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Chapter 11
Earth
Gerald Schubert and Richard L. Walterscheid
11.1
Oblate Ellipsoidal Reference Figure . . . . . . . . . . 240
11.2
Mass and Moments of Inertia . . . . . . . . . . . . . . 240
11.3
Gravitational Potential and Relation to
Products of Inertia . . . . . . . . . . . . . . . . . . . . 241
11.4
Topography
11.5
Rotation (Spin) and Revolution About the Sun . . . . 244
11.6
Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
11.7
Geoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
11.8
Coordinates . . . . . . . . . . . . . . . . . . . . . . . . 246
11.9
Solid Body Tides . . . . . . . . . . . . . . . . . . . . . 246
11.10
Geological Time Scale . . . . . . . . . . . . . . . . . . 248
11.11
Glaciations . . . . . . . . . . . . . . . . . . . . . . . . . 251
11.12
Plate Tectonics
11.13
Earth Crust . . . . . . . . . . . . . . . . . . . . . . . . . 252
11.14
Earth Interior
11.15
Earth Atmosphere, Dry Air at
Standard Temperature and Pressure (STP) . . . . . . 257
11.16
Composition of the Atmosphere . . . . . . . . . . . . 258
11.17
Water Vapor . . . . . . . . . . . . . . . . . . . . . . . . 259
11.18
Homogeneous Atmosphere, Scale Heights
and Gradients . . . . . . . . . . . . . . . . . . . . . . . 259
11.19
Regions of Earth’s Atmosphere and
Distribution with Height . . . . . . . . . . . . . . . . . 260
239
. . . . . . . . . . . . . . . . . . . . . . . . 243
. . . . . . . . . . . . . . . . . . . . . . 252
. . . . . . . . . . . . . . . . . . . . . . . 255
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11.1
E ARTH
11.20
Atmospheric Refraction and Air Path . . . . . . . . . 262
11.21
Atmospheric Scattering and Continuum Absorption . 265
11.22
Absorption by Atmospheric Gases at Visible
and Infrared Wavelengths . . . . . . . . . . . . . . . . 268
11.23
Thermal Emission by the Atmosphere . . . . . . . . . 270
11.24
Ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . 271
11.25
Night Sky and Aurora . . . . . . . . . . . . . . . . . . 279
11.26
Geomagnetism
11.27
Meteorites and Craters . . . . . . . . . . . . . . . . . . 285
. . . . . . . . . . . . . . . . . . . . . . 282
OBLATE ELLIPSOIDAL REFERENCE FIGURE [1, 2]
Equatorial radius a = 6.378 136 × 106 m.
Polar radius c = 6.356 753 × 106 m.
Mean radius R⊕ = (a 2 c)1/3 = 6.371 000 × 106 m.
Length of equatorial quadrant = 1.001 875 × 107 m.
Length of meridional quadrant = 9.985 164 × 106 m.
Ellipticity or Flattening (a − c)/a = 1/298.257 = 0.003 352 8.
Eccentricity e = (a 2 − c2 )1/2 /a = 0.081 818.
1/2 −1/2 2
2
2 2
2 2
Surface Area = 2π a + c 1 − c /a
ln a/c + a /c − 1
= 5.100 657 × 1014 m2 .
Volume = 43 πa 2 c = 1.083 207 × 1021 m3 .
11.2
MASS AND MOMENTS OF INERTIA [1–3]
Earth mass M⊕ = 5.973 7 × 1024 kg.
Moon–Earth mass ratio MMoon /M⊕ = 0.012 300 034.
Sun–Earth mass ratio M /M⊕ = 332 946.038.
Earth mass multiplied by the gravitational constant:
G M⊕ = 3.986 004 41 × 1014 m3 s−2 ,
(G M⊕ )1/2 = 1.996 498 × 107 m3/2 s−1 .
Earth mean density ρ ⊕ = 5514.8 kg m−3 .
Moments of inertia (see below):
about rotation axis C = 8.035 8 × 1037 kg m2 ,
average about equatorial axis (A + B)/2 = 8.009 5 × 1037 kg m2 ,
dynamical ellipticity or flattening {C − (A + B) /2} /C = 0.003 272 9,
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11.3 G RAVITATIONAL P OTENTIAL AND P RODUCTS OF I NERTIA / 241
J2 = {C − (A + B) /2} /M⊕ a 2 = 1.082 626 × 10−3 ,
C/M⊕ a 2 = 0.330 78,
M⊕ a 2 = 2.430 14 × 1038 kg m2 .
11.3 GRAVITATIONAL POTENTIAL AND RELATION TO
PRODUCTS OF INERTIA [1–3]
The gravitational potential is
l
∞ l G M⊕
a
U =
1+
P lm (sin φ) C lm cos mλ + Slm sin mλ ,
r
r
l=2
m=0
r = radial distance from Earth center of mass,
P lm = fully normalized associated Legendre polynomials, i.e., the mean square value of
P lm (sin φ)(cos mλ, sin mλ) over a spherical surface is unity,
P lm = {(2−δm,0 )(2l +1)[(l −m)!/(l +m)!]}1/2 Plm , where Plm is the ordinary associated Legendre
polynomial,
l, m = degree and order of normalized spherical harmonic P lm (sin φ)(cos mλ, sin mλ),
φ = latitude,
λ = longitude,
C lm , Slm
= coefficients in spherical harmonic expansion of Earth’s gravitational potential using fully
normalized functions.
With coordinate system origin at the center of mass C 01 = C 11 = S 11 = 0. Table 11.1 gives the
values of the zonal coefficients C l0 in a spherical harmonic expansion of the gravitational potential
using fully normalized functions.
Table 11.1. Zonal coefficients C l0 in units of 10−6 .
l
C l0
l
C l0
2.
4.
6.
8.
10.
12.
14.
16.
18.
20.
−484.165
0.539 52
−0.149 51
0.048 883
0.054 065
0.035 629
−0.021 555
−0.006 189 1
0.008 524 6
0.019 924
3.
5.
7.
9.
11.
13.
15.
17.
19.
0.957 20
0.068 343
0.091 301
0.026 862
−0.049 464
0.040 112
0.003 227 5
0.017 427
−0.002 155 1
Table 11.2 gives values of the coefficients C lm , Slm in a spherical harmonic expansion of the
gravitational potential using fully normalized functions. Note that C 12 = 0 and S 12 = 0.
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Table 11.2. Coefficients C lm , Slm in units of 10−6 .
l, m
C lm ,
2, 2
2.439,
3, 1
2.0277,
4, 1
4, 4
Slm
l, m
C lm ,
0.2492
3, 2
0.9045,
−0.5362,
−0.1888,
−0.4734
0.3094
4, 2
5, 1
5, 4
−0.0583,
−0.2956,
−0.0961
0.0497
6, 1
6, 4
−0.0769,
−0.0868,
7, 1
7, 4
7, 7
Slm
l, m
C lm ,
Slm
−0.6194
3, 3
0.7203,
1.4139
0.3502,
0.6630
4, 3
0.9909,
−0.2009
5, 2
5, 5
0.6527,
0.1738,
−0.3239
−0.6689
5, 3
−0.4523,
−0.2153
0.0270
−0.4713
6, 2
6, 5
0.0487,
−0.2673,
−0.3740
−0.5368
6, 3
6, 6
0.0572,
0.0097,
0.0094
−0.2371
0.2749,
−0.2756,
0.0010,
0.0975
−0.1238
0.0241
7, 2
7, 5
0.3278,
0.0013,
0.0932
0.0186
7, 3
7, 6
0.2512,
−0.3588,
−0.2153
0.1517
8, 1
8, 4
8, 7
0.0236,
−0.2463,
0.0675,
0.0588
0.0702
0.0751
8, 2
8, 5
8, 8
0.0776,
−0.0250,
−0.1242,
0.0660
0.0895
0.1202
8, 3
8, 6
−0.0178,
−0.0649,
−0.0863
0.3091
9, 1
9, 4
9, 7
0.1461,
−0.0101,
−0.1190,
0.0200
0.0190
−0.0970
9, 2
9, 5
9, 8
0.0225,
−0.0171,
0.1871,
−0.0336
−0.0538
−0.0024
9, 3
9, 6
9, 9
−0.1613,
0.0639,
−0.0481,
−0.0760
0.2226
0.0987
10, 1
10, 4
10, 7
10, 10
0.0815,
−0.0853,
0.0076,
0.0998,
−0.1303
−0.0787
−0.0034
−0.0225
10, 2
10, 5
10, 8
−0.0913,
−0.0510,
0.0401,
−0.0511
−0.0511
−0.0917
10, 3
10, 6
10, 9
−0.0086,
−0.0371,
0.1243,
−0.1550
−0.0784
−0.0380
−1.4001
A simplified expression for the gravitational potential is
G M⊕
U ≈
r
1−
∞ l
a
l=2
r
Jl Pl (sin φ) ,
where Pl is the Legendre polynomial of degree l. Values of the zonal coefficients Jl , defined by
Jl ≡ −C l0 (2l + 1)1/2 ,
l ≥ 2,
are given in Table 11.3.
Table 11.3. Zonal coefficients Jl , in units of
10−6 .
l
2.
4.
6.
8.
10.
Jl
1 082.626
−1.618 6
0.539 1
−0.201 5
−0.247 8
l
3.
5.
7.
9.
11.
Jl
−2.533
−0.226 7
−0.353 6
−0.117 1
0.237 2
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11.4 T OPOGRAPHY
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Table 11.3. (Continued.)
l
Jl
−0.178 1
0.116 1
0.003 555
−0.005 185 3
−0.127 58
12.
14.
16.
18.
20.
l
Jl
13.
15.
17.
19.
−0.208 4
−0.017 97
−0.103 10
0.013 459
The relation of the second degree coefficients in a spherical harmonic expansion of the gravitational
potential to products of inertia Ii j is
√ 0
1
I11 + I22
− 5 C 2 = J2 =
I33 −
,
2
M⊕ a 2
I
I13
5 1
5 1
C
=
,
S 2 = 23 2 ,
3 2
3
2
M⊕ a
M⊕ a
I12
I22 − I11
5
5 2
2
12 C 2 = 4M a 2 ,
12 S 2 = 2M a 2 .
⊕
⊕
The principal products of inertia I11 , I22 , I33 are often denoted A, B, C with C > B > A or
I33 > I22 > I11 ,
I11 = A = 8.009 4 × 1037 kg m2 ,
I22 = B = 8.009 6 × 1037 kg m2 ,
I33 = C = 8.035 8 × 1037 kg m2 .
11.4
TOPOGRAPHY [2, 4, 5]
The topography of solid Earth, T , is:
T (in 103 m) =
l
∞ P lm (sin φ) C T lm cos mλ + ST lm sin mλ .
l=0 m=0
P lm (sin φ), φ, λ are defined in the expression for the gravitational potential in Section 11.3. The
coefficients are given in Table 11.4.
Table 11.4. Values of the coefficients C T lm and ST lm (in units of 103 m).
l, m
C T lm ,
ST lm
l, m
C T lm ,
ST lm
0, 0
−2.3890,
—
1, 0
0.6605,
2, 0
0.5644,
3, 0
3, 3
−0.1683,
0.1299,
—
1, 1
0.6072,
0.4062
—
2, 1
0.3333,
3, 1
−0.1518,
—
0.5733
l, m
C T lm ,
ST lm
0.3173
2, 2
0.4208,
0.0839
0.1244
3, 2
0.4477,
0.4589
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Table 11.4. (Continued.)
l, m
C T lm ,
4, 0
4, 3
0.3162,
0.3761,
5, 0
5, 3
6, 0
6, 3
6, 6
ST lm
l, m
C T lm ,
—
−0.1291
4, 1
4, 4
−0.2241,
−0.6387,
−0.5514,
0.1232,
—
0.0386
5, 1
5, 4
0.2567,
0.0601,
0.0354,
—
0.1865
0.0282
6, 1
6, 4
ST lm
l, m
C T lm ,
ST lm
−0.2563
0.4703
4, 2
−0.3928,
0.0716
−0.0406,
0.5254,
−0.0770
−0.0654
5, 2
5, 5
−0.0216,
−0.0549,
−0.1577
0.2276
0.0013,
0.1960,
−0.0171
−0.1737
6, 2
6, 5
0.0247,
−0.1076,
−0.1323
−0.2075
Area = 5.100 657 × 1014 m2 .
Land area = 1.48 × 1014 m2 .
Water area = 3.62 × 1014 m2 .
Continental area including margins = 2.0 × 1014 m2 .
Mean land elevation = 825 m.
Mean ocean depth = 3770 m.
11.5
ROTATION (SPIN) AND REVOLUTION ABOUT THE SUN [1, 2, 6, 7]
Rotational period with respect to fixed stars = 24h 00m 00s.008 4 mean sidereal time,
= 23h 56m 04s.098 9 mean solar time.
−5
Mean angular velocity = 7.292 115 × 10 rad s−1 , 15.041 067 arcsec s−1 .
Equatorial rotational velocity = 465.10 m s−1 .
Centrifugal acceleration at equator = 3.391 57 × 10−2 m s−2 .
Angular momentum = ωC = 5.859 8 × 1033 m2 kg s−1 .
Rotational energy = 12 Cω2 = 2.136 5 × 1029 J.
The general precession in longitude per Julian century for J2000.0 is p = 5 029.096 6, where p is
the long period motion of the mean pole of the equator about the pole of the ecliptic with a period of
about 26,000 years. The general precession is due to the gravitational torques of the Sun, Moon, and
planets on the Earth’s dynamical figure.
Nutations are the motions of the Earth’s rotation axis with respect to inertially fixed axes. Nutation
includes the general precession and shorter period motions. A nutation induced by the Moon has a
period of 18.6 years and an amplitude of about 9 arcsec. The gravitation of the Sun causes the lunar
orbit to precess with respect to the plane of the ecliptic with a period of 18.6 years. Smaller nutations
have periods of a solar year and a lunar month and harmonics thereof.
Length of Day (LOD) variations comprise an overall linear increase from tidal dissipation (of about
1 to 2 ms per century). There are large irregular fluctuations with amplitudes of milliseconds and time
scales of decades, and smaller oscillations with shorter time scales. LOD variations with periods of
a year and less are generally attributable to exchange of angular momentum between the solid Earth
and the atmosphere–ocean system and to effects of solid Earth and ocean tides. LOD fluctuations with
decade time scales may be due to angular momentum exchange between the solid Earth and the liquid
outer core.
Polar motion or wobble is the motion of the solid Earth with respect to the spin axis of the Earth.
Polar motion is dominated by nearly circular oscillations at periods of one year, the annual wobble
with an amplitude of about 100 milliarcseconds, and at about 434 days, the Chandler wobble with an
amplitude of about 200 milliarcseconds. The Chandler wobble is a free oscillation of the Earth; its
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11.6 G RAVITY
/ 245
excitation mechanism is uncertain. Other components of polar motion occur over a wide range of time
scales from weeks to thousands of years. Loading of the solid Earth by the redistribution of mass in
the atmosphere, oceans, groundwater, and ice caps contributes to polar motion.
Mean orbital speed = 2.978 48 × 104 m s−1 .
Mean centripetal acceleration = 5.930 1 × 10−3 m s−2 .
Mean distance from Sun = 1.000 001 057 AU = 1.495 980 29 × 1011 m.
Mean eccentricity of orbit about the Sun = 0.016 708 617.
Obliquity of the ecliptic at J2000.0 = 23◦ 26 21.411 9.
1 AU = 1.495 978 706 6 × 1011 m.
Light time for 1 AU = 499.004 783 53 s.
11.6
GRAVITY [5, 7]
Gravity includes the gravitational attraction of the Earth’s mass and the centrifugal acceleration of the
Earth’s rotation.
Surface gravity on reference ellipsoid g(m s−2 ) = 9.806 21 − 0.025 93 cos 2φ + 0.000 03 cos 4φ
= 9.780 31 + 0.051 86 sin2 φ − 0.000 06 sin2 2φ.
φ is the geodetic latitude of point p, i.e., the angle between the equator of the reference ellipsoid and
the normal from p to the ellipsoid. Gravity anomalies are actual values of g minus the reference g
given above. A practical unit for the measurement of gravity anomalies is the mgal = 10−5 m s−2 .
Reference equatorial gravity = 9.780 31 m s−2 .
Reference polar gravity = 9.832 17 m s−2 .
Reference gravity at φ = 45◦ = 9.806 18 m s−2 .
Gravitation at the equator = G M⊕ /a 2 = 9.798 29 m s−2 .
Centrifugal acceleration at equator/gravitation at equator = 3.461 39 × 10−3 .
Variation of g with altitude at the Earth’s surface = 0.308 6 × 10−5 s−2
= 3.086 mm s−2 km−1
= 0.308 6 mgal m−1 .
−2
g decreases by 3.086 mm s per kilometer of elevation at the Earth’s surface.
Gravity anomalies corrected for altitude, i.e., evaluated on the reference ellipsoid, are known as free-air
gravity anomalies.
11.7
GEOID [2, 5, 7]
The gravity potential is the sum of the gravitational potential U (see above) and the centrifugal potential
1 2 2
2
2 ω r cos φ, where ω is the mean angular velocity.
The geoid is the equipotential of gravity that coincides with mean sea level in the oceans. The
geoid lies generally below the topography.
