DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

achronal set (semispacelike set) A set of
points S of a causal space such that there are
no two points in S with timelike separation.
acoustic tomography An inverse method
which infers the state of an ocean region from
measurements of the properties of sound waves
passing through it. The properties of sound in
the ocean are functions of temperature, water
velocity, and salinity, and thus each can be exploited
for acoustic tomography. The ocean
is nearly transparent to low-frequency sound
waves, which allows signals to be transmitted
over hundreds to thousands of kilometers.
actinides The elements of atomic number 89
through 103, i.e., Ac, Th, Pa, U, Np, Pu, Am,
Cm, Bk, Cf, Es, Fm, Md, No, Lr.
action In mechanics the integral of the Lagrangian
along a path through endpoint events
with given endpoint conditions:
I=
tb,x j
b
ta,x j a,C
L x i ,dx i
/dt,t dt
(or, if appropriate, the Lagrangian may contain
higher time derivatives of the pointcoordinates).
Extremization of the action over
paths with the same endpoint conditions leads
to a differential equation. If the Lagrangian is
a simple L=T−V , where T is quadratic in
the velocity and V is a function of coordinates
of the point particle, then this variation leads to
Newton’s second law:
d2xi =−∂V
dt2 ∂xi,i= 1, 2, 3.
By extension, the word action is also applied to
field theories, where it is defined:
I =
tb,x j
b
ta,x j a
L |g|d n x,
where L is a function of the fields (which depend
on the spacetime coordinates), and of the
gradients of these fields. Here n is the dimension
of spacetime. See Lagrangian, variational
principle.
activation energy (Ha ) That energy required
before a given reaction or process can
© 2001 by CRC Press LLC
active fault
proceed. It is usually defined as the difference
between the internal energy (or enthalpy) of the
transition state and the initial state.
activation entropy ( Sa ) The activation
entropy is defined as the difference between the
entropy of the activated state and initial state, or
the entropy change. From the statistical definition
of entropy, it can be expressed as
Sa = R ln ωa
ωI
where ωa is the number of “complexions” associated
with the activated state, and ωI is the
number of “complexions” associated with the
initial state. R is gas constant. The activation
entropy therefore includes changes in the configuration,
electronic, and vibration entropy.
activation volume ( V ) The activation volume
is defined as the volume difference between
initial and final state in an activation process,
which is expressed as
V = ∂G
∂P
where G is the Gibbs energy of the activation
process and P is the pressure. The activation
volume reflects the dependence of process on
pressure between the volume of the activated
state and initial state, or entropy change.
active continental margin A continental
margin where an oceanic plate is subducting beneath
the continent.
active fault A fault that has repeated displacements
in Quaternary or late Quaternary period.
Its fault trace appears on the Earth’s surface,
and the fault has a potential to reactivate
in the future. Hence, naturally, a fault which
had displacements associated with a large earthquake
in recent years is an active fault. The degree
of activity of an active fault is represented
by average displacement rate, which is deduced
from geology, topography, and trench excavation.
The higher the activity, the shorter the recurrence
time of large earthquakes. There are
some cases where large earthquakes take place
on an active fault with low activity.