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Dictionary of Geophysics, Astrophysic, and Astronomy.pdf

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focal mechanisms

rays arriving parallel from inﬁnity appear to diverge (negative focal length).

focal mechanisms Earthquakes send out compressional P-waves that are either compressional or tensional. The azimuthal variation in the ﬁrst arrivals deﬁnes the focal mechanism. This variation provides information on whether the fault displacement was thrust, normal, or strike-slip and information on the orientation of the fault.

focus In optics, the point where light rays converge and/or from which light rays (appear to) diverge.

In geometry, in a circle, the center of the circle. In an ellipse, each of the two points on the major axis located at a from the center, where a is the semimajor axis, and is the eccentricity. In a hyperbola, the point located inside the hyperbola, on the axis a distance of a( − 1) from the point the orbit crosses the axis, such that the transverse distance to the orbit at that point is a( 2 − 1). Here a is called the semiaxis of the hyperbola, and is 1/(cos α) with α the slope of the asymptote to the hyperbola.

In a parabola, the point inside the parabola on the axis of the parabola a distance p/2 from the point the orbit crosses the axis, such that the transverse distance to the orbit at that point is 2p.

In Newtonian physics, gravitational motion is an orbit that is a conic section (circle, ellipse, parabola, hyperbola) with the sun at one focus.

focused transport equation Model suggested by Roelof (1969) to describe the interplanetary transport of charged energetic particles in terms of ﬁeld-parallel propagation, focusing on the diverging interplanetary magnetic ﬁeld, and pitch-angle scattering:

∂t +		2ζ		∂µ	− ∂µ		∂µ
∂f	µv	1 − µ2	v	∂f		∂	κ(µ)	∂f

= Q(so, µ, t) .

Here f is the phase space density, v the particle speed, µ the particle’s pitch-angle, κ(µ) the pitch-angle diffusion coefﬁcient (see diffusion, in pitch-angle space, slab model), s the spatial coordinate along the Archimedian spiral, and

ζ = −B(s)/(∂B/∂s) the focusing length (see focusing). The term Q on the right-hand side describes a particle source.

focusing In plasma physics, reduction of a particle’s pitch angle as it propagates outward in a slowly diverging magnetic ﬁeld such as the interplanetary magnetic ﬁeld. Focusing can be characterized by a focusing length ζ

ζ = − B(s)

∂B/∂s

with s being the spatial scale along the magnetic ﬁeld B. In interplanetary space, the divergence of the magnetic ﬁeld would reduce a particle’s pitch-angle from nearly 90◦ on the sun to about 0.7◦ at the orbit of Earth.

Focusing is a direct consequence of the constancy of the magnetic moment (ﬁrst adiabatic invariant). Its reverse effect is the increase of the particle’s pitch angle in a convergent magnetic ﬁeld, eventually leading to mirroring. See adiabatic invariant, interplanetary propagation, magnetic mirror.

foehn Hot winds on the down-slope side of a mountain on which background winds impinge. There are two basic types of foehns of thermodynamic and dynamic causes, respectively. Thermodynamic foehns occur when the lower atmosphere is humid and the uplift by the mountain forces water vapor to condense on the upstream side, causing temperature increases on the down-slope side. Dynamic foehns occur when the atmosphere is strongly stratiﬁed on the up-slope side and the air near the surface cannot ﬂow over the mountain and is blocked. As the upper air is forced to descend downslope, adiabatic compression raises its temperature. The second-type of foehn occurs when the Froude number U/Nh is below a certain critical value, where U is the background wind speed, N the Brunt–Väisälä frequency, and h the height of the mountain.

fog A situation in which clouds form at ground level which reduces visibility below 1 km; consisting of water droplets too small to fall out of suspension.

force

folds In geophysics, when the continental crust is deformed under compression the result is often a near periodic, sinusoidal structure. These are folds, and they can occur on scales from a meter or less to hundreds of kilometers. Folding is usually associated with layered sedimentary rocks with some layers being rigid and others more ductile.

following spot A sunspot or sunspot group lying on the eastern side of an active region complex, i.e., following in the direction of solar rotation. Following spots tend to be smaller and greater in number than preceding (or “leader”) spots. During the evolution of an active region, the following spots tend to remain at the same longitude or move backwards (relative to the direction of solar rotation).

Fomalhaut 1.16 magnitude star of spectral type A at RA22h 57m 38.9s, dec 19◦37 20 .

forbidden lines Spectral emission lines violating quantum mechanics selection rules for electric dipole emission. In both permitted and forbidden transitions, the photon of a spectral line is emitted when an electron moves from an upper to a lower energy level. The photon energy is equal to the difference between the energy of the two levels. In the case of forbidden lines, the probability of a spontaneous transition between the upper and lower energy level is very small, and the electron remains a much longer time in the excited state than in the case of a permitted transition. In this case, the upper level is said to be metastable. Forbidden lines in several astronomical sources are collisionally excited, i.e., the electron bound to an ion is brought to a higher, metastable level via the collision with a free electron or with another ion. At densities typical of the terrestrial environment, subsequent collisions would quickly de-excite the atom without emission of radiation. At electron densities ne < 103 − 107 electrons cm−3, the probability of a collision is much lower, and the electron can decay to a lower level with the emission of a photon of the forbidden line. Forbidden lines are, therefore, very sensitive indicators of density in several gaseous nebulæ, for example HI regions, or planetary nebulæ.

forbidden orbits

See Störmer orbits.

forbidden region A term used in the study of cosmic ray ions or particles convecting into the Earth’s magnetic ﬁeld. It is a region in space, or among the directions of arrival, which (for some stated energy) contains no orbits that connect to inﬁnity, but only trapped orbits. Since the cosmic ray ions, or the convecting ions, come from great distances and are not trapped, the forbidden region contains none of them. Forbidden regions for convection particles are responsible for Alfvén layers.

