DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

harmonic model
harmonic model The representation of a
magnetic or gravitational field by a scalar potential
V(x,y,z) satisfying Laplace’s equation
∇ 2 V = 0, making V “harmonic”. Because
of the spherical geometry of the Earth, both its
gravity field and magnetic field are customarily
expanded in spherical harmonics, which naturally
group the expressions that make upV into
monopole, dipole, quadrupole, octopole (etc.)
terms, decreasing with radial distance r as 1/r,
1/r 2 , 1/r 3, , 1/r 4 , etc. The rate at which corresponding
field components decrease is larger by
one power of r, i.e., these decrease as 1/r 2 , 1/r 3, ,
1/r 4 , 1/r 5 , etc.
The Earth’s gravity field is dominated by its
monopole term, but the axisymmetric terms of
higherorderm,uptom= 6(termswhosepotential
decreases like 1/r m+1 ) are also needed in accurate
calculation of satellite orbits and careful
satellite studies give terms up to m≈ 20. The
magnetic field B of the Earth inherently lacks
the monopole term and its leading term, which
dominates it, is the dipole term. Higher orders
can also be fairly important near Earth, while
far from Earth additional field sources need to
be considered (see empirical models).
Since the Earth’s magnetic field gradually
changes with time (“secular variation”), scientists
periodically extract from magnetic surveys
and observations of each epoch (usually
10 years) an International Geomagnetic Reference
Field (IGRF), a harmonic model meant to
give (for that epoch) the best available representation
of the internal magnetic field and its rates
of change, expressed by a given set of spherical
harmonic coefficients and their time derivatives.
The magnetic fields of other planets have also
been represented in this manner, but because
of the scarcity of observations, their harmonic
models have a much lower accuracy.
heat capacity The thermodynamic quantity
dQ/dT , where dQ is an increment in heat energy,
and dT is the corresponding increment in
temperature. Always specified with some thermodynamic
variable held fixed, as heat capacity
at constant volume, or heat capacity at constant
pressure.
heat flow The study of how bodies generate
interior heat and transport this heat to their sur-
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faces; a subdiscipline of the field of geophysics.
Most planetary bodies begin with substantial
amounts of interior heat. Among the sources
of such heat are the heat leftover from the formation
of the body (accretion), heat produced
by differentiation, heat produced by radioactive
decay, tidal heating, and solar electromagnetic
induction. This heat can melt interior materials,
producing magma which can later erupt
onto the body’s surface as volcanism. The heat
contained in the body’s interior is transported
to the surface of the body, where it escapes to
space. The three ways in which this energy can
be transported through the interior are by radiation
(the absorption and reemission of energy
by atoms), convection (physical movement of
material, with hot material rising and cool material
sinking), and conduction (transfer of energy
by collisions between atoms). Larger bodies
are more efficient at retaining their interior
heat, which translates to a longer period of geologic
activity. The thermal evolution of a body
can be estimated by determining what mechanisms
are responsible for its heating, how the
body transports that energy to the surface, and
how long the body can retain its internal heat.
heat flow density See heat flux.
heat flux The flow of heat energy per unit
area and per unit time. It is often called heat
flow density or heat flow in geophysics.
Heaviside, Oliver (1850–1925) Physicist
and mathematician. Developed the modern vector
form of Maxwell’s equations and understanding
of the classical electrodynamics (via
fundamental physical effects predicted and evaluated
by him). He also developed the vector and
operational calculi, the ideas and applications
of δ- and step-functions, as well as many practical
applications of Maxwell’s theory in telephony
and electromagnetic waves propagation
in the atmosphere (the ionospheric layer, thus
long-range radio communications). Heaviside
wrote in the telegraph equation and analyzed its
technological consequences in 1887, predicted
Čerenkov radiation in 1888, was the first to introduce
the Lorentz force (in 1889, three years
before H.A. Lorentz), and he predicted the existence
of the Heaviside–Kennelly ionized atmo-