The height of the geoid N is given with respect to a reference ellipsoid with the observed flattening
of the Earth 1/298.257 and with the Earth’s equatorial radius 6 378.136 km.
The equation of the reference ellipsoid is r = a{1 + [(2 f − f 2 )/(1 − f )2 ] sin2 φ}−1/2 , where f
is the flattening. With f = 1/298.257
−1/2
r = a 1 + 0.673 95 sin2 φ
≈ a 1 − 0.336 98 sin2 φ + 0.170 33 sin4 φ .
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11.8
E ARTH
COORDINATES [7]
Geodetic latitude (φ) − geocentric latitude (φ ) = 692.74 sin 2φ − 1.16 sin 4φ.
Geocentric latitude of a point p is the angle between the equator of the reference ellipsoid and a
line from p to the center of the ellipsoid. Geodetic latitude is defined above.
1◦ of latitude = 110.575 + 1.110 sin2 φ, 103 m.
1◦ of longitude = (111.320 + 0.373 sin2 φ) cos φ, 103 m.
1 − e2 Nφ + h
tan φ =
tan φ.
Nφ + h
e is the eccentricity of the reference ellipsoid
e2 = 2 f − f 2 .
f is the flattening of the ellipsoid.
Nφ is the ellipsoidal radius of curvature in the meridian
Nφ = a
1/2
1 − e2 sin2 φ
.
h is the height of a point p above the reference ellipsoid.
With f = 1/298.257, e2 = 6.694 385 × 10−3 , e2 1, Nφ ≈ a,
h
tan φ ≈ tan φ 1 − e2 + e2
a
≈ tan φ 0.993 306 + 1.049 583 × 10−9 h(m) .
11.9
SOLID BODY TIDES [7, 8]
The tidal potential due to the gravitation of the Sun and the Moon UT is the gravitational potential of
these bodies expressed in the coordinate system of the Earth’s gravitational potential, but without the
l = 1 spherical harmonic terms. These l = 1 terms determine the orbital motion of the Earth. The
tidal potential is a differential gravitational potential. Each spherical harmonic component of the tidal
potential has contributions with different periods and amplitudes. Table 11.5 lists contributions to the
l = 2 tidal potential, the dominant tidal component.
Table 11.5. Periods and amplitudes for the l = 2 tidal potential.
m
Tidal contribution
Period
Long Period
m=0
Lunar nodal tides
Sa
Ssa
Mm
Mf
18.613 years
365.26 d
182.62 d
27.555 d
13.661 d
(Amplitude) g−1 , 10−2 m
2.79
0.49
3.10
3.52
6.66
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11.9 S OLID B ODY T IDES
/ 247
Table 11.5. (Continued.)
m
m
Tidal contribution
(Amplitude) g−1 , 10−2 m
Period
Diurnal
m=1
O1
P1
S1
K1
1
1
25.819 h
24.066 h
24. h
23.934 h
23.869 h
23.804 h
26.22
12.20
0.29
36.88
0.29
0.52
Semi-Diurnal
m=2
N2
M2
S2
K2
12.658 h
12.421 h
12. h
11.967 h
12.10
63.19
29.40
8.00
The perturbation in the Earth’s second degree gravitational potential at the surface of the Earth due
to tidal deformation of the Earth’s interior is the product of the second degree tidal potential evaluated
at the Earth’s surface with the second degree potential Love number k.
The product of the second degree body tide displacement Love number h with the second degree
component of UT /g evaluated at the Earth’s surface gives the tidally induced radial displacement of
the surface.
Southward and eastward displacements of the tidally deformed surface of the Earth are given in
terms of the body tide displacement Love number l by
−l ∂UT
g ∂θ
and
l
∂UT
,
g sin θ ∂λ
respectively, where θ is colatitude, λ is eastward longitude, and g, UT and its derivatives are evaluated
at the Earth’s surface. Second degree contributions are understood here.
Second degree tidal effects on surface gravity and surface tilt are represented by the gravimetric
factor
δ = 1 − 32 k + h
and the tilt factor
η = 1 + k − h,
respectively, similar to the above. Table 11.6 gives these Love numbers for a model of the Earth.
Table 11.6. Second degree Love numbers for a spherical, rotating, ellipsoidal,
elastic, oceanless Earth.
m
Tidal contributions
k
h
l
δ
η
0
Any long period tide
0.299
0.606
0.0840
1.155
0.689
1
O1
P1
S1
K1
0.298
0.287
0.280
0.256
0.603
0.581
0.568
0.520
0.0841
0.0849
0.0853
0.0868
1.152
1.147
1.144
1.132
0.689
0.700
0.707
0.730
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Table 11.6. (Continued.)
m
2
Tidal contributions
k
h
l
δ
η
1
1
0.466
0.328
0.937
0.662
0.0736
0.0823
1.235
1.167
0.523
0.660
Any semi-diurnal tide
0.302
0.609
0.0852
1.160
0.692
Values of the Love numbers for the real Earth are strongly modified by ocean tides and slightly
modified by anelasticity in the solid Earth.
11.10
GEOLOGICAL TIME SCALE [9]
Age of Earth = 4.5 − 4.7 Ga
Oldest Geological Dates:
Rocks at Isua in southern West Greenland have yielded dates of metamorphic events at about
3750 Ma.
Sand River gneisses in the Limpopo belt of Southern Africa have been dated at about 3800 Ma.
Detrital zircons from Western Australia have yielded dates of about 4200 Ma, indicative of preexisting crust.
Table 11.7 gives dates of various geologic eras in the Phanerozoic eon, and Table 11.8 gives dates in
the Precambrian eon. Table 11.9 lists the major geological and biological events in the Earth’s history.
Table 11.7. The Phanerozoic Eon (Present–570 Million Years Ago).
Period
Duration
Cenozoic Era
Quaternary Sub-Era
Holocene Epoch
Pleistocene Epoch
Tertiary Sub-Era
Neogene Period
Pliocene Epoch
Miocene Epoch
Paleogene Period
Oligocene Epoch
Eocene Epoch
Paleocene Epoch
Mesozoic Era
Cretaceous Period
Senonian Epoch
Gallic Epoch
Neocomian Epoch
K2 Gulf Epoch
K1
Jurassic Period
J3, Malm Epoch
J2, Dogger Epoch
J1, Lias Epoch
Triassic Period
Tr3 Epoch
Tr2 Epoch
Tr1, Scythian Epoch
Present–65 Ma
Present–1.64 Ma
Present–0.01 Ma
0.01–1.64 Ma
1.64–65 Ma
1.64–23.3 Ma
1.64–5.2 Ma
5.2–23.3 Ma
23.3–65 Ma
23.3–35.4 Ma
35.4–56.5 Ma
56.5–65 Ma
65–245 Ma
65–145.6 Ma
65–88.5 Ma
88.5–131.8 Ma
131.8–145.6 Ma
65–97 Ma,
97–145.6 Ma)
145.6–208 Ma
145.6–157.1 Ma
157.1–178 Ma
178–208 Ma
208–245 Ma
208–235 Ma
235–241.1 Ma
241.1–245 Ma
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11.10 G EOLOGICAL T IME S CALE
Table 11.7. (Continued.)
Period
Duration
Paleozoic Era
Permian Period
Zechstein Epoch
Rotliegendes Epoch
Carboniferous Period
Pennsylvanian Subperiod
Gzelian, Kasimovian, Moscovian, Bashkirian Epochs
Mississippian Subperiod
Serpukhovian, Visean, Tounaisian Epochs
Devonian Period
D3 Epoch
D2 Epoch
D1 Epoch
Silurian Period
Pridoli, Ludlow, Wenlock, Llandovery Epochs
Ordovician Period
Bala Subperiod
Ashgill, Caradoc Epochs
Dyfed Subperiod
Llandeilo, Llanvirn Epochs
Canadian Subperiod
Arenig, Tremadoc Epochs
Cambrian Period
Merioneth Epoch
St. David’s Epoch
Caerfai Epoch
245–570 Ma
245–290 Ma
245–256 Ma
256–290 Ma
290–362.5 Ma
290–323 Ma
323–362.5 Ma
362.5–408.5 Ma
362.5–377.5 Ma
377.5–386 Ma
386–408.5 Ma
408.5–439 Ma
439–510 Ma
439–464 Ma
464–476 Ma
476–510 Ma
510–570 Ma
510–517 Ma
517–536 Ma
536–570 Ma
Table 11.8. The Precambrian Eon (570–4550–4570 Ma)a .
Period
Duration
Sinian Era
Vendian Period
Sturtian Period
Riphean Era
Karatau Period
Yurmatin Period
Burzyan Period
Animikean Era
Gunflint Period
Huronian Era
Cobalt, Qurke Lake, Hough Lake, Eliot Lake Periods
Randian Era
Ventersdorp, Central Rand, Dominion Periods
Swazian Era
Pongola, Moodies, Figtree, Onverwacht Periods
Isuan Era
Hadean Era
Imbrian (pars) Period
Nectarian Period
Pre-Nectarian Period
Cryptic Division
570–800 Ma
570–610 Ma
610–800 Ma
800–1650 Ma
800–1050 Ma
1050–1350 Ma
1350–1650 Ma
1650–2200 Ma
1650–2200 Ma
2200–2400–2500 Ma
2400–2500–2800 Ma
2800–3500 Ma
3500–3800 Ma
3800–4550–4570 Ma
3800–3850 Ma
3850–3950 Ma
3950–4150 Ma
4150–4550–4570 Ma
Note
a The Precambrian is also divided as follows: Proterozoic Eon (570–2500 Ma);
Pt3 (570–900 Ma), Pt2 (900–1600 Ma), Pt1 (1600–2500 Ma) Subeons; Archean Eon
(2500–4000 Ma); Ar3 (2500–3000 Ma), Ar2 (3000–3500 Ma), Ar1 (3500–4000 Ma)
Subeons; Priscoan Eon (4000–4550–4570 Ma).
/ 249
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Table 11.9. Major “events” in Earth history.
Event
Approximate age
(Ma, million years ago)
Homo sapiens, Neanderthal man, Homo erectus, Australopithecus africanus, worldwide
glaciations
0–3 Ma
Gulf of California opens, Calabria collides Italy–Sicily
3–5 Ma
Mediterranean desiccation, Panama collides NW Columbia, Red Sea Opens
5–10 Ma
FA (First Appearance) Hipparion (horse), FA hominids, Sivapithecus, Kenyapithecus,
Khabylies collides Africa
10–15 Ma
Andaman Sea opens, South China Sea spreading ceases, Calabria rifts SE from Sardinia,
Corsica–Sardinia collide Apulia, Main Himalayan Orogeny
15–20 Ma
Okinawa trough opens, Japanese Sea opens, Corsica–Sardinia parts France, East African
and Red Sea rifting begins, Balearics/Khabalirs rift from Iberia
20–25 Ma
Norwegian Sea opens east of Jan Mayen,
Main Alpine Orogeny
South China Sea opens, Scotia Sea opens
Drake Passage opens, Caribbean Plate moves east
25–30 Ma
Late Eocene extinction, FA proboscideans (mastodons, elephants), early anthropoids,
Labrador Sea/Baffin Bay cease spreading, Jan Mayen Ridge rifts from Greenland
35–45 Ma
FA rodents, Cuba collides Bahama Bank, India Eurasia collision begins, Indian–Australian
plates united, Eurasia Basin opens, Norwegian Sea opens, Tasman Sea opens
45–55 Ma
FA horses, FA grasses, mammals diversify, FA primates
55–60 Ma
North Atlantic lavas, Indian Ocean spreads northwest of Seychelles, Yucatan Basin opens
as Cuba moves north, Laramide Orogeny
60–65 Ma
Terminal Cretaceous extinction, Deccan lavas
65–70 Ma
FA early grasses, LA (last appearance) pteridosperms (seed ferns)
70-75 Ma
Cretaceous anoxic event, Labrador Sea opens, India–Madagascar separate, Australia parts
Antarctica
85–95 Ma
FA diatoms (one-cell marine organisms), equatorial Atlantic opens, Bay of Biscay opens,
Iberia parts Grand Banks
105–120 Ma
FA angiosperms (flowering plants), South Atlantic opens, East Indian Ocean opens, India
parts from Australia–Antarctica, FA placental mammals
125–135 Ma
FA birds, Paleo Tethys closed
145–155 Ma
India–Madagascar Antarctica separate, Gulf of Mexico opens, Neo-Tethys opens, central
Atlantic opens, East Gondwana (India, Australia, Antarctica) parts West Gondwana
(Africa, South America)
155–170 Ma
Karoo volcanism
185–195 Ma
Early mammals, terminal Triassic extinction, Rifting between Gondwana and Laurasia
205–215 Ma
Iran, Crete, Turkey part from Gondwana, FA dinosaurs, Siberian lavas
235–250 Ma
Gondwana Laurasia collide, Appalachian Ocean finally closed
265–280 Ma
Iran, Tibet rift from Gondwana, FA conifers
280–300 Ma
FA winged insects, FA pelycosaurs (early mammal-like reptile)
300–320 Ma
30–35 Ma
South China rifts from Gondwana, FA sharks
350–380 Ma
FA wingless insects, firns, Iapetus Ocean finally closed
380–400 Ma
FA lungfish, land plants, jawed fish, North China rifts from Gondwana
400–430 Ma
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11.11 G LACIATIONS
/ 251
Table 11.9. (Continued.)
Approximate age
(Ma, million years ago)
Event
Ediacaran metazoans (soft body multicell animals), Skilogalee microbiota, Grenvilian
Orogeny
570–1000 Ma
Keweenawan, Mackenzie Volcanics, Duluth Muskox intrusives, Oldest megascopic algae
(large-celled algae), algal coals
1100–1400 Ma
Hudsonian and Penokean Orogenies, FA common red beds, Sudbury intrusion, Banded
iron formations, Oxygen buildup in atmosphere
1700–2000 Ma
Bushveld intrusion, Gunflint microbial structures in chert, Hammersley & Fortescue biota,
Kenoran Orogeny
2000–2500 Ma
FA red beds, Ventersdorp biota, Stilwater volcanics and intrusives
2500–2800 Ma
Kaap Valley Granite, Fig Tree Group with bacteria and blue green algae, Barberton
Gneisses
3200–3300 Ma
FA stromatolites (bacterial algal mats) in Onverwacht Group and Australia
≈ 3400 Ma
Amitsoq & Kaapvaal gneisses, evidence life well established (carbon isotopic ratios)
≈ 3800 Ma
Basin formation on the Moon
3800–4200 Ma
Zircons from early crust
4200–4300 Ma
≈ 4500 Ma
Lunar melting and differentiation of anorthositic crust
Accretion of Earth and Moon
11.11
4500–4600 Ma
GLACIATIONS [9–11]
The geological record contains evidence of major glaciations as listed in Table 11.10.
Table 11.10. Ages and locations of major glaciations.
Age (Ma)
Locations
0–15, Holocene, Pleistocene
250–380, Permian, Carboniferous, Devonian
430–450, Silurian, Ordovician
600, Vendian
650, Sturtian
800, Sturtian
900, Karatau
2300–2400, Huronian
2800, Randian, Swazian
Antarctica, North America, Eurasia
Gondwana
Gondwana
China, North Europe, North and South America
Eurasia, South Africa, Australia
Australia, North America, South Africa
Africa
North America, South Africa
South Africa
Some glaciations may be related to plate tectonics, e.g., Gondwana moved over the South Pole in
the Paleozoic.
The Quaternary glaciations (most geologically recent glaciations) may be related to cyclical
changes in the Earth’s orbital motion about the Sun and in the motion of the Earth’s rotation axis
(Milankovitch or astronomical theory of ice ages). The tilt of the Earth’s equator to the ecliptic varies
from 21.5◦ to 24.5◦ with a period of about 41,000 years. The eccentricity of the Earth’s orbit varies
with periods of about 100,000 years and 400,000 years and the Earth’s axis of rotation wobbles with a
period of about 22,000 years. Pleistocene glaciations have occurred cyclically with a period of about
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105 years. Typically there has been a relatively slow glaciation phase lasting about 9 x 104 years and a
relatively fast deglaciation phase lasting about 104 years. The last deglaciation event of the current ice
age began about 18,000 years ago and ended about 7000 years ago.
11.12
PLATE TECTONICS [5, 12]
Earth’s outer shell is divided into units known as tectonic plates that behave essentially rigidly on
geological time scales. Plates move with respect to each other and the underlying mantle which
deforms like a very viscous fluid on geological time scales. Tectonic plates comprise the lithosphere
or rheologically stiff outer shell of the Earth. Plates are separated by four types of boundaries:
(1) midocean ridges or sites of seafloor spreading and generation of new oceanic crust; (2) subduction
zones or sites of plate submergence into the mantle; (3) transform faults or sites of fault-parallel relative
horizontal motion or sliding; and (4) collisional zones or sites of horizontal convergence characterized
by strong deformation and mountain building. Nonrigid deformation of the lithosphere occurs mainly
at plate boundaries.
Major tectonic plates include Eurasia, Pacific, Antarctic, North America, South America, Africa,
Australia, Philippine, Arabia, Nazca, Cocos, Caribbean, and Juan de Fuca.
