Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet
Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet
Let us first consider the case m = 2. Assume that there are L uni- ------ (3 ------ I z =o form layers below z = z2 with conz=zl ductivities (3 I' (3 2~ * s t a1,r and upper edges at z = hlr h2, ..., hL ' (hl = z2). In applications, the z=z,=h, vertical grid width z - z2 will be '. 4 ' so small that zo is in the first z=z o uniform layer. Then a solution of ?=h - -2 ,r (3.26) having the correct singu- U 2 z=h3 larity is ., IIowever, the boundary condition (3.27) is not yet satisfied. and the normal conductivity structure has not yet been taken into account. To achieve this let in m . o: (z-z ) -a (z-z ) z
4. Having determined B;, the coefficients 6o and 6L are determined from the fact that the difference between upward (downward) travelling waves of (3.33a) ar:d (3.33b) at z = zo must be due to the primary excitation given by (3.32). Hence, whence From (3.30~~) + -- Since (3.35) involves only the ratio B1(B1, it can be expressed in terms of the transfer function C'at z = jz2 (cf. (2.64)): For a uniform half space 13.35) is simply (2 x . . .~y-y~.,.z~) 1 - -a1 (2-2 ) (zo-z2)k = ; 1 e O cos~(y-y~)iix= 1 ~ 1 o . r: - -0 For kl + 0 (isolator) this yields [ r-r. [. . . . . . . (kl l_r_-hll
- Page 1 and 2: Electromagnetic Induction in the Ea
- Page 3 and 4: 6.2. Generalized matrix inversion 6
- Page 5 and 6: A1~Lernativel.y p = 30. m, where T
- Page 7 and 8: The e1ectrica:L effect - of the cha
- Page 9 and 10: The vari.ables x,y, and t which do
- Page 11 and 12: - d IufM12 > 0 . dz - - On the othe
- Page 13 and 14: a) TM-mode From (2.251, (2.26); (2.
- Page 15 and 16: with " the abbreviation + - 1 - ? =
- Page 17 and 18: 2n -i~cr cos (8-$1 -iKrcU J e ~B=J
- Page 19 and 20: In the 1irnl.t a -+ o, I +- m, M =
- Page 21 and 22: -- 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
- Page 31 and 32: where L is a positively oriented cl
- Page 33 and 34: 1 2 3 4 CPD 1 2 3 4 CPD - g) Depend
- Page 35 and 36: The TE-mode has no vertical electri
- Page 37 and 38: i I Earth Anomalous domain 3.2. Air
- Page 39 and 40: Hence, the conductivity is to be av
- Page 41: The RHS i.s a closed line integral
- 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
4.<br />
Having determined B;, the coefficients 6o and 6L are determined<br />
from the fact that the difference between upward (downward)<br />
travelling waves of (3.33a) ar:d (3.33b) at z = zo must be due to<br />
the primary excitation given by (3.32). Hence,<br />
whence<br />
From (3.30~~)<br />
+ --<br />
Since (3.35) involves only the ratio B1(B1, it can be expressed<br />
in terms of the transfer function C'at z = jz2 (cf. (2.64)):<br />
For a uniform half space 13.35) is simply<br />
(2<br />
x . . .~y-y~.,.z~)<br />
1 - -a1 (2-2 ) (zo-z2)k<br />
= ; 1 e O cos~(y-y~)iix= 1 ~ 1<br />
o<br />
. r: - -0<br />
For kl + 0 (isolator) this yields<br />
[ r-r. [. . . . . . .<br />
(kl l_r_-hll
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