Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

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(=disturbed)-variations: After magnetic storms the hor,j.zontal Dst -- - H-component of the Ear-th's magnetic field shows a worldwide de- crease. Within a week after stormbeginn H returns asymptotj.cally to its pre-storm level. This so-called Dst-phase of storms shows negligible longitudinal dependence, while its latitude dependence is well described in geomagnetic coordinates by 3 L is the geomagnetic latitude of the location considered. The source of the Dst-phase may be visualized as an equatorial - ring - current (ERC) which encircles the Earth in the equatorial plane in geomagnetic coordinates: Tf the interior of the Earth were a perfect insulator and no eddy currents were induced, the vertical Dst-coniponent would be ZDst - H, sin @. In reality, only one fourth to one fifth of this value is observed due to the field of eddy currents which oppose in Z the primary field of the ERC. Let LDst denote the inductive scale r - ijw Q=kso length of DPt, a be the Earth's radius, then for @ : 45' ., - - - 2C~st 'DS t a H~st4 (cf. sec. 8.2) Hence, with ZDStfHDSt 0.2 the depth of penetration will be 600 km'.
9 (solar quiet) varia-tions: On the da)l-lit side of the Earth thermal convection in combination with tidal motions generate large-scale wind-systems in the high atmosphere. 1; the ionosphere these winds produce electric currents which - for an observer fixed to the Earth, - move with the sun around the Earth. During equinoxes there will be two current vortices of equal strength in the northern and 0 0 southern hemisphere, their centers being at roughly 30 N and 30 S. Due.-to these currents local-time dependent geomagnetic variations will be observed at a fixed site at the Earth's surface. They are repeated from day to day in similar form and are called "diurnal" or Sq-variations: -- Aiai-n the Z Ampli-tude is much smaller than to be expected from SQ- D for an insulating Earth. Tf and D (") deno-te the amplitudes s Q SQ s ? of the m1 th subharmonic of the diurnal varl.;i.tions (m=1,2,3 ,I! (I7 the corresponding to the periods T = 24, 12, 8, 6 hours) and C s Q inductive scale length of this subharmonj.~,
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Electromagnetic Induction in the Ea
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6.2. Generalized matrix inversion 6
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A1~Lernativel.y p = 30. m, where T
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The e1ectrica:L effect - of the cha
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The vari.ables x,y, and t which do
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- d IufM12 > 0 . dz - - On the othe
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a) TM-mode From (2.251, (2.26); (2.
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with " the abbreviation + - 1 - ? =
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2n -i~cr cos (8-$1 -iKrcU J e ~B=J
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In the 1irnl.t a -+ o, I +- m, M =
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-- 2.5. Definition -- of the transf
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we arrive at - v The same appl-ies
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) Computation of ---- C for a laxez
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The approximate interpretation of C
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I ~ispersi-on relations I Dispersio
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where L is a positively oriented cl
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1 2 3 4 CPD 1 2 3 4 CPD - g) Depend
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The TE-mode has no vertical electri
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i I Earth Anomalous domain 3.2. Air
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Hence, the conductivity is to be av
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The RHS i.s a closed line integral
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4. Having determined B;, the coeffi
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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 94 and 95: Model : wo+ Solution for uniform ha
Page 96 and 97: parameter u and that the pressure d
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
Page 144 and 145: The field within the conducting sph
Page 146 and 147: and An algorithm for the direct pro
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with I - and- a = gn g-n I 1 6-n-1
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with ~ = - T E + as sheet current d
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E~~ T r: j = const. or E T + E a r
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Field equations and boundary condit
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with N (w,y) being the Fourier tran
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is calculated as function of freque
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Both types of anomaly can be explai
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A field line segment with the horiz
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- 160 - below can neither enter nor
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I '. - L.. . . - I . --.> . ~ 4 The
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This law can be used to i-nterpret
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Only in this special case will be j
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anomalous conductivity oat OP the a
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the product WUL' constant with L de
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One of the thin plates represents t
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low conductivity requires the use o
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Other derivable properties of mantl
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11. References for general reading
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Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

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