Plate motions are well described by rigid body rotations of the plates about axes through the center
of the Earth and intersecting the surface at poles of rotation generally located remotely from the plates
(Euler’s theorem). The angular velocity vector of plate rotation is known as the Euler vector. Each
plate rotates counterclockwise relative to the fixed Pacific plate (PA). These main plates are given in
Table 11.11.
Table 11.11. NUVEL–1 Euler vectors of plate rotation.
Plate
Africa, AF
Antarctica, AN
Arabia, AR
Australia, AU
Caribbean, CA
Cocos, CO
Eurasia, EU
India, IN
Nazca, NZ
North America, NA
South America, SA
Juan de Fucaa
Philippinea
Latitude of
rotation pole
◦N
59.16
64.315
59.658
60.080
54.195
36.823
61.066
60.494
55.578
48.709
54.999
35.0
0.
Longitude of
rotation pole
◦E
Magnitude of
rotation rate
ω (deg. Myr−1 )
−73.174
−83.984
−33.193
+1.742
−80.802
−108.629
−85.819
−30.403
−90.096
−78.167
−85.752
+26.0
−47.
0.9695
0.9093
1.1616
1.1236
0.8534
2.0890
0.8985
1.1539
1.4222
0.7829
0.6657
0.53
1.0
Note
a Listed Euler vectors are not part of the NUVEL-1 model.
11.13
EARTH CRUST [5, 11]
The crust is the outermost layer of the Earth. The rocks of the crust are chemically and physically
distinct from underlying mantle rocks; the major distinction between crust and mantle is compositional.
Crustal rocks are less dense than mantle rocks and contain greater concentrations of heat-producing
radiogenic elements. The base of the crust is defined by a discontinuity in the depth profiles of seismic
velocities known as the Mohorovičić discontinuity or Moho.
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11.13 E ARTH C RUST
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There are two major subdivisions of the crust—the oceanic crust and the continental crust. Both
types of crust generally consist of a sediment layer, an upper layer, and a lower layer. The average
properties of these crustal layers are given in Table 11.12.
Table 11.12. Average properties of oceanic and continental crust.
Property
Sediment layer thickness (km)
Upper layer thickness (km)
Lower layer thickness (km)
Total thickness (km)
Areal abundance (%)
Volume abundance (%)
Heat flow (mW m−2 )
Bouguer anomaly (mgal)a
v p , upper layer (km s−1 )b
v p , lower layer (km s−1 )b
Oceanic
Continental
0–1
1.5(0.7–2)
5(3–7)
7(5–15)
59
21
78
250
5.1
6.6
0–5
17(10–20)
21(15–25)
36(30–80)
41
79
56.5
−100
6.1
6.8
Notes
a Bouguer anomaly = free air gravity anomaly (see above) −2π Gρ h
c
(a correction for the gravitational attraction of topography with elevation
h and density ρc , G is the universal gravitational constant).
b v = velocity of seismic P or compressional waves; 1 mgal =
p
10−2 mm s−2 . Seismic shear velocities of crustal rocks vs are about
3.7 km s−1
The average composition of the oceanic crust is primarily that of a tholeiitic basalt (Table 11.13).
Oceanic tholeiitic basalt is extruded and intruded at mid-ocean ridges as a consequence of pressurerelease melting of upper mantle material that rises beneath the ridges. Oceanic basalts undergo varying
degrees of alteration by reactions with seawater and hydrothermal fluids especially at and near midocean ridges.
The average composition of the upper layer of the continental crust is similar to that of granodiorite.
The lower layer of the continental crust may be largely similar to mafic granulites in composition
though a more felsic composition is possible. Whereas the oceanic crust is produced in a one stage
melting of the upper mantle, continental crustal rocks involve multiple melting events.
Table 11.13. Estimated average composition of the oceanic and continental crust
(excluding sediments).
Continental crust
Upper
Lower, mafic
Lower, felsic
Oceanic crust
Oxides (in weight %)
SiO2
TiO2
Al2 O3
FeOT
MgO
CaO
Na2 O
K2 O
MnO
P2 O5
65.5
0.5
15.0
4.3
2.2
4.2
3.6
3.3
0.1
0.2
49.2
1.5
15.0
13.0
7.8
10.4
2.2
0.5
0.2
0.2
61.0
0.5
15.6
5.3
3.4
5.6
4.4
1.0
0.1
0.2
49.6
1.5
16.8
8.8
7.2
11.8
2.7
0.2
0.2
0.2
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Table 11.13. (Continued.)
Continental crust
Upper
Lower, mafic
Lower, felsic
Oceanic crust
Trace Elements (in ppm)
Rb
Ba
Sr
La
Yb
Zr
Nb
U
Th
Cr
Ni
110.
800.
325.
30.
2.0
220.
25.
2.5
11.
35.
20.
2.
50.
500.
10.
1.0
30.
3.
0.1
0.3
200.
150.
10.
780.
570.
20.
1.2
200.
5.
0.1
0.5
90.
60.
4.
60.
180.
3.5
2.7
100.
5.
0.2
0.6
230.
80.
Properties of the main crustal rocks are given in Table 11.14.
Table 11.14. Properties of crustal rocks.ab
Density
(kg m−3 )
Young’s modulus
(1011 Pa)
Shale
Sandstone
Limestone
Dolomite
Marble
2100–2700
2200–2700
2200–2800
2200–2800
2200–2800
0.1–0.3
0.1–0.6
0.6–0.8
0.5–0.9
0.3–0.9
Gneiss
Amphibole
2700
3000
0.04–0.7
—
Basalt
Granite
Diabase
Gabbro
Diorite
Anorthosite
Granodiorite
2950
2650
2900
2950
2800
2750
2700
0.6–0.8
0.4–0.7
0.8–1.1
0.6–1.0
0.6–0.8
0.83
—
Rock
Shear modulus
(1011 Pa)
Poisson’s ratio
Thermal
conductivity
W m−1 K−1
Thermal
expansivity
10−5 K−1
—
0.2–0.3
0.25–0.3
—
0.1–0.4
1.2–3
1.5–4.2
2–3.4
3.2–5
2.5–3
—
3.
2.4
—
—
0.04–0.15
0.4
2.1–4.2
2.5–3.8
—
—
0.25
0.1–0.25
0.25
0.15–0.2
—
0.25
—
1.3–2.9
2.4–3.8
1.7–2.5
1.9–2.3
2.8–3.6
1.7–2.1
2.6–3.5
—
2.4
—
1.6
—
—
—
Sedimentary
0.14
0.04–0.3
0.2–0.3
0.3–0.5
0.2–0.35
Metamorphic
0.1–0.35
0.5 - 1.0
Igneous
0.3
0.2–0.3
0.3–0.45
0.2–0.35
0.3–0.35
0.35
—
Notes
a The specific heats of crustal rocks are all approximately 1 kJ kg−1 K−1 .
b Mean density of the continental crust = 2 750 kg m−3 . Mean density of the oceanic crust = 2 900 kg m−3 .
The radioactive heat sources in the Earth’s interior are listed in Table 11.15.
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11.14 E ARTH I NTERIOR
/ 255
Table 11.15. Radiogenic heat production rates per unit mass H and
half-lives τ1/2 of the important radioactive isotopes in the Earth’s
interior.a
Isotope or
element
238 U
235 U
U
232 Th
40 K
K
H (W kg−1 )
τ1/2 (Gyr)
Mantle concentration
(kg kg−1 )
9.37 × 10−5
5.69 × 10−4
9.71 × 10−5
2.69 × 10−5
2.79 × 10−5
3.58 × 10−9
4.47
0.704
—
14.0
1.25
—
25.5 × 10−9
1.85 × 10−10
25.7 × 10−9
1.03 × 10−7
3.29 × 10−8
2.57 × 10−4
Note
a U is 99.27% by weight 238 U and 0.72% 235 U. Th is 100% 232 Th.
K is 0.0128% 40 K. Assumes kg K/kg U = 104 , kg Th/kg U = 4, and
H = 6.18 × 10−12 W kg−1 in present mantle. [1]
Reference
1. Turcotte D.L., & Schubert, G. 1982, Geodynamics (Wiley, New
York)
The abundances of uranium, thorium and potassium in the Earth and meteorite rocks is given in
Table 11.16.
Table 11.16. Representative concentrations (by weight) of heatproducing elements in several rocks and chondritic meteorites.a
Concentrations
Rock
Depleted Peridotites
Tholeiitic Basalt
Granite
Chondritic Meteorites
U (ppm)
0.012
0.1
4.
0.013
Th (ppm)
K (%)
0.035
0.35
17.
0.04
0.004
0.2
3.2
0.078
Note
a Radiogenic elements are highly concentrated in the continental crust.
11.14
EARTH INTERIOR [13]
The structure of the Earth’s interior has been determined mainly from seismology. Table 11.17
summarizes the values of the physical properties of a spherically symmetric model of the Earth as
a function of radius from the center of the Earth based on seismological data. The major divisions of
the solid Earth model are the core (radius r = 0 to 3480 km), the mantle (r = 3480 to 6346.6 km), and
the crust (r = 6346.6 to 6368 km). The model core is divided into a solid inner core (r = 0 to 1221.5
km) and a liquid outer core. The model mantle is divided into the lower mantle (r = 3480 to 5701
km) and upper mantle (5701 to 6368 km). Subregions of the model mantle are the D -layer at the base
of the mantle (r = 3480 to 3630 km), the transition zone in the mid-mantle (r = 5701 to 5971), the
seismic low velocity zone (r = 6151 to 6291 km) and the lithosphere or lid (r = 6291 to 6346.6 km).
Similar terms are used to describe regions of the real Earth whose radial thicknesses are not so readily
defined. The real Earth is, of course, laterally heterogeneous.
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Table 11.17. Physical properties of the Earth’s interior according to PREM (Preliminary Earth Reference Model).a
Radius
(km)
vp
(m s−1 )
vs
(m s−1 )
ρ
(kg m−3 )
Ks
(GPa)
µ
(GPa)
ν
p
(GPa)
g
(m s−2 )
Inner core
0.
200.
400.
600.
800.
1000.
1200.
1221.5
11266.20
11255.93
11237.12
11205.76
11161.86
11105.42
11036.43
11028.27
3667.80
3663.42
3650.27
3628.35
3597.67
3558.23
3510.02
3504.32
13088.48
13079.77
13053.64
13010.09
12949.12
12870.73
12774.93
12763.60
1425.3
1423.1
1416.4
1405.3
1389.8
1370.1
1346.2
1343.4
176.1
175.5
173.9
171.3
167.6
163.0
157.4
156.7
0.4407
0.4408
0.4410
0.4414
0.4420
0.4428
0.4437
0.4438
363.85
362.90
360.03
355.28
348.67
340.24
330.05
328.85
0
0.7311
1.4604
2.1862
2.9068
3.6203
4.3251
4.4002
Outer core
1221.5
1400.
1600.
1800.
2000.
2200.
2400.
2600.
2800.
3000.
3200.
3400.
3480.
10355.68
10249.59
10122.91
9985.54
9834.96
9668.65
9484.09
9278.76
9050.15
8795.73
8512.98
8199.39
8064.82
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
12166.34
12069.24
11946.82
11809.00
11654.78
11483.11
11292.98
11083.35
10853.21
10601.52
10327.26
10029.40
9903.49
1304.7
1267.9
1224.2
1177.5
1127.3
1073.5
1015.8
954.2
888.9
820.2
748.4
674.3
644.1
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
328.85
318.75
306.15
292.22
277.04
260.68
243.25
224.85
205.60
185.64
165.12
144.19
135.75
4.4002
4.9413
5.5548
6.1669
6.7715
7.3645
7.9425
8.5023
9.0414
9.5570
10.0464
10.5065
10.6823
D 3480.
3600.
3630.
13716.60
13687.53
13680.41
7264.66
7265.75
7265.97
5566.45
5506.42
5491.45
655.6
644.0
641.2
293.8
290.7
289.9
0.3051
0.3038
0.3035
135.75
128.71
126.97
10.6823
10.5204
10.4844
Lower
mantle
3630.
3800.
4000.
4200.
4400.
4600.
4800.
5000.
5200.
5400.
5600.
13680.41
13447.42
13245.32
13015.79
12783.89
12544.66
12293.16
12024.45
11733.57
11415.60
11065.57
7265.97
7188.92
7099.74
7010.53
6919.57
6825.12
6725.48
6618.91
6563.70
6378.13
6240.46
5491.45
5406.81
5307.24
5207.13
5105.90
5002.99
4897.83
4789.83
4678.44
4563.07
4443.17
641.2
609.5
574.4
540.9
508.5
476.6
444.8
412.8
380.3
347.1
313.3
289.9
279.4
267.5
255.9
244.5
233.1
221.5
209.8
197.9
185.6
173.0
0.3035
0.3012
0.2984
0.2957
0.2928
0.2898
0.2864
0.2826
0.2783
0.2731
0.2668
126.97
117.35
106.39
95.76
85.43
75.36
65.52
55.90
46.49
37.29
28.29
10.4844
10.3095
10.1580
10.0535
9.9859
9.9474
9.9314
9.9326
9.9467
9.9698
9.9985
5600.
5701.
11065.57
10751.31
6240.46
5945.08
4443.17
4380.71
313.3
299.9
173.0
154.8
0.2668
0.2798
28.29
23.83
9.9985
10.0143
5701.
5771.
10266.22
10157.82
5570.20
5516.01
3992.14
3975.84
255.6
248.9
123.9
121.0
0.2914
0.2909
28.83
21.04
10.0143
10.0038
5771.
5871.
5971.
10157.82
9645.88
9133.97
5516.01
5224.28
4932.59
3975.84
3849.80
3723.78
248.9
218.1
189.9
121.0
105.1
90.6
0.2909
0.2924
0.2942
21.04
17.13
13.35
10.0038
9.9883
9.9686
5971.
6061.
6151.
8905.22
8732.09
8558.96
4769.89
4706.90
4643.91
3543.25
3489.51
3435.78
173.5
163.0
152.9
80.6
77.3
74.1
0.2988
0.2952
0.2914
13.35
10.20
7.11
9.9686
9.9361
9.9048
Lowvelocity
zone
6151.
6221.
6291.
7989.70
8033.70
8076.88
4418.85
4443.61
4469.53
3359.50
3367.10
3374.71
127.0
128.7
130.3
65.6
66.5
67.4
0.2796
0.2796
0.2793
7.11
4.78
2.45
9.9048
9.8783
9.8553
Lid
6291.
8076.88
4469.53
3374.71
130.3
67.4
0.2793
2.45
9.8553
Region
Transition
zone
Sp.-V/AQuan/1999/10/08:17:45
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11.15 E ARTH ATMOSPHERE , D RY A IR AT STP / 257
Table 11.17. (Continued.)
Region
Crust
Ocean
Radius
(km)
vp
(m s−1 )
vs
(m s−1 )
ρ
(kg m−3 )
Ks
(GPa)
µ
(GPa)
ν
6346.6
8110.61
4490.94
3380.76
131.5
68.2
0.2789
0.604
9.8394
6346.6
6356.
6800.00
6800.00
3900.00
3900.00
2900.00
2900.00
75.3
75.3
44.1
44.1
0.2549
0.2549
0.604
0.337
9.8394
9.8332
6356.
6368.
5800.00
5800.00
3200.00
3200.00
2600.00
2600.00
52.0
52.0
26.6
26.6
0.2812
0.2812
0.337
0.300
9.8332
9.8222
6368.
6371.
1450.00
1450.00
0.
0.
1020.00
1020.00
2.1
2.1
0.
0.
0.5
0.5
0.300
0.
9.8222
9.8156
p
(GPa)
g
(m s−2 )
Note
a K is the bulk modulus, µ is the shear modulus, and ν is Poisson’s ratio.
s
11.15 EARTH ATMOSPHERE, DRY AIR AT
STANDARD TEMPERATURE AND PRESSURE (STP) [14, 15]
Standard temperature T0 = 273.15 K.
Standard pressure p0 = 1 013.250 × 102 Pa = 1 013.25 mbar.
Standard gravity g0 = 9.806 65 m s−2 .
Mass density of air ρ0 = 1.292 8 kg m−3 .
Molecular weight M0 = 28.964 × 10−3 kg mole−1 .
Mean molecular mass m 0 = 4.810 × 10−26 kg.
Molecular root-mean-square velocity (3RT0 /M0 )1/2 = 4.850 × 102 m s−1 .
Speed of sound (γ p0 /ρ0 )1/2 = (γ RT0 /M0 )1/2 = 3.313 × 102 m s−1 .
Specific heat at constant pressure c p = 1005 J kg−1 K−1 .
Specific heat at constant volume cv = 717.6 J kg−1 K−1 .
Ratio of specific heats γ = c p /cv = 1.400.
Number density of air N0 = 2.688 × 1025 m−3 .
Molecular diameter σ = 3.65 × 10−10 m.
Mean free path L = 1/(21/2 π N σ 2 ) = 6.285 × 10−8 m.
Coefficient of viscosity = 1.72 × 10−5 Pa s.
Thermal conductivity = 2.41 × 10−2 W m−1 K−1 .
Refractive index n
288.15
(n − 1) × 106 =
273.15
255.4 × 10−6
64.328 + 29 498.1 × 10−6
+
146 × 10−6 − σ 2
41 × 10−6 − σ 2
σ = 1/λ(m).
Rayleigh scattering (molecular) volume attenuation coefficient
k = 1.06
32π 3
(n − 1)2 .
