Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

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the product WUL' constant with L denoting the length scale, The primary inducing field is produced by an oscilla-ting dipole source or-by extended current loops, situated as "ionospheric sources" above an arrangeme& of conductors which represent the conducting material below the Earth's surface. Alternatively, the conductors as a whole can be placed into the interior of coils, say Helmholtz coils, and thus be exposed to a uniform source field, .- \ I / I . 1 i: /' .
width, however, forces the induced currents to flow in loops which in strength and phase may be totally controlled by the edges of the conductor. In order to avoid this unwanted effect the source field at the level of the conductors should die away before reaching the edges of - the scale model. For instance, if a line current source is used, the half-width of the line current field on the surface of the scale model' should be considerably smaller then the width of the model.. These complicati.ons do not arise of course, when no attempt is made to simulate local anomal-ies of a large-scale induced current system, i.e. when the scale model is placed into the interior of coils in order to simulate local induction in isolated bodies (cf. subsection on this topLc in Sec. 9.4). Here are to men-tion the scale model experiments by GREWET and LAUNAY who showed how ,a large-scale induction can be simvlated also by the induction in the interior of coils. Their objective was to make a scale model of the coast effect at complicated coastlines. They nptedthat the i.nductive coupling between the ocean and highly conduc-ting ma-terial at some depth within the Earth is well represented by a system of image currents at the level 2 -hx below the ocean. Here h" is again the depth of a perfect substi-tute conductor for the oceanic substructure at the considered frequency. GRENCT and LAUNAY use as model conductors two thin metallic plates which are connected along two edges by vertical conducting strips.
Page 1 and 2:
Electromagnetic Induction in the Ea
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6.2. Generalized matrix inversion 6
Page 5 and 6:
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
Page 23 and 24:
we arrive at - v The same appl-ies
Page 25 and 26:
) Computation of ---- C for a laxez
Page 27 and 28:
The approximate interpretation of C
Page 29 and 30:
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
Page 41 and 42:
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
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- 6 and 6= can be so adjusted that
Page 49 and 50:
From the generalized Green's theore
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and y can again be so adjusted that
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4.2. In3ral - --- equation method L
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The element GZx is needed for all z
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With this knowledge of the behaviou
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After having determined Qzr VJ,; @,
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4.3. The surface inteyral approach
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F At the vertical boundaries the co
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The four equations A A A A H = i sg
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6. Approaches to the inverse proble
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to minimize the quantity a s = 12 /
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It remains to show a way to minimiz
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Agai-n, from a finite erroneous dat
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Here lJ - is a N x P matrix contain
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small eigenvalues. The parameter ve
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Then - 77 - A(E2 - E ) = iwu U (E -
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whence 2k d -2k d where a = CA:(A;)
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. 7. Basic concepts of geomagnetic
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orders of magnitude smaller' than t
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Elimination of - E or .,. H yields
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Observing that rot pot rot g = - ro
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Two special types of such anomalies
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Model : wo+ Solution for uniform ha
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parameter u and that the pressure d
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(=disturbed)-variations: After magn
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with 4 as geographic latitude. From
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Very rapid oscillations with freque
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! 8. Data Collection - and Analysis
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A horizontal electric -- field comp
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For a data reducti.on in the fr3equ
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Let q be the tranfer function betwe
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. A as transfer function between A
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-- Structural soundi~z with station
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Since it follows that - E 1 = - T E
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- - . the same or from different si
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The Fourier integral - +- -io t T -
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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
Page 148 and 149: with I - and- a = gn g-n I 1 6-n-1
Page 150 and 151: with ~ = - T E + as sheet current d
Page 152 and 153: E~~ T r: j = const. or E T + E a r
Page 154 and 155: Field equations and boundary condit
Page 156 and 157: with N (w,y) being the Fourier tran
Page 158 and 159: is calculated as function of freque
Page 160 and 161: Both types of anomaly can be explai
Page 162 and 163: A field line segment with the horiz
Page 164 and 165: - 160 - below can neither enter nor
Page 166 and 167: I '. - L.. . . - I . --.> . ~ 4 The
Page 168 and 169: This law can be used to i-nterpret
Page 170 and 171: Only in this special case will be j
Page 172 and 173: anomalous conductivity oat OP the a
Page 176 and 177: One of the thin plates represents t
Page 178 and 179: low conductivity requires the use o
Page 180 and 181: Other derivable properties of mantl
Page 182: 11. References for general reading
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Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

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