Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet
Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet
Model : wo+ Solution for uniform half-space: CI = CII = lk( (a = oO) Recurrence formula foY layered half-space'{Cn = C(zn)}: - C~~ - C~~~ = Jioy o + [kr2 0 L The TE-field within the n'th layer at the depth z = zn + E, Z < Z + E < Z n+l' can be calculated from its surface value n n according to: with gtzr,zs) = cosh Bps - sinh Brs/(K,Cr) h(zr,z ) = cosh @, - sinh B K C s rs r r for s.< - n and gCzn, z~+E) = cosh(Kn~)-sinh(K n E)/K n C n
, , The formula for E applies also to E and HZ, the formula for X Y Hx also to H . Y 7.4 Penetration depth of various types of geomagnetic variations and the overall distribution of conductivity within the Earth Three types of conduction which vary by orders of magnitude have to be distinguished: 1. Conduction through rock forming minerals 2. Conduction through fluids in pores and cracks between rockfor- mine minerals 3. Metallic conduction li: Since the minerals of crustal and mantle material are expected to be silicates, the conduction through these minerals will be that of semi-conductors. Their resistivity is in the order 5 of 10 Om at room temperature but decreases with temperature T is the absolute temperate, k Boltzmann's constant; a and A 0 are pressure-dependent and composition-dependent constants within a limited temperature range, for which one specific mechanism of semi-conduction is predominant. Hence, in plots of in o versus T-' the o-T dependence should be represented by joining segments of straight lines. Laboratory experiments with rocks and minerals at high temperature and varying pressure have confirmed this piece-wise linear dependence of lno from T-l. Furthermore, they showed that the composition- dependence of u is mainly contained in the pre-exponential
- Page 43 and 44: 4. Having determined B;, the coeffi
- Page 45 and 46: 3.4. Anomalous region as basic doma
- Page 47 and 48: - 6 and 6= can be so adjusted that
- Page 49 and 50: From the generalized Green's theore
- Page 51 and 52: and y can again be so adjusted that
- Page 53 and 54: 4.2. In3ral - --- equation method L
- Page 55 and 56: The element GZx is needed for all z
- Page 57 and 58: With this knowledge of the behaviou
- Page 59 and 60: After having determined Qzr VJ,; @,
- Page 61 and 62: 4.3. The surface inteyral approach
- Page 63 and 64: F At the vertical boundaries the co
- Page 65 and 66: The four equations A A A A H = i sg
- Page 68 and 69: 6. Approaches to the inverse proble
- Page 70 and 71: to minimize the quantity a s = 12 /
- Page 72 and 73: It remains to show a way to minimiz
- Page 74 and 75: Agai-n, from a finite erroneous dat
- Page 76 and 77: Here lJ - is a N x P matrix contain
- Page 78 and 79: small eigenvalues. The parameter ve
- Page 80 and 81: Then - 77 - A(E2 - E ) = iwu U (E -
- Page 82 and 83: whence 2k d -2k d where a = CA:(A;)
- Page 84 and 85: . 7. Basic concepts of geomagnetic
- Page 86 and 87: orders of magnitude smaller' than t
- Page 88 and 89: Elimination of - E or .,. H yields
- Page 90 and 91: Observing that rot pot rot g = - ro
- Page 92 and 93: Two special types of such anomalies
- Page 96 and 97: parameter u and that the pressure d
- Page 98 and 99: (=disturbed)-variations: After magn
- Page 100 and 101: with 4 as geographic latitude. From
- Page 102 and 103: Very rapid oscillations with freque
- Page 104 and 105: ! 8. Data Collection - and Analysis
- Page 106 and 107: A horizontal electric -- field comp
- Page 108 and 109: For a data reducti.on in the fr3equ
- Page 110 and 111: Let q be the tranfer function betwe
- Page 112 and 113: . A as transfer function between A
- Page 114 and 115: -- Structural soundi~z with station
- Page 116 and 117: Since it follows that - E 1 = - T E
- Page 118 and 119: - - . the same or from different si
- Page 120 and 121: The Fourier integral - +- -io t T -
- Page 122 and 123: The weigh-t . function W is then fo
- Page 124 and 125: Two convenient filters are 3 sinx I
- Page 126 and 127: (e.g. X), their realizations by obs
- Page 128 and 129: Observe that the residual, of which
- Page 130 and 131: Example: n = 12 and @ = 95%: 1 n =
- Page 132 and 133: - As a consequence, the real and im
- Page 134 and 135: This relati-on implies .that .the l
- Page 136 and 137: 9. --- Data 5.nterpretatj.on on the
- Page 138 and 139: The "modified apparent - - resistiv
- Page 140 and 141: Exercise Geomagne-tic varj.ations.
- Page 142 and 143: 9.2 Layered Sphere - The sphericity
, ,<br />
The formula for E applies also to E and HZ, the formula for<br />
X Y<br />
Hx also to H .<br />
Y<br />
7.4 Penetration depth of various types of geomagnetic variations<br />
and the overall distribution of conductivity within the Earth<br />
Three types of conduction which vary by orders of magnitude have<br />
to be distinguished:<br />
1. Conduction through rock forming minerals<br />
2. Conduction through fluids in pores and cracks between rockfor-<br />
mine minerals<br />
3. Metallic conduction<br />
li: Since the minerals of crustal and mantle material are expected<br />
to be silicates, the conduction through these minerals will<br />
be that of semi-conductors. Their resistivity is in the order<br />
5<br />
of 10 Om at room temperature but decreases with temperature<br />
T is the absolute temperate, k Boltzmann's constant; a and A<br />
0<br />
are pressure-dependent and composition-dependent constants<br />
within a limited temperature range, for which one specific<br />
mechanism of semi-conduction is predominant. Hence, in plots<br />
of in o versus T-' the o-T dependence should be represented<br />
by joining segments of straight lines. Laboratory experiments<br />
with rocks and minerals at high temperature and varying<br />
pressure have confirmed this piece-wise linear dependence of<br />
lno from T-l. Furthermore, they showed that the composition-<br />
dependence of u is mainly contained in the pre-exponential
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