3N λ4
.
Sp.-V/AQuan/1999/10/08:17:45
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258 / 11
11.16
E ARTH
COMPOSITION OF THE ATMOSPHERE [14, 16–21]
Table 11.18 gives the composition of the atmospheric gases.
Table 11.18. Gases in the well-mixed atmosphere.
Gas
N2 b
O2 c
H2 Ode f
Arg
CO2 c
Neg
Heg
CH4 h
Krg
COde
SO2 de
H2 i
N2 O j
O3 dek
Xeg
NO2 d
HNO3 d
NOde
CFCl3 l
CF2 Cl2 l
Molecular
weight
28.013
31.999
18.015
39.948
44.010
20.183
4.003
16.043
83.80
28.010
64.06
2.016
44.012
47.998
131.30
46.006
63.02
30.006
137.37
120.91
Fraction of dry air at surface
volume percent
78.08
20.95
2 × 10−6 − 3 × 10−2
9.34 × 10−3
3.45 × 10−4
18.2 × 10−6
5.24 × 10−6
1.72 × 10−6
1.14 × 10−6
1.5 × 10−7
3 × 10−10
5.0 × 10−7
3.1 × 10−7
3.0–6.5 × 10−8
8.7 × 10−8
2.3 × 10−11
5 × 10−11
3 × 10−10
2.8 × 10−10
4.8 × 10−10
weight percent
Column amount
(atm-cm)a
75.52
23.14
3 × 10−6 − 5 × 10−2
12.9 × 10−3
5.24 × 10−4
12.7 × 10−6
0.724 × 10−6
0.95 × 10−6
3.30 × 10−6
1.5 × 10−7
7 × 10−10
0.35 × 10−7
4.7 × 10−7
5.0–11 × 10−8
39.4 × 10−8
3.9 × 10−11
11 × 10−11
3 × 10−10
13 × 10−10
20 × 10−10
6.24 × 105
1.67 × 105
1760
7470
276
14.6
4.2
1.3
0.91
0.089
1.1 × 10−4
0.4
0.25
0.343
0.07
2.0 × 10−4
3.6 × 10−4
3.1 × 10−4
2.2 × 10−4
3.8 × 10−4
Notes
a 1 atm-cm = thickness of gas column when reduced to STP = 2.687 × 1023 molecules m−2 .
Gases are well mixed (constant fractional amount with altitude) in the troposphere unless otherwise
noted. Column amounts are nominal mid-latitude values [1, 2, 3]. Values for fractional amounts are
from [1, 2, 3, 4, 5].
b Photochemical dissociation in the thermosphere (see Table 11.20 for definition of thermosphere). Well mixed at lower levels [4].
c Photochemical dissociation above 95 km. Well mixed at lower levels [4].
d Considerable tropospheric vertical variation in the fractional amount. Very dry above the
tropopause [1, 2]. See Table 11.20 for definitions of troposphere and tropopause.
e Factor of 102 or more local variability related to local sources such as anthropogenic pollution
and geothermal activity [1, 2, 4, 5, 6].
f Fractional amounts are 1% extremes [1].
g Well mixed up to ∼ 110 km (turbopause). Diffusive separation at higher levels [4].
h Dissociated in the mesosphere (see Table 11.20 for definition of mesosphere). Well mixed at
lower levels [4, 7].
i Increase with altitude in the mesosphere because of dissociation of H O. Minimum value in the
2
stratosphere (see Table 11.20 for definition of stratosphere) [1, 7].
j Dissociated in the stratosphere and mesosphere [4].
k Range in fractional amount refers to monthly averages [5].
l Dissociated in the stratosphere [4].
References
1. COESA, U.S. Standard Atmosphere 1976, (Government Printing Office, Washington DC)
2. Anderson, G.P. et al. 1986, AFGL-TR-86-0110, Atmospheric Constituent Profiles 10–120 km,
Air Force Geophysics Laboratory (now Air Force Research Laboratory).
3. Allen, C.W. 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London)
4. Goody R.M., & Yung, Y.L. 1989, Atmospheric Radiation: Theoretical Basis, 2nd ed. (Oxford
Sp.-V/AQuan/1999/10/08:17:45
Page 259
11.18 H OMOGENEOUS ATMOSPHERE , S CALE H EIGHTS AND G RADIENTS
/ 259
University Press, New York)
5. Watson, R.F. et al. 1990, Greenhouse gases and aerosols, in Climate Change: The IPCC Scientific
Assessment edited by J.T. Houghton, G.H. Henkins, and J.H. Ephraums (Cambridge University
Press, New York)
6. Logan, J.A. et al. 1981, J. Geophys. Res., 86, 7210
7. Allen, M., Lunine, J.I., & Yung, Y.L. 1984, J. Geophys. Res. 89, 4841
11.17
WATER VAPOR [22, 23]
The water vapor pressure in saturated air is given in Table 11.19.
Table 11.19. Water vapor pressure e in saturated air.
Over pure water
T (◦ C)
e (Pa)
−30
50.88
−20
125.4
−10
286.3
0
610.8
10
1227
20
2337
30
4243
40
7378
Over ice
T (◦ C)
e (Pa)
−30
37.98
−20
103.2
−10
259.7
0
610.7
Water vapor density (perfect gas law) = (2.167 × 10−3 e/T) kg m−3 with T in K and e the water vapor
pressure in Pa.
1 cm precipitable water = 1245 cm STP water vapor.
Density of moist air (perfect gas law) = 3.484 × 10−3 ( p − 0.378e)/T (kg m−3 ) with P the total
pressure, p the water vapor pressure, e in Pa, and T in K.
Mean change of water vapor pressure with height h
log(eh /e0 ) = −h/2,
h ≤ 7.2 km
= −(h − 2.16)/1.4,
7.2 km ≤ h ≤ 13.6 km.
h = height above surface (km).
eh = water vapor pressure at height h.
e0 = water vapor pressure at surface.
11.18 HOMOGENEOUS ATMOSPHERE, SCALE HEIGHTS
AND GRADIENTS [17]
The scale height of the atmosphere (height for e-fold change of pressure in an isothermal atmosphere)
RT /g = R ∗ T /M W g = 2.93 × 10−2 T (km),
where R is the gas constant of dry air = 287.05 J kg−1 K−1 , R ∗ is the universal gas constant =
8.314 kJ K−1 kmole−1 , M W is the molecular weight of dry air = 28.964 kg kmole−1 , g is the
acceleration of gravity = 9.8 m s−2 , and T is in K.
Height of homogeneous atmosphere. (An idealized atmosphere of finite height, constant temperature
equal to the surface temperature, and constant density equal to the surface density.) = H =
R ∗ T /M W g.
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260 / 11
E ARTH
Surface Air T (◦ C)
H km
−30
7.11
−15
7.55
0
7.99
15
8.43
30
8.87
Mass of atmosphere per m2 = 1.035 × 104 kg.
Total mass of Earth’s atmosphere = 5.136 × 1018 kg.
Moment of inertia of the Earth’s atmosphere = 1.413 × 1032 kg m2 .
Magnitude of the dry adiabatic temperature gradient g/c p (c p is the specific heat at constant pressure =
1 005 J kg−1 K−1 for dry air) = 9.75 K km−1 .
Mean temperature gradient in troposphere = −6.5 K km−1 .
Mass per unit area of 1 atm-cm of gas of molecular weight M W = 4.462 × 10−4 M W (kg m−2 ) where
M W is in kg kmole−1 .
11.19 REGIONS OF EARTH’S ATMOSPHERE AND
DISTRIBUTION WITH HEIGHT [14, 17, 24]
The Earth’s atmospheric layers are detailed in Table 11.20.
Table 11.20. Atmospheric layers and transition levels.
Layer
Troposphere
Tropopause
Stratosphere
Stratopause
Mesosphere
Mesopause
Thermosphere
Exobase
Exosphere
Ozonosphere
Ionosphere
Homosphere
Heterosphere
Height, h
(km)
0–11
11
11–48
48
48–85
85
85–exobase
500–1000 km
> exobase
15–35 km
> 70 km
< 85 km
> 85 km
Characteristics
Weather, T decreases with h, radiative-convective equilibrium
Temperature minimum, limit of upward mixing of heat
T increases with h due to absorption of solar UV by O3 , dry
Maximum heating due to absorption of solar UV by O3
T decreases with h
Coldest part of atmosphere, noctilucent clouds
T increases with h, solar cycle and geomagnetic variations
Region of Rayleigh–Jeans escape
Ozone layer (full width at e−1 of maximum)
Ionized layers
Major constituents well-mixed
Constituents diffusively separate
Radiation belts
Inner belt
Outer belt
r/R⊕ at magnetic equator
∼ 1.3–2.4
∼ 3.5–11
Magnetosphere
In direction of Sun
Bow shock in direction of Sun
In direction normal to ecliptic
r/R⊕ at magnetic equator
10
12
18
Profiles of physical quantities in the atmosphere are given in Table 11.21.
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11.19 R EGIONS OF E ARTH ’ S ATMOSPHERE / 261
Table 11.21. Altitude profiles of mean physical conditions at latitude 45◦ [1].
Altitude
(km)
0
1
2
3
4
5
6
8
10
15
20
30
40
50
60
70
80
90
100
110
120
150
220
250
300
400
500
700
1000
log P
(Pa)
T
(K)
log ρ
(kg m−3 )
log N
(m−3 )
Ha
(km)
log l b
(m)
+5.006
+4.95
+4.90
+4.85
+4.79
+4.73
+4.67
+4.55
+4.42
+4.08
+3.74
+3.08
+2.46
+1.90
+1.34
+0.72
+0.022
−0.74
−1.49
−2.15
−2.60
−3.34
−4.07
−4.61
−5.06
−5.84
−6.52
−7.50
−8.12
288
282
275
269
262
256
249
236
223
217
217
227
250
271
247
220
199
187
195
240
360
634
855
941
976
996
999
1000
1000
+0.0881
+0.0460
+0.00286
−0.0413
−0.087
−0.133
−0.180
−0.279
−0.384
−0.71
−1.05
−1.73
−2.40
−2.99
−3.51
−4.08
−4.73
−5.47
−6.25
−7.01
−7.65
−8.68
−9.59
−10.22
−10.72
−11.55
−12.28
−13.51
−14.45
25.41
25.36
25.32
25.28
25.23
25.19
25.14
25.04
24.93
24.61
24.27
23.58
22.92
22.33
21.81
21.24
20.58
19.85
19.08
18.33
17.71
16.71
15.86
15.28
14.81
14.02
13.34
12.36
11.74
8.4
8.3
8.1
7.9
7.7
7.5
7.3
6.9
6.6
6.4
6.4
6.7
7.4
8.0
7.4
6.6
6.0
5.6
6.0
7.7
12.1
23.
36.
45.
51.
60.
69.
131.
288.
−7.2
−7.1
−7.1
−7.0
−7.0
−7.0
−6.9
−6.8
−6.7
−6.4
−6.0
−5.4
−4.7
−4.1
−3.6
−3.0
−2.4
−1.6
−0.85
−0.10
+0.52
+1.52
+2.38
+2.95
+3.41
+3.80
+4.89
+5.86
+6.49
Notes
a H = pressure scale height (km).
b l = mean free path (m).
Reference
1. COESA, U.S. Standard Atmosphere 1976, (Government Printing Office,
Washington DC)
Variations in physical quantities during the day and during the solar cycle are given in Table 11.22.
Table 11.22. Diurnal and solar cycle variations from mean values [1].ab
Altitude
(km)
200
500
1000
Diurnal
Solar
±δρ (%)
6.0
46.
43.
33
84
71
Diurnal
Solar
±δN (%)
6.2
44.
25.
32
80
51
Diurnal
Solar
±δp (%)
12.3
52.
35.
45
87
64
Diurnal
Solar
±δT (K)
59
121
122
145
207
207
Diurnal
Solar
±δMW (kg kmol)−1
0.041
0.49
0.99
0.32
1.62
1.40
Notes
a δ is the maximum departure in absolute value from mean values.
b Values obtained from the Mass Spectrometer Incoherent Scatter (MSIS) model for the following conditions. Diurnal:
Solar Activity Index F10.7 = 150, geomagnetic activity index A p = 10, day of year = 91, latitude = 45◦ N ; Solar:
Maximum F10.7 = 200, minimum F10.7 = 75, A p = 10, day of year = 91, latitude = 45◦ N, local time of day = 0900 h.
Reference
1. Hedin, A.E. 1983, J. Geophys. Res. A, 88, 170
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262 / 11
E ARTH
Composition and other atmosphere profile data are given in Table 11.23.
Table 11.23. Mean molecular weight, composition and molecular collision frequency ν [1, 2].a
Altitude
(km)
100
150
200
300
400
500
700
1000
MW
(kg kmol−1 )
N2
O2
Composition (% by volume)
O
He
Ar
28.44
24.18
21.55
18.11
16.42
15.23
10.63
4.48
77.
61.
42.
17.
6.0
1.9
0.1
< 0.05
19.
5.6
3.0
0.8
0.2
< 0.05
< 0.05
< 0.05
3.4
34.
55.
81.
91.
90.
55.
5.7
< 0.05
< 0.05
.01
0.8
2.7
8.2
43.
88.
0.8
0.1
< 0.05
< 0.05
< 0.05
< 0.05
< 0.05
< 0.05
H
< 0.05
< 0.05
< 0.05
< 0.05
< 0.05
0.2
1.6
6.7
log(ν)
ν in s −1
3.42
1.36
0.59
−0.377
−1.143
−1.796
−2.66
−3.12
Note
a Quantities obtained from the MSIS model for the following conditions: Solar activity index F
10.7 =
150, geomagnetic index A p = 10, day of year = 91, latitude = 45◦ N, and local time of day = 0900 h.
References
1. COESA, U.S. Standard Atmosphere 1976, (Government Printing Office, Washington DC)
2. Hedin, A.E. 1983, J. Geophys. Res. A, 88, 170
11.20
ATMOSPHERIC REFRACTION AND AIR PATH
The refractive index n of dry air at pressure ps = 1 013.25 × 102 Pa and temperature Ts = 288.15 K
is given by
29498.1 × 10−6
255.4 × 10−6
(n s − 1) × 106 = 64.328 +
+
,
146 × 10−6 − σ 2
41 × 10−6 − σ 2
where σ = λ−1 and λ is the vacuum wavelength in nm [15]. For other temperatures and pressures the
refractive index is found from
n − 1 = ( pTs / ps T )(n s − 1).
Water vapor reduces the refractive index by
p
w
43.49 1 − 7.956 × 103 σ 2
,
ps
where pw is the partial pressure of water vapor [15].
Refractive index of air for radio waves [25]
(n − 1) × 106 = 0.776
pw
p
pw
− 0.056
+ 3.75 × 103 2 .
T
T
T
Atmospheric refraction R is defined by
R ≡ zt − za ,
where z t is true zenith distance and z a is apparent zenith distance.
The constant of refraction R0 is
R0 =
n 20 − 1
2n 20
= 0.000 292 6 = 60.35 ,
where n 0 refers to n evaluated at p0 = 1 013.25 × 102 Pa and T0 = 273.15 K.
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11.20 ATMOSPHERIC R EFRACTION AND A IR PATH / 263
For n = n 0 refraction is [26]
z t 80◦ ,
Rn 0 ∼
= R0 tan z t ,
2.06
Rn 0 ∼
− 3.71 ,
= R0
0.058 9 + (π/2 − z t )
z t 80◦ .
For other temperature and pressure conditions
R = Rn0 ( pT0 / p0 T ).
Table 11.24 presents refraction data for the atmosphere.
Table 11.24. Refractive index n and refraction R versus wavelength λ.a
λ(nm)
(n d − 1) × 106
−(n w − 1) × 106
(n − 1) × 106
R (arcsec)
200
220
240
260
280
300
320
340
360
380
400
450
500
550
600
650
700
800
900
1000
1200
1400
1600
1800
2000
3000
4000
5000
7000
10000
341.9
329.4
321.2
315.3
310.9
307.6
304.9
302.7
301.0
299.5
298.3
295.9
294.3
293.1
292.2
291.5
290.9
290.1
289.6
289.2
288.7
288.4
288.2
288.1
288.0
287.7
287.7
287.6
287.6
287.6
0.19
0.20
0.20
0.21
0.21
0.22
0.22
0.22
0.22
0.22
0.22
0.23
0.23
0.23
0.23
0.23
0.23
0.23
0.23
0.23
0.23
0.24
0.24
0.24
0.24
0.24
0.24
0.24
0.24
0.24
341.7
329.2
321.0
315.1
310.7
307.2
304.7
302.5
300.8
299.3
298.1
295.7
294.1
292.9
292.0
291.3
290.7
289.9
289.4
289.0
288.5
288.2
288.0
287.9
287.8
287.5
287.5
287.4
287.4
287.4
70.44
67.87
66.18
64.96
64.06
63.34
62.82
62.37
62.02
61.71
61.46
60.97
60.64
60.39
60.20
60.06
59.94
59.77
59.67
59.58
59.48
59.42
59.38
59.36
59.34
59.28
59.28
59.26
59.26
59.26
Note
a Refractive index n is for dry air at T = 273.15 K and P = 1 013.25 × 102 Pa
d
0
0
and the correction n w for water vapor is for Pw = 550 Pa. For other temperatures
and pressures multiply n d − 1 by P T0 /P0 T and for other vapor pressures multiply
n w − 1 by pw / p0 . Refraction R = (n 2 − 1)/(2n 2 ) ∼
= n − 1 in arc seconds.
