the water molecule,
there are no electrons in the conduction band until
they are pumped up to that energy level by applying high amplitude electric fields. If the field reaches
a few megavolts=cm, pure water will undergo a dielectric breakdown forming an electric arc in the process.
Although pure water is a very good insulator, seawater
is a good electric conductor.
The disassociated salt ions in seawater cause it to be
a good electric conductor at all field levels. Although
electrons are the primary charge carriers in metallic conductors, the positively charged salt ions, called
cations and negatively charged anions, are both charge
carriers in seawater. If a source of electric potential gradient is introduced into the seawater, the cations will
migrate toward the source’s cathode (negative pole),
while the anions travel toward the anode (positive pole).
Electrochemical reactions occur at the anode, releasing
electrons in the process that then flow in the source’s
metallic conductor to the cathode where they recombine
with the cations.
The mobility of seawater ions is hampered by their
interaction with water molecules as they migrate, resulting in loss of energy in the form of heat. At the
engineering level, seawater can be treated as a simple
conductor with an electric conductivity ranging from
about 2:5 S=m in cold deep waters, and approaches
6 S=m in very warm waters. (A value of 4 S=m is
typically used for open ocean seawater.) This finite
conductivity attenuates electromagnetic energy as it
propagates through seawater, which is categorized as
a lossy medium.
Fortunately, seawater is nonmagnetic. Its magnetic
permeability is the same as free-space given by 0 D
410
7 H=m. This means the only way that seawater
can be a source of a static magnetic field is by electric
current flowing through it.
This chapter will focus on the science of electromagnetic field propagation and attenuation in seawater,
and the reflection and transmission of the fields at the
sea’s surface. Emphasis will be placed on electromagnetic field theory in the ultralow frequency (ULF) band
of 0 to 3 Hz, and the extremely low frequency (ELF)
band from 3 Hz to 3 kHz. Since the attenuation of electromagnetic waves increases rapidly with frequency,
radio frequency bands will not be covered here. Although remote observations of the sea surface from
airborne and satellite-based microwave radiometers and
radars are important tools for oceanographic research,
they are beyond the scope of this discussion. (The interested reader should consult [8.1, pp. 405–510] on this
topic.) A brief cursory discussion of ocean electromagnetics at optical wavelengths will be given at the end of
this chapter.
8.2 Electromagnetic Field Theory
It is not possible to give an in-depth description of general electromagnetic field theory here. A comprehensive
treatment of engineering electromagnetics is presented
in [8.2]. In order to introduce some basic principles for
electromagnetic fields in a lossy media such as seawater, the formulations for magnetic and electric fields in
an unbounded ocean will be presented first.
All electromagnetic field theories are based on
Maxwell’s equations. In differential form, they are
r r E D D
@B
@t
;
(8.1)
r r H D J C
@D
@t
;
(8.2)
r r D D q e ;
(8.3)
r r B D 0 ;
(8.4)
where E (v=m) and H (A=m) are the electric and magnetic field intensity vectors, D (c=m
2 ) and B (wb=m
2
or T) are the electric and magnetic flux density vectors,
J (A=m
2 ) is the electric current density, q e (c=m
3 ) represents the electric charge density, and t stands for time
(seconds). Maxwell’s equations by themselves are sufficient to solve any problem in electromagnetics.
Although magnetic charge and magnetic current
densities are not realizable, they can be included in
Maxwell’s equations through the generalized current
concept to aid mathematically in the solutions of certain problems. For example, a magnet can be represented mathematically as two opposite polarity magnetic charges at its ends. Adding the virtual magnetic
sources to Maxwell’s equations, and separating the
current density into its impressed and conduction components, allows (8.1) through (8.4) to be written in
a more symmetrical form as
r r E D DM i
@B
@t
;
(8.5)