Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

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The "modified apparent - - resistivity" p can be used as an estimator I r. of the resistivity at the depth zf= Re{Cnl = h 4 ~p with m ,. pX = 1 f i k as apparent skin-depth of the substratum. The representation UlJ0 of the true resistivity distribution p(z) by the modified apparent , x . resistivity distribu-tion p CZ~)'~S usually adquate, if p decreases with increasing depth. It is-less satisfactory, if p increases with depth. (e) Multiple frequency interpretation with a three-layer model: 'Is - L X This interpretation cornbines the single frequency in-terpretat3.ons (b) and (c) , i. e. -TL-.A,.~.-'- I-.- the model consists of a thin top layer with 2 h dl the conductance T , a non-conducting inter- mediate layer of the thickness h above a perfectly conducting substratum. Then = wp ~h = is the induction parameter of the model wi-th dl 0 pi as thickness of the top layer and pl = /l& as its ~%in-depth W0T with the requirement that pl > 1, implying that h >>> p the induction is predominan-t1.y 1' j.n the surface sheet, the response functions al-e independent of h, thus allowing a unique cleterrr~ination of T. Ln particular, Pa -. - 1 W ~ J ,r2 0 Hence, if y = log pa/p and x = l.og T/To (T = period; po and To 0 are reference values), then e . the p vs, period curve in log-log prcsen'cati.on is a straigh-t a 4 b?i.~:h w as curve parameter -
0 line ascending under 45 , its intersection point on the x-axis - given hy Po .r2) = log(21ry - To with TI = 1 . lox1 in seconds and po in Qm. 0 If, on the other hand, 11~
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
Page 9 and 10:
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
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 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 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 174 and 175: the product WUL' constant with L de
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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