For radio waves and dry air with P0 = 1 013.25×102 Pa, T0 = 273.15 K, n d is (n d −1)×106 = 288.0.
The correction n w for water vapor with Pw = 550 Pa is (n w − 1) × 106 = 30.2.
The refractive index n is (n − 1) × 106 = 318.2.
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264 / 11
E ARTH
Transmission data for atmosphere components are in Table 11.25.
Table 11.25. Atmosphere transmission—absorber/scatterer [1, 2, 3, 4, 5, 6, 7, 8, 9, 10].
λ (µm)
10.00
7.50
5.00
4.00
3.00
2.00
1.00
0.90
0.80
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.38
0.36
0.34
0.32
0.30
0.28
0.26
0.24
0.22
0.20
H2 O
0.971
0.126
0.415
0.994
0.462
0.828
0.990
0.790
0.967
0.943
0.981
0.990
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
CO2
0.995
0.723
0.994
0.970
0.980
0.565
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
0.525
0.0014
0.0000
0.0000
O3
0.851
1.000
0.999
1.000
1.000
1.000
1.000
1.000
1.000
0.993
0.978
0.959
0.972
0.990
0.999
1.000
1.000
1.000
0.986
0.765
0.037
0.0000
0.0000
0.0000
0.0000
0.055
H2 O
continuum
0.946
0.280
0.728
0.983
0.859
0.982
1.000
0.990
1.000
0.999
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
Molecular
scattering
1.000
1.000
1.000
1.000
1.000
1.000
0.991
0.987
0.979
0.964
0.952
0.934
0.908
0.867
0.802
0.698
0.641
0.572
0.492
0.399
0.298
0.196
0.105
0.040
0.0083
0.0005
Aerosolsa
Other
Total
0.977
0.983
0.979
0.975
0.966
0.961
0.862
0.836
0.811
0.787
0.765
0.744
0.723
0.689
0.657
0.627
0.615
0.604
0.592
0.578
0.564
0.551
0.538
0.526
0.514
0.502
0.999b
0.759
0.025
0.294
0.837
0.376
0.441
0.846
0.645
0.767
0.709
0.699
0.659
0.637
0.591
0.527
0.438
0.394
0.345
0.287
0.177
0.0062
0.0000
0.0000
0.0000
0.0000
0.0000
0.993cd
1.000
0.906e
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
Notes
a Lowtran rural aerosol model.
b Trace gasses.
c Trace gasses (0.999).
d HNO (0.934).
3
e N continuum.
2
References
1. Anderson, G.P. et al. 1986, AFGL-TR-86-0110, Atmospheric Constituent Profiles 10–120 km, Air Force
Geophysics Laboratory (now Air Force Research Laboratory).
2. Kneizys, F.X. et al. 1983, AFGL-TR-0187, Atmospheric Transmittance/Radiance: Computer Code
LOWTRAN6, Air Force Geophysics Laboratory (now Air Force Research Laboratory)
3. McClatchey, R.A. et al. 1973, AFCRL-TR-73-0096, Atmospheric Absorption Line Parameters Compilation, Air Force Cambridge Research Laboratory (now Air Force Research Laboratory)
4. Rothman, L.S. & McClatchey, R.A. 1976, Appl. Optics, 15, 2616
5. Rothman, L.S. 1978, Appl. Optics, 17, 507
6. Rothman, L.S. 1978, Appl. Optics, 17, 3517
7. Rothman, L.S. 1981, Appl. Optics, 20, 791
8. Rothman, L.S. 1981, Appl. Optics, 20, 1323
9. Rothman, L.S. 1983, Appl. Optics, 22, 1616
10. Rothman, L.S. 1985, Appl. Optics, 22, 2247
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11.21 ATMOSPHERIC S CATTERING AND C ONTINUUM A BSORPTION / 265
11.21
ATMOSPHERIC SCATTERING AND CONTINUUM ABSORPTION
by David Crisp
At wavelengths shorter than about 300 nm, scattering and continuum absorption by gases and airborne
particles (aerosols) renders the Earth’s atmosphere virtually opaque to incoming radiation. The depth
of penetration of ultraviolet radiation is shown in Figure 11.1. For cloud-free conditions, Rayleigh
scattering by the atmosphere’s principal molecular constituents, N2 and O2 , accounts for the majority
of the scattering, while continuum absorption is produced primarily by O2 and O3 .
The extinction (scattering and absorption) at these wavelengths obeys the Beer–Bougher–Lambert
law, which states that the intensity I at wavelength λ and altitude z is given by
I (z, , λ) = I (∞, , λ) exp{−M()τ (z)},
I (∞, , λ) is the intensity at the top of the atmosphere at zenith angle , M() is the air-mass factor
(M() ∼ sec for for < 80◦ ), and τ (z) is the vertical extinction optical depth
τ (z) =
m i=1
∞
N (i, z)σ (i, z) dz,
0
N (i, z) is the altitude-dependent number density (particles m−3 ) and σ (i, z) is the effective extinction
cross section of a particle (molecule or aerosol m2 ).
Figure 11.1. Depth of penetration of solar radiation as a function of wavelength. Altitudes correspond to an
attenuation of l/e. The principal absorbers and ionization limits are indicated.
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11.21.1
E ARTH
Rayleigh Scattering
The Rayleigh scattering cross section per molecule σ R (λ) is given by
σ R (λ) =
8π 3 (n g − 1)(6 + 3δ)
,
3λ4 N 2 (6 − 7δ)
δ is the depolarization factor and n g is the wavelength-dependent refractive index of air. The Rayleigh
scattering optical depth for air can be approximated by
σ R (λ) ∼
= 0.008 569λ−4 1 + 0.001 13λ−2 + 0.000 13λ−4 p/ p0 ,
p is the pressure (mbar) at altitude z, and p0 = 1 013.25 mbar is the sea-level pressure. The slight
difference from the λ−4 dependence is introduced by the wavelength dependence of n g [27].
11.21.2
Aerosol Extinction
The continuum absorption and scattering by aerosols cannot be specified uniquely because the aerosol
abundance, composition, and size distribution can vary dramatically with location and time. However,
representative global-annual-average values of the wavelength-dependent aerosol extinction optical
depths have been derived for climate modeling studies. Tropospheric aerosols considered in these
models include sea salt, sulfates, natural dust, hydrocarbons, and other more minor constituents. The
stratospheric aerosols include sulfuric acid and silicates from volcanic eruptions, ammonium sulfates
and persulfates and ammonium hydrates.
The integrated aerosol optical depths above sea-level (0 km), 3 km, and 12 km from one such
modeling study [28] are shown in Figure 11.2. For hazy conditions, actual values of optical depth
can be more than an order of magnitude larger. The wavelength dependence of the optical depths
results from the particle size distribution (particles usually produce the most extinction at wavelengths
Figure 11.2. The calculated aerosol optical depth of the atmosphere.
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11.21 ATMOSPHERIC S CATTERING AND C ONTINUUM A BSORPTION / 267
comparable to their radius) as well as wavelength-dependent variations in the complex refractive
indices of these materials.
11.21.3
Continuum Absorption by Gases at UV and Visible Wavelengths
Molecular oxygen O2 and ozone O3 are the principal continuum absorbers at ultraviolet and visible
wavelengths. The principal O2 features include the ionization continuum at λ < 120 nm, the
Schumann–Runge continuum at 140 < λ < 180 nm, the Schumann–Runge bands at 180 < λ <
200 nm, and the Herzberg continuum at λ > 200 nm [29]. Several other gases, such as H2 O, CO2 ,
N2 O, and NO2 also contribute absorption at these wavelengths.
The wavelength-dependent absorption optical depths for these gases can be derived from their cross
sections once their number densities are known. If we neglect the temperature dependence of the gas
continuum cross sections, the column-integrated optical depths can be simplified further and expressed
as the product of the mean cross section, and the gas column abundance X which can be derived from
the pressure-dependent gas mixing ratios, r ( p),
∞
p
A0
X =
N (z) dz =
r ( p ) d p ,
µa g 0
0
A0 is Avogadro’s number (6.02 × 1023 molecules mol−1 ), µa is the molecular weight of air (≈
29 kg kmol−1 ), g is the gravitational acceleration, and p is pressure. The wavelength-dependent,
column-integrated optical depth is then given by
τ (λ) = σ (λ)X.
Global-annual average gas mixing ratio profiles for the gases mentioned above are shown in
Figure 11.3. Column abundances derived from these profiles are included in Table 11.26.
Figure 11.3. Global annual average gas mixing ratios.
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E ARTH
Table 11.26.
Column abundances of atmospheric gases.
11.22
Gas
X (molecules cm−2 )
O2
O3
H2 O
CO2
N2 O
NO2
4.47 × 1024
7.97 × 1018
8.12 × 1022
7.04 × 1021
6.36 × 1018
1.27 × 1016
ABSORPTION BY ATMOSPHERIC GASES AT VISIBLE AND
INFRARED WAVELENGTHS
by David Crisp
At wavelengths longer than 500 nm, the principal sources of atmospheric extinction are the vibration–
rotation bands of gases. Unlike the slowly-varying ultraviolet gas absorption features described in
the previous section, these bands consist of large numbers of narrow, overlapping absorption lines.
Because the cores of these lines can become completely opaque while their wings remain much
more transparent, the absorption within these bands does not strictly obey the Beer–Bougher–Lambert
absorption law, except in spectral regions that are sufficiently narrow to completely resolve the
individual line profiles (< 0.1 cm−1 ). The absorption coefficients within vibration–rotation bands
also vary much more strongly with pressure and temperature than those at ultraviolet wavelengths.
The absorption by these gases has therefore been characterized by an effective vertical optical depth.
Figures 11.4–11.6 show the vertical optical depth above sea level (top, thick line) and above a
high-altitude site, e.g., Mauna Kea Observatory in Hawaii (z = 4 km, p = 600 mbar, lower thin
line). These synthetic spectra were generated with an atmospheric line-by-line model. This model
employs a spectral resolution adequate to completely resolve the individual absorption lines (0.1 to
10−4 cm−1 ), but the spectra shown here were then smoothed with a rectangular slit function with a
full-width of 10 cm−1 (Figure 11.4) or 5 cm−1 (Figures 11.5 and 11.6). These figures therefore do
not resolve individual absorption lines. Absorption line parameters for all gases are from the HITRAN
database [30].
Figure 11.4. Vertical optical depth versus wavelength.
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11.22 A BSORPTION BY ATMOSPHERIC G ASES / 269
Figure 11.5. Vertical optical depth for near-infrared wavelengths.
Figure 11.6. Vertical optical depth at long wavelengths.
Figure 11.4 confirms that Rayleigh scattering and O3 continuum absorption dominate the extinction
optical depth at wavelengths less than 0.5 µm. At longer wavelengths, water vapor is the principal
absorber with its strongest features near 0.7, 0.82, and 0.94 µm. O2 also has four significant bands
between 0.65 and 1 µm. This figure also illustrates the advantage of working at a high-altitude site,
where the atmospheric pressure and scattering optical depth are only 60% of their sea level values.
Much less of an advantage is seen within the strong gas absorption bands, which are opaque even at
the high-altitude site.
Figure 11.5 shows that water is also the principal absorber at near-infrared wavelengths between 1
and 6 µm, with very strong bands centered near 1.1, 1.38, 1.88, 2.7, and beyond 6 µm. CO2 is the next
most important absorber at these wavelengths, with strong bands near 2.0, 2.7, and 4.3 µm, and much
weaker absorption near 1.22, 1.4, 1.6, 4.0, 4.8, and 5.2 µm. Other trace gases including CH4 (2.4 and
3.3 µm), O3 (3.3, 3.57, and 4.7 µm), and N2 O (2.1, 2.2, 2.47, 2.6, 2.9, and 4.7 µm) also produce some
extinction at these wavelengths.
Water vapor absorption continues to dominate the spectrum at wavelengths beyond 5 µm
(Figure 11.6). The most prominent water vapor bands at thermal wavelengths are the ν2 fundamental
centered near 6.3 µm and the rotation band beyond 20 µm, but this gas contributes significant
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E ARTH
absorption throughout this wavelength region. For example, the far wings of water vapor lines in
the ν2 and rotation bands provide much of the absorption in the atmospheric window regions near
8.5 and 12 µm. Within these windows, the high-altitude site (thin solid line) has up to a factor of
5 less absorption than the sea-level site (thick solid line), because the H2 O absorption coefficients
at these wavelengths are very strong functions of pressure (proportional to density-squared), and the
high-altitude site is above the majority of the water vapor. CO2 and O3 are the next most important
absorbers at thermal wavelengths, with strong features near 15 and 9.6 µm, respectively. CH4 , N2 O,
and NO2 also have strong absorption bands at these wavelengths, but their bands are largely obscured
by the stronger water vapor bands.
11.23
THERMAL EMISSION BY THE ATMOSPHERE
by David Crisp
The atmosphere emits as well as absorbs thermal radiation. This emission can enhance the sky
brightness significantly at some wavelengths and reduce the detectability of faint astronomical sources.
The intensities of the downwelling thermal radiance at a zenith angle of 21◦ are shown for a sea-level
site (solid line), and a high-altitude site, e.g., Mauna Kea, Hawaii (z = 4 km, p = 600 mbar, dotted
line) in Figures 11.7 and 11.8. At wavelengths within strong absorption bands, the atmosphere emits
almost like a black body. Within the atmospheric window regions centered near 3.5 and 10 µm, the
atmosphere emits much less radiation. The downward thermal radiation above a high-altitude site is
substantially less than over the sea-level site because the overlying atmosphere is both cooler and less
opaque.
Figure 11.7. Downward thermal radiance in the near-infrared part of the spectrum.
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11.24 I ONOSPHERE
/ 271
Figure 11.8. Downward thermal radiance at long wavelengths.
11.24
IONOSPHERE [17, 31]
The Earth’s ionosphere is the partially ionized part of its atmosphere. It is divided into layers or regions,
the main ones being the D, E, F1, and F2 regions, based principally on the altitude (z) profile of the
electron density n e (the number of electrons per unit volume). Ionospheric structure, n e (z), varies
strongly with time of day and month, latitude and solar activity. At night, the D and F1 regions vanish,
the E region weakens considerably, and the F2 region tends to persist at reduced intensity. Table 11.27
summarizes the characteristics of the ionospheric layers. The quantities are explained in the text below
the table.
Table 11.27. Properties of daytime ionospheric layers at middle and low latitudes.
Quantity
R
D
Approx. altitude range (km)
Approx. height of max. n e (km)
Range of max. n e (m−3 )
f 0 (MHz), χ = 0,
···
···
0
100
0
100
0
100
···
0
100
60–95
At top
108 –1010
0.2
0.28
5.0 × 108
109
2 × 105
—
15
1.2 × 1013
—
0
100
—
—
Max. n e (m−3 ), χ = 0,
q (m−3 s−1 )
(km)
Layer thickness
q dz (m−2 s−1 )
Ionizing emission at Sun
Surface (photons m−2 s−1 )
E
F1
F2
105–160
105–110
1011
3.3
3.82
1.35 × 1011
1.81 × 1011
5 × 108
109
25
4 × 1013
2.5 × 1013
160–180
170
1011 –1012
4.25
5.34
2.24 × 1011
3.54 × 1011
7 × 108
1.5 × 109
60
3 × 1013
9 × 1013
> 180
200–400
1012
6.9
11.95
5.91 × 1011
1.77 × 1012
108
3 × 108
300
5 × 1017
12 × 1017
18 × 1017
40 × 1017
14 × 1013
40 × 1013
9 × 1013
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E ARTH
Table 11.27. (Continued.)
Quantity
Neutral density at height
of maximum n e (m −3 )
T at height of max. n e (K)
Behavior
R
···
Recombination coefficient
α (m3 s−1 )
Attachment β (s−1 ), day
νei (s−1 )
νen (s−1 )
D
E
F1
F2
1018
2 × 1016
1015
10−12
300
α-Chapman
layer
10−14 –10−13
900
Chapman
layer
4 × 10−14
1100
Anomalous,
strongly variable
10−15
—
3
7 × 105
10−3
400
3 × 103
4 × 1020
180
Regular
10−3
200
250
3 × 10−4
400
10
f 0 = critical frequency = maximum plasma frequency of an ionospheric layer =
(e2 (maximum n e )/4π 2 0 m e )1/2 , m e = electron mass, e = electron charge, 0 = permittivity of
free space, n e = electron number density.
( f 0 (Hz))2 = 80.5 (maximum n e (m−3 )).
R = Wolf sunspot number = k( f + 10 g) , f = total number of spots seen, g = number of disturbed
regions (either single spots or groups of spots), k = a constant for a particular observatory.
q = ionization rate = rate of production of ion–electron pairs per unit volume (derived, e.g., from the
Sun’s spectrum and ionospheric absorption coefficients).
α = recombination coefficient, rate of electron loss by recombination = αn i n e (n i = number density
of ions) = αn 2e (normally, n i = n e ). Electron loss rate αn 2e has units of number per unit volume per
unit time.