Forbush decrease The sudden dramatic reduction in the ﬂux of cosmic rays detected at the Earth (e.g., with a neutron monitor) due to the interaction of solar ﬂare induced shock waves with the interplanetary medium. The shock waves sweep across the geomagnetic ﬁeld lines and deﬂect the galactic cosmic ray particles. One to three days after a strong ﬂare counting rates decrease sharply by a few percent. This decrease coincides with the passage of the shock. Sometimes the decrease occurs in two steps, the ﬁrst step coinciding with shock passage, the second with the arrival of the magnetic cloud. Although the decrease is sharp, the recovery is slow, lasting for some days.

force In Newtonian physics, a vector quantity describing the external inﬂuence on an object which tends to accelerate the object. Force may be measured by its effect in compressing a spring:

F = −kx ,

where k is a constant, and x is the amount of displacement of the spring from its resting position. Newton’s second law relates force to acceleration:

F = ma ,

where m is the mass, and a is the acceleration. Thus, force is the rate of change of momentum with time.

Units: dynes = gm cm/sec2; Newtons = kg m/sec2.

In relativity, a number of formulations of force have been given, all of which reduce to the Newtonian form in the limit of small velocities.

force balance

force balance A term used in the study of plasmas in space, referring to the requirement (inherent in Newton’s laws of motion) that the sum of all forces on any volume element of plasma equals its mass times its acceleration. In collision-free plasmas, mass is small and the acceleration term can generally be neglected, leading to the requirement that all forces on the element balance. In general, gravity is negligible, and the two main terms are the magnetic force j × B and the pressure gradient p (or · P, if pressure is a tensor P). This equation (non-linear in B, since j = × B) and its modiﬁcations are among the conditions imposed by MHD.

force-free magnetic ﬁeld A magnetic ﬁeld and associated current system for which the Lorentz force vanishes. Equivalently, the current density and magnetic ﬁeld must be parallel, i.e., curlB = αB, where B is the magnetic ﬁeld and α is a scalar quantity such that B· α = 0. The force-free approximation is often appropriate for plasmas whose ﬂuid pressure is small in comparison with the magnetic pressure (a “lowbeta” plasma), and may be regarded as intermediate between the potential ﬁeld (zero current density) approximation and a full magnetohydrodynamic description.

Forchhammer’s Principle Principle of Constant Proportions: the ratio of major salts in samples of seawater from various locations is invariant.

forearc basin A sedimentary basin on the trench side of a volcanic arc at a subduction zone.

forearc sliver At a subduction zone where plate convergence is oblique (not normal to strike), there is often a strike-slip fault or shear zone in the upper plate trenchward of the volcanic arc. The narrow block of the upper plate between the subduction thrust fault and the shear zone is called the forearc sliver. Forearc slivers are observed to move in the tangential component of the direction of subduction and, as a result, the relative motion of the subducting plate with respect to the sliver is less oblique. This phenomenon is called slip partitioning.

forecasting (wave) The process of predicting ocean wave conditions from anticipated wind and weather conditions. May refer to the prediction of bulk quantities, such as wave height or period, or of wave energy spectra.

foreshock The region ahead of the Earth’s bow shock, linked to the shock by magnetic ﬁeld lines. Although the velocity of the solar wind is super-Alfvénic, preventing the shock from affecting the approaching solar wind by Alfvén waves, fast ions and electrons can travel upstream and can affect the foreshock region, creating a noisy plasma regime.

In seismology, a preceding earthquake which has smaller magnitude than the main earthquake. Unfortunately, a foreshock cannot be identiﬁed as a foreshock until a subsequent, perhaps larger earthquake occurs, so the concept has no predictive ability.

foreshore The part of a beach that lies nearest the sea, from the low-tide line to the high-tide line; often taken as synonymous with the term beachface. May be used to indicate the beachface plus a short region of the beach proﬁle offshore of the beachface.

Foucault pendulum A pendulum constructed for little dissipation, and suspended so that it can swing freely in any plane. Over a period of (up to) days, the plane of the swing relative to the Earth turns at a rate:

? = 2ω sin θ ,

where θ is the latitude and ω is the rotational rate of the Earth. The motion is clockwise looking down at the pendulum in the northern hemisphere, vanishes at the equator, and is counterclockwise in the southern hemisphere.

four-velocity In relativity, the coordinates x, y, z, t of a series of events along a world line are considered functions of the proper time measured by an observer traveling along that world line. The four-velocity is the four-vector obtained by differentiating the four-coordinates with respect to the proper time τ associated with the orbit:

uα = dxα/dτ, α = 0, 1, 2, 3 .

frame dragging

Thus, four-velocity is the tangent four-vector uα = dxα/ds of an afﬁnely parametrized timelike curve γ = {xα(s)} in the space-time. The norm is g(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.

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
		c2r3 .
˙

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
		e2)3/2 .
˙ = a3(1	−

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:

?	3rˆ(J · rˆ) − J	,
	r3
˙ δ =

where rˆ 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

2 r2 (rˆ × v) ,

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