DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

Thus, four-velocity is the tangent four-vector
u α =dx α /ds of an affinely parametrized timelike
curve γ ={x α (s)} in the space-time. The
norm isg(u,u) =−1. See signature, spacelike
vector, timelike vector.
f-plane approximation In calculating motions
on the Earth’s surface, the effects of the
Earth’s sphericity are retained by approximating
the value of the Coriolis parameter, f, as a
constant.
fractal A geometrical object that is selfsimilar
under a change of scale; i.e., that appears
similar at all levels of magnification. Fractals
can be considered to have fractional dimensionality.
A statistical distribution is fractal if the
number of “objects” N has a fractional inverse
power dependence on the linear dimension of
the objects r.
N ∼ r −D
where D is the fractal dimension. Examples
occur in diverse fields such as geography
(rivers and shorelines), biology (trees), geology,
and geophysics (the number-size distribution of
fragments often satisfies this fractal relation; the
Guttenberg–Richter frequency-magnitude relation
for earthquakes is fractal), and solid state
physics (amorphous materials).
fractionation In geophysics, separation of
different minerals during the melting of rocks,
and refreezing of a solid; applied to the geophysical
processes modifying rocks.
fracture In geophysics, the Earth’s crust is
filled with fractures on a range of scales from
centimeters to thousands of kilometers. The
term fracture covers both joints and faults. If
no lateral displacement has occurred across a
fracture, it is classified as a joint; if a lateral
displacement has occurred, it is classified as a
fault.
fracture zone In geophysics, deep valleys
caused by faults on the ocean floor. The ocean
floor on the two sides of a fracture zone can be of
very different ages and this leads to differential
elevations and subsidence.
© 2001 by CRC Press LLC
frame dragging
fragmentation The breaking up of a mass
into fragments. Applied in astrophysics to discuss
collisions of minor planets, and in geophysics
to describe rock processing where fragmentation
takes place on a wide range of scales
and occurs on joints and faults. On the largest
scale the plates of plate tectonics are fragments
that are the result of fragmentation.
frame dragging The phenomenon in relativistic
theories of gravitation, particularly in
general relativity in which the motion of matter,
e.g., translating or rotating matter “drags” the
inertial frame, meaning the inertial frames near
the moving matter are set in motion with respect
to the distant stars, in the direction of the matter
motion. For instance, the plane of a circular
polar orbit around a rotating primary rotates in
the direction of the central rotating body. In the
case of an orbit around the Earth, the gravitational
fields are weak, and the effect was first
calculated by Lense and Thining in 1918. The
plane of the polar orbit rotates in this case at a
rate:
˙ = 2GJ
c 2 r
3 .
Here c is the speed of light, G is Newton’s gravitational
constant, and J is the angular momentum
of the isolated rotating planet. For an orbit
close to the surface of the Earth, this rate is approximately
220 milliarc sec/year.
This result actually applies to the dragging of
the line of nodes of any orbit, with the following
modification due to eccentricity e:
2J
˙ =
a3 (1 − e2 .
) 3/2
The pointing direction of a gyroscope near
a rotating object is also affected by the frame
dragging. The precession rate due to this effect
for a gyroscope in circular orbit is:
3ˆr(J · ˆr) − J
˙δ =
r3 ,
where ˆr is the unit vector to the gyroscope position.
For a gyroscope in orbit at about 650 km
altitude above this rate is approximately 42 milliarc
sec/year. A second relativistic effect, the
deSitter precession, constitutes
3 M
(ˆr × v),
2 r2 181