α-Chapman layer = idealized model of an ionospheric layer, single species neutral atmosphere
with constant scale height H , solar radiation absorption ∝ neutral gas number density, absorp
tion coefficient is constant, q = qmo exp(1 − z − (sec χ )e−z ), z = (z − z mo )/H , z is altitude,
z mo is the height of maximum production rate when the Sun is overhead (χ = 0), qmo is the
production rate at z mo (when χ = 0), χ = solar zenith angle, production = loss, q = αn 2e ,
n e = n e (z mo ) exp 12 (1 − z − e−z sec χ ), qm is the maximum production rate = qmo cos χ , z m is the
height of maximum production = z mo + H ln(sec χ ), n e (z m ) = n e (z mo ) cos1/2 χ .
β = attachment coefficient, rate of electron loss by attachment to neutral particles to form negative
ions = βn e (neutral species number density n e ). β has units of inverse time.
β-Chapman layer = similar to α- Chapman layer except for electron loss which occurs by attachment,
q = βn e , n e = n e (z mo ) exp(1 − z − e−z sec χ ), n e (z m ) = n e (z mo ) cos χ .
dn e /dt = q − αn 2e − βn e , usually either α or β.
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11.24 I ONOSPHERE
/ 273
νei , νen = collision frequency of mean electron with ions, and neutral particles.
νen (s−1 ) = (6.93 × 105 n(N2 ) + 4.37 × 105 n(O2 )) u, u is electron energy in J, n(N2 ) and n(O2 ) are
number densities in m−3 .
w B (rad s−1 ) = gyrofrequency = Q B/m, Q = charge on particle (C), B = magnetic flux density
(T), m = charged particle mass (kg).
f B (Hz) = w B (rad s−1 )/2π.
w B (rad s−1 ) for an electron = 1.759 × 1011 B (T).
f B (Hz) for an electron = 2.799 × 1010 B (T).
w N (rad s−1 ) plasma frequency = (n e e2 /0 m e )1/2 , e = charge on an electron.
ω2N = 3182n e (ωn in rad s−1 and n e in m−3 ).
φ = Faraday rotation = rotation of the polarization angle of a radio wave propagating through the
ionosphere
=
1
2cω2
ω2N ω B B̂ · dl =
e3 µ0
=
2c0 m 2e 4π 2 f 2
1
e3
2c0 m 2e ω2
n e B · dl =
2.969 × 10−2
n e H · dl =
f2
9.327 × 105
ω2
n e B · dl
n e H · dl,
c is the speed of light, B̂ is a unit vector in the direction of B, dl is a path increment along the wave
propagation direction, integration is along the path of the radio wave, ω is the circular frequency of the
wave, f is the frequency of the wave in Hz, µ0 is the permeability of free space, H is the magnetic
field strength (A m−1 ), all units are SI, it is assumed that ω ω B , the formula is approximate for
cross-field propagation but accurate to within a few degrees of the normal to B, the rotation follows
the right-hand rule.
Photon efficiency of ionization η is the ratio of the rate of production of ion–electron pairs (number
m−3 s−1 ) to the total number of photons absorbed per unit volume and per unit time. Ionization of
atomic species yields one ion–election pair for every 5.45 × 10−18 J absorbed. Accordingly,
η=
1
5.45 × 10−18 J/(hc/λ)
= 36.5/λ (nm),
2 < λ < 100 nm,
h is Planck’s constant and λ is the wavelength of the radiation. For λ < 2 nm, η is approximately 20.
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11.24.1
E ARTH
Ionosphere as a Whole
The total electron content of the ionosphere is
∝
I ≡
n e dz,
0
where z is altitude. More generally, I can be defined as a line integral along an arbitrary path. Typically,
I is about 1017 electrons m−2 .
The equivalent thickness or slab thickness τ of the ionosphere is
τ ≡
I
.
max n e
This is the thickness of a hypothetical layer with uniform electron density equal to the maximum value
of n e and total electron content equal to I . Typically, τ is about 250 km.
11.24.2
Effects of Earth Curvature
The factor sec χ in the formulas for ionization and absorption should be replaced by Ch(x, χ ) to
account for Earth curvature, where x = (a + z)/H , H = scale height, a = Earth radius, z = altitude,
and χ is the zenith angle.
Curvature effects of the atmosphere are listed in Table 11.28.
Table 11.28. The function Ch(x, χ ).a
Q
50
100
200
400
800
1000
χ=
sec χ =
30◦
1.155
45◦
1.414
Ch(x, χ )
60◦
75◦
2.000
3.864
80◦
5.76
85◦
11.47
90◦
∞
95◦
1.148
1.151
1.153
1.154
1.154
1.155
1.389
1.401
1.407
1.411
1.412
1.413
1.901
1.946
1.972
1.985
1.993
1.994
4.19
4.70
5.10
5.38
5.55
5.59
5.82
7.07
8.28
9.33
10.15
10.35
8.93
12.58
17.76
25.09
35.46
39.65
16
30
68
220
1476
3.228
3.473
3.646
3.742
3.800
3.812
Note
a Q ≡ (a + z )/H , z = altitude of maximum ionization rate.
0
0
11.24.3
International Reference Ionosphere (IRI)
IRI is an empirical reference model of ionospheric electron density, electron and ion temperatures, and
ion composition recommended by COSPAR (Committee on Space Research) and URSI (International
Union of Radio Science). It is updated bi-yearly; the 1990 model is used below. IRI is distributed
by the National Space Science Data Center and World Data Center A for Rockets and Satellites
(NSSDC/WDC-A-R&S) in Greenbelt, Md. IRI is available online on SPAN (Space Physics Analysis
Network) now called NSI-DECNET (NASA Science Internet) and can be accessed interactively on
NSSDC’s Online Data Information Service (NODIS) account. Tables 11.29 to 11.36 give data about
this IRI ionosphere model.
Sp.-V/AQuan/1999/10/08:17:45
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11.24 I ONOSPHERE
Table 11.29. IRI-90 electron density.a
Noon
z (km)
n e (m−3 )
65
70
75
80
85
90
95
100
8.3 × 107
2.1 × 108
3.7 × 108
5.1 × 108
1.1 × 109
1.2 × 1010
5.2 × 1010
1.1 × 1011
Midnight
n e /n e F2(max)
n e (m−3 )
3 × 10−4
7 × 10−4
1.3 × 10−3
1.8 × 10−3
3.7 × 10−3
4.0 × 10−2
1.8 × 10−1
3.7 × 10−1
0
0
0
0
2.6 × 108
4.8 × 108
1.6 × 109
1.6 × 109
n e /n e F2(max)
0
0
0
0
2.3 × 10−3
4.2 × 10−3
1.4 × 10−2
1.4 × 10−2
Note
a Latitude = 45◦ , Longitude = 260◦ E, R = 0, Day = 6/22, F10.7 = 63.8,
χ = 21.6◦ (Noon), 111.6◦ (Midnight).
Table 11.30. IRI-90 electron density.a
Noon
z (km)
65
70
75
80
85
90
95
100
n e (m−3 )
2.7 × 108
6.7 × 108
1.2 × 109
1.6 × 109
3.4 × 109
3.3 × 1010
1.1 × 1011
1.8 × 1011
Midnight
n e /n e F2(max)
4 × 10−4
n e (m−3 )
0
0
0
0
2.6 × 108
4.8 × 108
2.8 × 109
3.9 × 109
1 × 10−3
1.7 × 10−3
2.4 × 10−3
5.0 × 10−3
4.8 × 10−2
1.6 × 10−1
2.6 × 10−1
n e /n e F2(max)
0
0
0
0
6 × 10−4
1.1 × 10−3
6.2 × 10−3
8.8 × 10−3
Note
a Latitude = 45◦ , Longitude = 260◦ E, R = 150, Day = 6/22, F10.7 = 193,
χ = 21.6◦ (Noon), 111.6◦ (Midnight).
Table 11.31. IRI-90 electron density.a
3/21
6/22
9/23
12/22
1.8 × 108
4.4 × 108
1.0 × 1010
9.5 × 1010
1.5 × 108
3.8 × 108
8.0 × 109
7.0 × 1010
5.8 × 108
1.0 × 109
2.9 × 1010
1.6 × 1011
1.6 × 108
4.1 × 108
9.0 × 109
1.0 × 1011
R=0
ne
ne
ne
ne
(70 km)
(80 km)
(90 km)
(100 km)
1.9 × 108
(70 km)
(80 km)
(90 km)
(100 km)
5.9 × 108
4.5 × 108
1.0 × 1010
9.5 × 1010
2.1 × 108
5.1 × 108
1.2 × 1010
1.1 × 1011
R = 150
ne
ne
ne
ne
1.4 × 109
2.9 × 1010
1.6 × 1011
6.7 × 108
1.6 × 109
3.3 × 1010
1.8 × 1011
Note
a Time = Noon, Latitude = 45◦ , Longitude = 260◦ E, F10.7 = 63.8
(R = 0), 193 (R = 150), χ = 44.5◦ (3/21), 21.6◦ (6/22), 45.4◦ (9/23),
68.5◦ (12/22), units of n e are number m−3 .
/ 275
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276 / 11
E ARTH
Table 11.32. IRI-90 electron density.a
Latitude (◦ N)
45
60
1.2 × 108
3.7 × 108
6.0 × 109
3.8 × 1010
75
90
0
0
4.7 × 108
4.4 × 109
—
—
—
—
0
0
4.7 × 108
6.3 × 109
1.6 × 108
3.8 × 108
3.4 × 109
4.0 × 109
R=0
ne
ne
ne
ne
(70 km)
(80 km)
(90 km)
(100 km)
1.5 × 108
3.8 × 108
8.0 × 109
7.0 × 1010
ne
ne
ne
ne
(70 km)
(80 km)
(90 km)
(100 km)
1.6 × 108
4.1 × 108
9.0 × 109
1.0 × 1011
R = 150
1.2 × 108
3.7 × 108
6.3 × 109
5.4 × 1010
Note
a Time = Noon, Longitude = 260◦ E, F10.7 = 63.8 (R = 0), 193
(R = 150), χ = 68.5◦ (45◦ N), 83.5◦ (60◦ N), 98.5◦ (75◦ N), 113.5◦ (90◦ N),
Day = 12/22, units of n e are number m−3 .
Table 11.33. IRI-90 model ionosphere.a
z (km)
100
200
300
400
500
600
700
800
900
1000
n e (m−3 )
Tn (K)
Ti (K)
Te (K)
O+
H+
He+
O+
2
NO+
1.08 × 1011
2.74 × 1011
2.40 × 1011
1.11 × 1011
4.63 × 1010
2.41 × 1010
1.61 × 1010
1.28 × 1010
1.14 × 1010
1.07 × 1010
—
786
821
822
822
822
822
822
822
822
—
786
1011
1237
1513
1813
2113
2413
2712
3012
—
1419
2689
2831
2835
2846
2936
3042
3148
3254
0
23
99
100
96
88
80
69
59
50
0
0
0
0
4
10
18
28
37
45
0
0
0
0
0
1
2
3
4
5
48
21
0
0
0
0
0
0
0
0
52
56
1
0
0
0
0
0
0
0
Note
a Latitude = 45◦ , Longitude = 260◦ E, R = 0, Day = 6/22, F10.7 = 63.8, χ = 21.6◦ ,
Time = Noon, Tn = neutral temperature, Ti = ion temperature, Te = electron temperature, ion
composition is given in percent.
Table 11.34. IRI-90 model ionosphere.a
z (km)
100
200
300
400
500
600
700
800
900
1000
n e (m−3 )
Tn (K)
Ti (K)
Te (K)
O+
H+
He+
O+
2
NO+
1.79 × 1011
3.92 × 1011
6.85 × 1011
6.25 × 1011
4.63 × 1011
3.29 × 1011
2.51 × 1011
2.10 × 1011
1.89 × 1011
1.77 × 1011
—
1187
1361
1385
1389
1390
1390
1390
1390
1390
—
1187
1361
1385
1513
1813
2113
2413
2712
3012
—
1421
2689
2831
2835
2846
2936
3042
3148
3254
0
59
100
100
96
88
80
69
59
50
0
0
0
0
4
10
18
28
37
45
0
0
0
0
0
1
2
3
4
5
58
6
0
0
0
0
0
0
0
0
42
35
0
0
0
0
0
0
0
0
Note
a Latitude = 45◦ , Longitude = 260◦ E, R = 150, Day = 6/22, F10.7 = 193, χ = 21.6◦ ,
Time = Noon, Tn = neutral temperature, Ti = ion temperature, Te = electron temperature, ion
composition is given in percent.
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11.24 I ONOSPHERE
Table 11.35. IRI-90 model ionosphere.a
Noon
Midnight
R=0
n e (m−3 )
Tn (K)
Ti (K)
Te (K)
%O+
%H+
%He+
2.87 × 1011
815
899
2076
53b
0
0
Noon
Midnight
R = 150
9.07 × 1010
692
817
1010
42c
0
0
5.94 × 1011
1314
1314
2076
99
0
0
3.70 × 1010
1090
1090
1090
99
0
0
Note
a Latitude = 45◦ , Longitude = 260◦ E, Day = 6/22, F10.7 = 63.8
(R = 0), 193 (R = 150), Tn = neutral temperature, Ti = ion temperature,
Te = electron temperature, Altitude = 250 km, χ = 21.6◦ (Noon), 111.6◦
(Midnight).
b The other ions in this case are 46% NO+ and 1% O+ .
2
c The other ions in this case are 57% NO+ and 1% O+ .
2
Table 11.36. IRI-90 model ionosphere.a
Date
3/21
6/22
n e (m−3 )
Tn (K)
Ti (K)
Te (K)
%O+
%H+
%He+
%O+
2
%NO+
3.07 × 1011
777
867
1882
76
0
0
0
23
2.87 × 1011
815
899
2076
53
0
0
1
46
n e (m−3 )
Tn (K)
Ti (K)
Te (K)
%O+
%H+
%He+
%O+
2
%NO+
1.15 × 1012
1221
1221
1882
95
0
0
0
5
5.94 × 1011
1314
1314
2076
99
0
0
0
0
9/23
12/22
3.27 × 1011
773
864
1882
76
0
0
0
23
4.27 × 1011
687
802
1780
95
0
0
0
5
8.60 × 1011
1219
1219
1882
95
0
0
0
5
1.63 × 1012
1089
1089
1782
95
0
0
0
5
R=0
R = 150
Note
a Latitude = 45◦ , Longitude = 260◦ , F10.7 = 63.8 (R = 0), 193
(R = 150), Tn = neutral temperature, Ti = ion temperature, Te = electron
temperature, Altitude = 250 km, χ = 44.5◦ (3/21), 21.6◦ (6/22), 45.4◦ (9/23),
68.5◦ (12/22).
/ 277
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278 / 11
11.24.4
E ARTH
Irregularities of Ionospheric Behavior [31]
Storm
Magnetic Storm
F-Region Ionospheric Storm
11.24.5
A severe departure from normal behavior lasting from one to
several days.
A magnetic storm consists of three phases: (1) an increase of
magnetic field lasting a few hours; (2) a large decrease in the
horizontal component of magnetic field building up to a maximum
in about a day; (3) a recovery to normal over a few days. The initial
phase (1) is caused by the compression of the magnet sphere by a
burst of solar plasma. The main phase (2) is due to the ring current
in the magnetosphere which flows around the Earth from east to
west.
This storm is characterized by an initial positive phase of increasing electron density lasting a few hours followed by a main or
negative phase of decreasing n e . The ionosphere gradually returns
to normal over one to several days during the recovery phase.
Sq Current System
The Sq current system is an ionospheric current system due to neutral winds blowing ions across
magnetic field lines. The Sq winds and currents are driven by solar (S) tides under quiet (q)
geomagnetic conditions. The winds have speeds of tens of meters per second and associated electric
fields are a few millivolts per meter. The Sq currents produce daily magnetic field variations at the
Earth’s surface.
Node of EW currents is at latitude 38◦ .
Current between node and either pole or equator (at equinox and zero sunspots) = 5.9 × 104 A.
11.24.6
Magnetic Indices [31]
K p is based on the range of variation within 3 hour periods of the day observed in the records from
about a dozen selected magnetic observatories. The K p value for each 3 hour interval of the day is
reported on a scale from 0 (very quiet) to 9 (very disturbed). Integer values are subdivided into thirds
by use of the symbols + and −. The K p scale is quasi-logarithmic.
a p —similar to K p , but a linear scale of geomagnetic activity. The value of a p is approximately
half the range of variation of the most disturbed magnetic component measured in nT .
The relation between K p and A p is shown in Table 11.37.
Table 11.37. Relation between K p and a p .
Kp
ap
0
0
1
3
2
7
3
15
4
27
5
48
6
80
7
140
8
240
9
400
A p is a daily index, the average of a p over a day.
AE is a geomagnetic index measuring the activity level of the auroral zone, particularly valuable
as an
indicator of magnetic substorms.
K p is the sum of the eight K p values over a U T day.
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11.25 N IGHT S KY AND AURORA
11.25
/ 279
NIGHT SKY AND AURORA [17, 32–36]
The units for expressing the night sky brightness of spectroscopic features (lines or bands of restricted
extent in wavelength) are:
1 Rayleigh = R = 106 photons emitted in 4π sr per cm2 vertical column per sec
= 1.58 × 10−7 λ−1 J m−2 sr−1 s−1 at zenith (λ in nm)
= 1.95 × 10−7 nit for λ = 555 nm.
1 Photon = 1.986 × 10−16 λ−1 J (λ in nm)
1 m v = 10 star deg−2 near 550 nm through clear atmosphere
= 3.6 × 10−2 R nm−1
= 7.1 × 10−7 nit (for a bandwidth of 100 nm).
Components of the night sky brightness are given in Table 11.38.
Table 11.38. Night sky brightness.
Source
Photographic
10th mag stars
Visual
deg −2
Photometry
10−5 nit
Airglow
(near zenith)
Atomic lines
Bands and continuum
Zodiacal light (away from zodiac)
Faint stars, m > 6 (galactic pole)
(mean sky)
(gal. equator)
Diffuse galactic light
Total brightness (zenith, mean sky)
(15◦ lat, mean sky)
30
60
16
48
140
10
145
190
40
50
100
30
95
320
20
290
380
3
4
6
2
7
23
1
21
28
Color index of night sky C ∼
= 0.7 (C = B − V − 0.11, where B is the apparent magnitude at 555
nm and V is the apparent magnitude at 435 nm).
Airglow variation with latitude: Generally brighter at middle and high latitudes than at low
latitudes, a factor of ∼ 2 increases with latitude for some emissions [35].
Airglow variation with solar cycle activity: Good correlation with sunspot activity for OI red line
(630 nm), ambiguous evidence for variation in green line (557.7 nm) [35].
Van Rijin function: Off-zenith path length through a spherically symmetric airglow layer is
increased relative to the zenith viewing by a factor
−1/2
V = 1 − (r/(r + h))2 sin2 z
,
where r is the Earth’s radius, h is the height of the emitting layer above the Earth’s surface, and z is the
zenith angle.
The full moon brightness is 1100 tenth magnitude stars per square degree in the photographic
spectral region and 100 in the visual band. For other phases of the Moon multiply by φ(α), where α is
the phase angle, the angle between the Sun and Earth seen from the Moon, and φ(α) is the phase law
or the change of the Moon’s brightness with α(φ(0) = 1) [17].
The sky brightness during twilight is given in Table 11.39.
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E ARTH
Table 11.39. Variation of sky brightness throughout twilight
relative to 0◦ solar depression angle [1].
Solar depression angle
0◦
6◦
12◦
18◦
Log relative brightness
0
−2.7
−4.7
−5.8
Reference
1. Allen, C.W. 1973, Astrophysical Quantities, 3rd ed.
(Athlone Press, London)
Table 11.40 lists the night sky emissions from various components.
Table 11.40. Spectral emissions in the night sky [1, 2, 3, 4, 5].a
Intensity
λ, etc.
nm
Night
R
Twilight
R
Aurora
kR
250
100
180
1000
100
2–100
6
30 ± 20
10
12
6
1
0.1–2
45
HI
HI
CaII
LiI
N2
N2
N2
N2
N2
557.7
630.0–636.4
297.2
130.4–135.6
777.4
844.6
1040
346.6
519.9
VIS. and FUV
589.0–589.6
summer
winter
656.3
121.6
393.3–396.7
670.8
IR
UV
FUV
Blue
EUV
N+
2
N+
2
O2
O2
O2
O2
O+
2
OH
OH
OH
OH
NO2
NOγ
HeI
NUV, VIS.
630–890
300–400
864.5
1270
1580
VIS., IR
1580
VIS.
8342
Total
500–650
MUV
1083
Emitter
OI
OI
OI
OI
OI
OI
NI
NI
NI
NII
NaI
150
13
10
Remarks
< 100 R to > 500 R night to night variation
Sporadic enhancements in tropical nightglow
ICB III Aurora
Observed from satellites, ICB III Aurora
ICB III Aurora
ICB III Aurora
ICB III Aurora
NaD, Strong seasonal variation
30
200
15
2500
1000
5000
1
1
10
100
Hα
Lα
150
30
880
110
200–400
55
2000
100
1000
1500
500
6000
20 000
150
630
60
1200
2500
26
150 000
130
2000
4.5 × 106
250
20–60
1st positive, ICB III Aurora
2nd positive, ICB III Aurora
LBH bands, ICB III Aurora
VK bands, ICB III Aurora
BH, WK, ICB III Aurora, rough value
deduced from photometer data
1st negative, ICB III Aurora
M, ICB III Aurora
Hertzberg bands
Atm. (0–1), ICB III Aurora
Atm. (0–0), not seen at ground, ICB III Aurora
IR Atm, ICB III Aurora
1st negative, ICB III Aurora
(4–2) Strongest bands are in NIR
(5–0) (7–1) (8–2) (9–3) bands
(6, 2) band
Nightglow continuum
ICB III Aurora
1000
Note
a LBH = Lyman–Birge–Hopfield, M = Meinel, VK = Vegard–Kaplan, WK = Watson–Koontz, BH = Birge–
Hopfield, ICB III = OI(557.7) = 100 k R [1, 2, 3, 4].
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11.25 N IGHT S KY AND AURORA
/ 281
References
1. Allen, C.W. 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London)
2. Vallance Jones, A. 1974, Aurora (Reidel, Boston)
3. Roach, F.E., & Gordon, J.L. 1973, The Light of the Night Sky, (Reidel, Boston)
4. Krassovsky, V.I. et al. 1962, Planet. Space Sci., 9, 883
5. Chamberlain, J.W. 1961, Physics of the Aurora and Airglow, (Academic Press, New York)
Zone of maximum auroral activity = 60–75◦ geomagnetic latitude [32].
Seasonal variation: Minima in auroral frequency at solstices, maxima at equinoxes (approximately
a factor of 2 increase from minima to maxima as seen from Yerkes Observatory) [36].
Table 11.41 gives details of the types of aurorae.
Table 11.41. Auroral heights [1, 2].
Aurora
Height
Lower border strong aurora
Lower border weak aurora
Average value
Average height of maximum emission
Vertical extents
Upper extremity
95 km
114 km
105–108 km
110 km
20–40 km
frequently > 200 km
Type c (normal aurora)
Sunlit upper extremity
700 km (1000 km in extreme cases)
Type b: red lower border
Type d (red overall) lower border
80–100 km
250 km
References
1. Allen, C.W. 1973, Astrophysical Quantities, 3rd ed. (Athlone Press, London)
2. Meinel, A.B. et al. 1954, J. Geophys. Res., 59, 407
The proton input needed to produce auroral Hα is given in Table 11.42.
Table 11.42. Flux of monoenergetic protons required to produce 10 kR of Hα in the zenith [1].
Initial energy
keV
Minimum
penetration height
km
Hα
photons
Proton flux
cm−2 s−1
Total incident
energy flux
eV cm−2 s−1
130
27
8.5
100
110
120
60
27
7
1.6 × 108
5 × 108
14 × 108
2.1 × 1013
1.4 × 1013
1.2 × 1013
Reference
1. Chamberlain, J.W. 1961, Physics of the Aurora and Airglow (Academic Press, New York)
Auroral International Coefficients of Brightness:
I.C.B.
I
II
III
IV
557.7 brightness = 1 kR ≈ 10−4 nit,
557.7 brightness = 10 kR ≈ 10−3 nit,
557.7 brightness = 100 kR ≈ 10−2 nit,
557.7 brightness = 1000 kR ≈ 10−1 nit.
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11.26
E ARTH
GEOMAGNETISM [37–39]
The geomagnetic field arises from sources both interior and exterior to the solid Earth, including
electric currents in the liquid outer core and the ionosphere and the magnetization of crustal rocks.
Models of the global magnetic field are intended to describe the field originating in the core (the main
field). The description of the main field is based on a spherical harmonic description of the potential
V (r, θ, φ, t) for magnetic induction B(r, θ, φ, t)
B = −∇V,
where r, θ, φ are spherical polar coordinates and t is time. The spherical harmonic expansion of V is
V (r, θ, φ, t) = a
l l+1 L a
l=1 m=0
r
glm (t) cos mφ + h lm (t) sin mφ P̃lm (cos θ),
where a is the mean radius of the Earth (a = 6371.2 km), L is the truncation level of the expansion,
and the P̃lm (cos θ ) are Schmidt quasi-normalized associated Legendre functions, i.e., the integral of
P̃lm squared over all solid angles is 4π/(2l + 1). The quantities glm (t) and h lm (t) are known as Gauss
geomagnetic coefficients; they vary with time over a broad range of time scales from less than a year
to hundreds of millions of years. The core dynamo responsible for generating the main magnetic field
is fundamentally time dependent in its behavior. If the small electrical conductivity of the mantle is
neglected, then the above representation of the main geomagnetic field can be used to extrapolate the
surface field down to the core–mantle boundary.
The components of the magnetic field are given by
Br = −
l
L a l+2 ∂V
glm (t) cos mφ + h lm (t) sin mφ P̃lm (cos θ),
=
(l + 1)
∂r
r
l=1 m=0
Bθ = −
l l+2 L d P̃lm
1 ∂V
a
glm (t) cos mφ + h lm (t) sin mφ
=−
(cos θ),
r ∂θ
r
dθ
l=1 m=0
Bφ = −
l l+2 L m P̃lm (cos θ)
1 ∂V
a
glm (t) sin mφ − h lm (t) cos mφ
=
.
r sin θ ∂φ
r
sin θ
l=1 m=0
Magnetic field observations are generally described in terms of the quantities:
X = −Bθ = north magnetic field component,
Y = Bφ = east magnetic field component,
Z = −Br = vertically downward magnetic field component,
H = (X 2 + Y 2 )1/2 = horizontal magnetic field intensity,
F = (X 2 + Y 2 + Z 2 )1/2 = total magnetic field intensity,
I = arctan(Z /H ) = magnetic inclination,
D = arctan(Y/ X ) = magnetic declination.
Historically, there has been much discussion of the westward drift of the main field or components
thereof, particularly the nondipole part of the field (see below). While some features of the field may
participate in a westward drift, the secular variation of the main field is more complex than a simple
westward drift.
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11.26 G EOMAGNETISM
11.26.1
/ 283
Geomagnetic Dipole
The contributions to V of the l = 1 terms in the spherical harmonic representation of V are from
magnetic dipoles situated at r = 0 and oriented along the coordinate axes.
a 3 cos θ 0
g1
r2
a 3 cos φ sin θ 1
g1
r2
a 3 sin φ sin θ 1
h1
r2
is the potential of a magnetic dipole in the +z-direction
(along the Earth’s rotation axis),
is the potential of a magnetic dipole in the +x-direction
(along the Greenwich meridian),
is the potential of a magnetic dipole in the +y-direction.
The total dipole potential V dipole is the sum of the above terms.
The total dipole magnetic field B dipole = −∇V dipole has components
dipole
Br
dipole
Bθ
dipole
Bφ
2a 3 0
1
1
cos
θ
+
sin
θ(g
cos
φ
+
h
sin
φ)
,
g
1
1
1
r3
a3 = 3 g10 sin θ − cos θ(g11 cos φ + h 11 sin φ) ,
r
=
=
a3 1
(g sin φ − h 11 cos φ).
r3 1
The magnetic dipole moment m has magnitude
1/2
m = 4πa 3 (g10 )2 + (g11 )2 + (h 11 )2
.
The magnetic dipole moment pierces the surface of the Earth at colatitude θm and longitude φm ,
given by
1/2 (g11 )2 + (h 11 )2
h 11
θm = arctan
,
φ
.
=
arctan
m
g11
g10
Table 11.43 lists the values of m/4πa 3 , θm , and φm for the years 1945–1990.
The orientation and magnitude of the centered, tilted, magnetic dipole from the l = 1 terms in the
spherical harmonic representation of the main field is given in Table 11.43.
Table 11.43. Orientation and magnitude of the centered, tilted, magnetic dipole.
(m/4πa 3 ), 104 nT
Colatitude of
Geomagnetic Pole
(θm , degrees)
Longitude of
Geomagnetic Pole
(φm , degrees)a
1945
1950
1955
1960
1965
1970
1975
1980
1985
1990
3.122
3.118
3.113
3.104
3.095
3.083
3.070
3.057
3.043
3.032
11.53
11.53
11.54
11.49
11.47
11.41
11.31
11.19
11.03
10.87
291.5
291.2
290.8
290.5
290.1
289.8
289.5
289.2
289.1
288.9
Note
a East from the Greenwich meridian.
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E ARTH
The time rate of change of the magnetic dipole is obtained by differentiating the above expressions
for m, θm , and φm with respect to time.
11.26.2
Eccentric Dipole
The Cartesian coordinates (x0 , y0 , z 0 ) of the eccentric dipole that best represents the main field are
given by
x0 =
a(L 1 − g11 T )
,
3(m/4πa 3 )2
y0 =
a(L 2 − h 11 T )
,
3(m/4πa 3 )2
z0 =
a(L 0 − g10 T )
,
3(m/4πa 3 )2
where
√
L 0 = 2g10 g20 + 3(g11 g21 + h 11 h 12 ),
√
L 1 = g11 g20 + 3(g10 g21 + g11 g22 + h 11 h 22 ),
√
L 2 = −h 11 g20 + 3(g10 h 12 + g11 h 22 − h 11 g22 ),
T =
11.26.3
L 0 g10 + L 1 g11 + L 2 h 11
.
4(m/4πa 3 )2
Dipole Coordinate System
A coordinate system with its z-axis along the direction of the centered, tilted dipole is the dipole
coordinate system or the geomagnetic coordinate system. The pole of this coordinate system is located
at θm , φm , given above. This is the geomagnetic pole or dipole pole. If x d is a vector in the dipole
coordinate system and x is a vector in the standard coordinate system, then
x d = R · x,
where R is the rotation matrix with elements

cos θm cos φm
R =  −sin φm
sin θm cos φm
11.26.4
cos θm sin φm
cos φm
sin θm sin φm

−sin θm
0 .
cos θm
Magnetic Dip-Poles
A magnetic dip-pole is a location at which the horizontal magnetic field is zero. At the north and south
dip-poles the magnetic potential has its maximum and minimum values, respectively. Table 11.44 gives
the coordinates of the dip-poles at different times.
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Table 11.44. Coordinates of the magnetic dip-poles.
Year
Latitude (N)
Longitude (W)
North Dip-Pole
1831.4
1904.5
1948.0
1962.5
1973.5
70◦ 05
70◦ 30
73◦ 00
75◦ 06
76◦ 00
96◦ 46
95◦ 30
100◦ 00
100◦ 48
100◦ 36
South Dip-Pole
1841.0
1899.8
1909.0
1912.0
1931.0
1952.0
1962.1
11.26.5
75◦ 05
72◦ 40
72◦ 55
71◦ 10
70◦ 20
68◦ 42
67◦ 30
154◦ 08
152◦ 30
155◦ 16
150◦ 45
149◦ 00
143◦ 00
140◦ 00
Centered, Tilted Dipole Field [39]
Vertical magnetic field at geomagnetic poles, at r = a,
m = 6.064 × 104 nT.
=2
4πa 3
Horizontal magnetic field at geomagnetic equator, at r = a,
=
m
= 3.032 × 104 nT.
4πa 3
In the dipole coordinate system
m
cos θmag
4πr 2
a 3 cos θmag m ,
=
r2
4πa 3
m V (r = a) =
a cos θmag ,
4πa 3
V =
where θmag is the magnetic colatitude. Numerical values are for the IGRF (1991 Revision).
11.27
METEORITES AND CRATERS [17, 40–44]
Classes of meteorites (natural objects of extraterrestrial origin that survive passage through the
atmosphere) and statistics on falls and finds are given in Table 11.45. Falls refer to meteorites that were
seen to fall; they are usually recovered soon after fall. Finds refer to meteorites that were not seen to fall
but were found and recognized subsequently. Meteorites are broadly classified into stones, irons (pure
metal, essentially nickel–iron alloy), and stony–irons. Additional classifications are required because
of the great diversity of objects in these broad classes. Stony meteorites are divided into chondrites
(meteorites containing distinctive features known as chondrules with compositions very similar to
that of the solar photosphere for all but the most volatile elements) and achondrites (differentiated
meteorites with compositions considerably different from the Sun).
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Table 11.45. Meteorite classes and statistics on falls and finds [1].
Class
Chondrites
CI
CM
CO
CV
H
L
LL
EH
EL
Other
Anchondrites
Eucrites
Howardites
Diogenites
Ureilites
Aubrites
Shergottites
Nakhlites
Chassignites
Anorthositic
breccias
Stony-irons
Mesosiderites
Pallasites
Irons
IAB
IC
IIAB
IIC
IID
IIE
IIF
IIIAB
IIICD
IIIE
IIIF
IVA
IVB
Other irons
Falls
Fall frequency
(%)b
5
18
5
7
276
319
66
7
6
3
25
18
9
4
9
2
1
1
Findsa
Non-Antarctic
Antarcticc
0.60
2.2
0.60
0.84
33.2
38.3
7.9
0.84
0.72
0.36
0
5
2
4
347
286
21
3
4
3
0
34
6
5
671
224
42
6
1
3
3.0
2.2
1.1
0.48
1.1
0.24
0.12
0.12
8
3
0
6
1
0
2
0
13
4
9
9
17
2
0
0
0
0
0
1
6
3
0.72
0.36
22
34
2
1
6
0
5
0
3
1
1
8
2
0
0
3
0
13
0.73
0.08
0.45
0.05
0.09
0.10
0.03
1.42
0.14
0.10
0.05
0.39
0.09
1.32
97
11
60
7
12
13
4
189
19
13
6
52
12
175
4
0
6
0
0
0
0
0
0
0
0
1
0
0
Notes
a Data for finds are given to provide an indication of available material. The
unusual conditions in the Antarctic favor the recovery of large numbers of
meteorites without the selection biases of non-Antarctic regions (e.g., in nonAntarctic regions, stony meteorites, especially anchondrites are more easily
confused with terrestrial rocks than iron meteorites). The statistics for Antarctic
finds, therefore, more closely resemble those of falls than non-Antarctic finds.
In fact, several rarer classes are overrepresented in the Antarctic collections.
b Iron–meteorite fall statistics calculated from finds, scaled to percentage of
total iron–meteorite falls.
c US finds in the Antarctic. In addition, > 6000 meteorites have been
recovered from the Antarctic by Japanese teams.
Reference
1. Sears, D.W.G., & Dodd, R.T. 1988, in Meteorites and the Early Solar System,
edited by J.F. Kerridge and M.S. Matthews (University of Arizona Press,
Tucson, Arizona), pp. 3–31
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11.27.1
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Meteorite Infall Rates
Fall of meteorites large enough to be seen and found, ≈ 2 meteorites per day over the whole Earth.
The cumulative flux of meteoroids F in the vicinity of the Earth–Moon system is given by
#
F
= 7.9(m (kg))−1.16 ,
10−10 < m < 105 kg,
2
6
10 km yr
where F is the number of meteoroids with mass greater than m per 106 km2 per year. Accordingly,
meteoroids with masses greater than about 6 kg will arrive in the vicinity of the Earth–Moon system at
a rate of about one per 106 km2 per year.
11.27.2
Meteorite Masses
The most probable size of found meteorites for iron is 15 kg and for stones 3 kg. Meteoroid masses
before entry to the Earth’s atmosphere are ≈ 100 kg. The mass of the greatest known meteorite (Hoba,
an iron meteorite) is 6 × 104 kg.
11.27.3
Cratering Efficiency
Mass displaced from crater/mass of impactor = cratering efficiency
−0.65
1.61gL
= 0.2
,
vi2
g = gravity(m s−2 ),
L = projectile diameter (m),
vi = impact velocity (m s−1 ).
11.27.4
Crater Diameter Scaling Relations for Terrestrial Craters [42]
1/2 −1/2
D = 0.0133W 1/3.4 + 1.51ρ P ρT
−1/3 −0.2 0.13
D = 1.8ρ 0.11
P ρT
1/6 −1/2
D = 0.2ρ P ρT
g
L
W 0.28 ,
L,
W 0.22 ,
D 1 km.
All units in the above formulas are SI.
D = diameter of a transient impact crater,
ρ P = impactor density,
ρT = target density,
W = impactor energy,
L = impactor diameter.
Formulas valid for vertical impacts.
Energy of 1 kiloton of TNT = 4.2 × 1012 J.
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11.27.5
E ARTH
Crater Dimensions
Rim height h R above original ground surface of many fresh (unrelaxed) lunar, terrestrial, explosion,
and laboratory impact craters with diameter (rim to rim), D 15 km,
h R (m) = 0.036(D (m))1.014 .
For craters with D > 15 km on the Moon (collapsed craters)
h R (m) = 0.236(D (m))0.399 .
Crater depth H (rim to floor) of fresh lunar craters with diameter D 11 km
H (m) = 0.196(D (m))1.01 .
Crater depth of collapsed lunar craters
H (m) = 1.044(D (m))0.301
11 km < D < 400 km.
Crater depth of simple (relatively young) terrestrial impact craters (e.g., Meteor Crater, Arizona)
H (m) = 0.14(D (m))1.02 .
Crater depth of collapsed or complex terrestrial impact craters
H (m) = 0.27(D (m))0.16 .
Estimated cratering rate from relatively young (< 120 Myr) large craters on the North American and
European cratons
(5.4 ± 2.7) × 10−15 km−2 yr−1
for D ≥ 20 km.
Estimated cratering rate from smaller craters on a nonglaciated area in the U.S.
(2.2 ± 1.1) × 10−14 km−2 yr−1
for
D ≥ 10 km.
Important impact craters are listed in Table 11.46.
Table 11.46. Terrestrial impact structures [1].
Name
Latitude
Longitude
Diameter
(km)
Age
(Myr)
Amguid, Algeria
Aouelloul, Mauritaniaa
Araguainha Dome, Brazil
Azuara, Spain
Barringer, Arizona, USAa
Bee Bluff, Texas, USA
Beyenchime-Salaatin, Russia
Bigatch, Kazakhstan
Boltysh, Ukraine
Bosumtwi, Ghana
Boxhole, Northern Territory,
Australiaa
B.P. Structure, Libya
Brent, Ontario, Canadaa
26◦ 05 N
20◦ 15 N
16◦ 46 S
41◦ 01 N
35◦ 02 N
29◦ 02 N
71◦ 50 N
48◦ 30 N
48◦ 45 N
06◦ 32 N
004◦ 23 E
012◦ 41 W
052◦ 59 W
000◦ 55 W
111◦ 01 W
099◦ 51 W
123◦ 30 E
082◦ 00 E
032◦ 10 E
001◦ 25 W
0.45
0.37
40.
30.
1.2
2.4
8.
7.
25.
10.5
< 0.1
3.1 ± 0.3
< 250
< 130
0.025
< 40
< 65
6±3
100 ± 5
1.3 ± 0.2
22◦ 37 S
25◦ 19 N
46◦ 05 N
135◦ 12 E
024◦ 20 E
078◦ 29 W
0.18
2.8
3.8
—
< 120
450 ± 30
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11.27 M ETEORITES AND C RATERS
Table 11.46. (Continued.)
Name
Campo del Cielo,
Argentina (20)ab
Carswell, Saskatchewan, Canada
Charlevoix, Quebec, Canada
Clearwater Lake East, Quebec,
Canada
Clearwater Lake West, Quebec,
Canada
Connolly Basin, Western
Australia, Australiaa
Crooked Creek, Missouri, USA
Dalgaranga, Western
Australia, Australiaa
Decaturville, Missouri, USA
Deep Bay, Saskatchewan,
Canada
Dellen, Sweden
Eagle Butte, Alberta, Canada
El’gygytgyn, Russia
Flynn Creek, Tennessee, USA
Glover Bluff, Wisconsin, USA
Goat Paddock, Western
Australia, Australia
Gosses Bluff, Northern
Territory, Australia
Gow Lake, Saskatchewan,
Canada
Gusev, Russia
Haughton, Northwest
Territories, Canada
Haviland, Kansas, USAa
Henbury, Northern Territory,
Australia (14)ab
Holleford, Ontario, Canada
Ile Rouleau, Quebec, Canada
Ilintsy, Ukraine
Ilumetsy, Estonia
Janisjärvi, Russia
Kaalijärvi, Estonia (7)ab
Kaluga, Russia
Kamensk, Russia
Kara, Russiaa
Karla, Russia
Kelly West, Northern
Territory, Australia
Kentland, Indiana, USA
Kjardla, Estonia
Kursk, Russia
Lac Couture, Quebec, Canada
Lac La Moinerie, Quebec,
Canada
Lappajärvi, Finlanda
Liverpool, Northern Territory,
Australia
Logancha, Russia
Logoisk, Byelorussia
Lonar, India
Latitude
Longitude
Diameter
(km)
Age
(Myr)
27◦ 38 S
58◦ 27 N
47◦ 32 N
061◦ 42 W
109◦ 30 W
070◦ 18 W
0.09
37.
46.
—
117 ± 8
360 ± 25
56◦ 05 N
074◦ 07 W
22.
290 ± 20
56◦ 13 N
074◦ 30 W
32.
290 ± 20
23◦ 32 S
37◦ 50 N
124◦ 45 E
091◦ 23 W
9.
5.6
< 60
320 ± 80
27◦ 43 S
37◦ 54 N
117◦ 05 E
092◦ 43 W
0.21
6.
—
< 300
56◦ 24 N
61◦ 55 N
49◦ 42 N
67◦ 30 N
36◦ 17 N
43◦ 58 N
102◦ 59 W
016◦ 32 E
110◦ 30 W
172◦ 05 E
085◦ 40 W
089◦ 32 W
12.
15.
10.
23.
3.8
6.
100 ± 50
109.6 ± 1
< 65
3.5 ± 0.5
360 ± 20
< 500
18◦ 20 S
126◦ 40 E
5.
< 50
23◦ 50 S
132◦ 19 E
22.
142.5 ± 0.5
56◦ 27 N
≈ 54◦ N
104◦ 29 W
≈ 22◦ E
5.
3.
< 250
65
75◦ 22 N
37◦ 35 N
089◦ 40 W
099◦ 10 W
20.
0.011
21.5 ± 1.2
—
24◦ 34 S
44◦ 28 N
50◦ 41 N
49◦ 06 N
57◦ 58 N
61◦ 58 N
58◦ 24 N
54◦ 30 N
48◦ 20 N
69◦ 10 N
57◦ 54 N
133◦ 10 E
076◦ 38 W
073◦ 53 W
029◦ 12 E
025◦ 25 E
030◦ 55 E
022◦ 40 E
036◦ 15 E
040◦ 15 E
065◦ 00 E
048◦ 00 E
0.15
2.
4.
4.5
0.08
14.
0.11
15.
25.
60.
10.
—
550 ± 100
< 300
395 ± 5
0.002
698 ± 22
0.004
380 ± 10
65
57 ± 9
10
19◦ 30 S
40◦ 45 N
57◦ 00 N
51◦ 40 N
60◦ 08 N
132◦ 50 E
087◦ 24 W
022◦ 42 E
036◦ 00 E
075◦ 20 W
2.5
13.
4.
5.
8.
< 550
< 300
510 ± 30
250 ± 80
425 ± 25
57◦ 26 N
63◦ 09 N
066◦ 36 W
023◦ 42 E
8.
14.
400 ± 50
77 ± 4
12◦ 24 S
65◦ 30 N
54◦ 12 N
19◦ 58 N
134◦ 03 E
095◦ 50 E
027◦ 48 E
076◦ 31 E
1.6
20.
17.
1.83
150 ± 70
50 ± 20
40 ± 5
0.05
/ 289
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E ARTH
Table 11.46. (Continued.)
Name
Latitude
Longitude
Diameter
(km)
Age
(Myr)
Machi, Russia (5)b
Manicouagan, Quebec, Canada
Manson, Iowa, USA
Middlesboro, Kentucky, USA
Mien, Swedena
Misarai, Lithuania
Mishina Gora, Russia
Mistastin, Newfoundland, and
Labrador, Canada
Monturaqui, Chilea
Morasko, Poland (7)ab
New Quebec, Quebec, Canada
Nicholson Lake, Northwest
Territories, Canadaa
Oasis, Libya
Obolon’, Ukraine
Odessa, Texas, USA (3)ab
Ouarkziz, Algeria
Piccaninny, Western Australia,
Australia
Pilot Lake, Northwest
Territories, Canada
Popigai, Russia
Puchezh-Katunki, Russia
Red Wing Creek, North Dakota,
USA
Riacho Ring, Brazil
Ries, Germanya
Rochechouart, Francea
Rogozinskaja, Russia
Rotmistrovka, Ukraine
Sääksjärvi, Finlanda
Saint Martin, Manitoba, Canada
Serpent Mound, Ohio, USA
Serra da Canghala, Brazil
Shunak, Kazakhstan
Sierra Madera, Texas, USA
Sikhote Alin, Russia (122)ab
Siljan, Sweden
Slate Island, Ontario, Canada
Sobolev, Russiaa
Söderfjärden, Finland
Spider, Western Australia,
Australia
Steen River, Alberta, Canada
Steinheim, Germany
Strangways, Northern
Territory, Australiaa
Sudbury, Ontario, Canada
Tabun-Khara-Obo, Mongoliaa
Talemzane, Algeria
Teague, Western Australia,
Australia
Tenoumer, Mauritania
Ternovka, Ukraine
Tin Bider, Algeria
Ust-Kara, Russia
57◦ 30 N
51◦ 23 N
42◦ 35 N
36◦ 37 N
56◦ 25 N
54◦ 00 N
58◦ 40 N
116◦ 00 E
068◦ 42 W
094◦ 31 W
083◦ 44 W
014◦ 52 E
023◦ 54 E
028◦ 00 E
0.3
100.
32.
6.
5.
5.
2.5
55◦ 53 N
23◦ 56 S
52◦ 29 N
61◦ 17 N
063◦ 18 W
068◦ 17 W
016◦ 54 E
073◦ 40 W
28.
0.46
0.1
3.2
38 ± 4
1
0.01
<5
62◦ 40 N
24◦ 35 N
49◦ 30 N
31◦ 45 N
29◦ 00 N
102◦ 41 W
024◦ 24 E
032◦ 55 E
102◦ 29 W
007◦ 33 W
12.5
11.5
15.
0.168
3.5
< 400
—
215 ± 25
—
< 70
17◦ 32 S
128◦ 25 E
7.
60◦ 17 N
71◦ 30 N
57◦ 06 N
111◦ 01 W
111◦ 00 E
043◦ 35 E
6.
100.
80.
47◦ 36 N
07◦ 43 S
48◦ 53 N
45◦ 30 N
58◦ 18 N
49◦ 00 N
61◦ 23 N
51◦ 47 N
39◦ 02 N
08◦ 05 S
42◦ 42 N
30◦ 36 N
46◦ 07 N
61◦ 02 N
48◦ 40 N
46◦ 18 N
63◦ 02 N
103◦ 33 W
046◦ 39 W
010◦ 37 E
000◦ 56 E
062◦ 00 E
032◦ 00 E
022◦ 25 E
098◦ 32 W
083◦ 24 W
046◦ 52 W
072◦ 42 E
102◦ 55 W
134◦ 40 E
014◦ 52 E
087◦ 00 W
138◦ 52 E
021◦ 35 E
9.
4.
24.
23.
8.
2.5
5.
23.
6.4
12.
2.5
13.
0.0265
52.
30.
0.05
5.5
200
—
14.8 ± 0.7
160 ± 5
55 ± 5
140 ± 20
< 330
225 ± 40
< 320
< 300
12
100
—
368 ± 1
< 350
—
< 600
16◦ 30 S
59◦ 31 N
48◦ 41 N
126◦ 00 E
117◦ 38 W
010◦ 04 E
5.
25.
3.4
—
95 ± 7
14.8 ± 0.7
15◦ 12 S
46◦ 36 N
44◦ 06 N
33◦ 19 N
133◦ 35 E
081◦ 11 W
109◦ 36 E
004◦ 02 E
24.
140.
1.3
1.75
< 472
1850 ± 150
< 30
<3
25◦ 50 S
22◦ 55 N
48◦ 01 N
27◦ 36 N
69◦ 18 N
120◦ 55 E
010◦ 24 W
033◦ 05 E
005◦ 07 E
065◦ 18 E
28.
1.9
8.
6.
25.
1685 ± 5
2.5 ± 0.5
330 ± 30
< 70
57 ± 9
<1
210 ± 4
61 ± 9
< 300
118 ± 3
395 ± 145
< 360
< 360
440 ± 2
39 ± 9
183 ± 5
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Table 11.46. (Continued.)
Diameter
(km)
Age
(Myr)
Name
Latitude
Longitude
Upheaval Dome, Utah, USA
Veevers, Western Australia,
Australiaa
Vepriaj, Lithuania
Vredefort, South Africa
Wabar, Saudi Arabia (2)ab
Wanapitei Lake, Ontario,
Canadaa
Wells Creek, Tennessee, USA
West Hawk Lake, Manitoba,
Canada
Wolf Creek, Western Australia,
Australiaa
Zeleny Gai, Ukraine
Zhamanshin, Kazakhstan
38◦ 26 N
109◦ 54 W
5.
—
22◦ 58 S
55◦ 06 N
27◦ 00 S
21◦ 30 N
125◦ 22 E
024◦ 36 E
027◦ 30 E
050◦ 28 E
0.08
8.
140.
0.097
< 450
160 ± 30
1970 ± 100
—
46◦ 44 N
36◦ 23 N
080◦ 44 W
087◦ 40 W
8.5
14.
37 ± 2
200 ± 100
49◦ 46 N
095◦ 11 W
2.7
100 ± 50
19◦ 10 S
48◦ 42 N
48◦ 24 N
127◦ 47 E
035◦ 54 E
060◦ 48 E
0.85
1.4
10.
—
120 ± 20
0.75 ± 0.06
Notes
a Structures with meteoritic fragments or geochemical anomalies considered to have a
meteoritic source.
b Sites with multiple craters, with (n) indicating number of craters. Diameter given
corresponds to largest crater.
Reference
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There is increasing acceptance of the importance of impacts in the evolution of the Earth and
planets. Examples of possible impact-related events in the Earth’s history include the formation of the
Moon by a Mars-sized impactor early in the Earth’s evolution and the Cretaceous–Tertiary extinctions
(about 65 Ma) by the effects of an impactor of mass about 1015 kg, energy about 1023 J, and diameter
about 100 km.
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