Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet
Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet
(2.82a1b) simply results when (2.80) is split into real and. imagL- , nary; it has already been given above (Eq. (2.61 a,b) ) . (2.83) is proved as follows The other constraints are proved in a similar way. There are other constraints involving second and higher derivatives. In terms of apparent resistivity and phase $ Rqs. (2,83b1a) read: The slope of a double-logarithmically plotted sounding curve is - Dpa/pa. As a consequence of (2.85a,b) we have alvrays The monotone decrease of the real part of C with frequency is a consequence of The following figure shows data (full lines) which are inconsistent a on the basis of one-dimensional model., since the constraints (2.83a, b) : are partly-violated. Then the least corrections to the data are determined that the inequal-ities are satisfied. Since this is only a necessa-ry coridition, interpretability is not yet granted.
1 2 3 4 CPD 1 2 3 4 CPD - g) Dependence of interpretation - on wave-ru~S7er The fundamental equation is By the transformations - 1 z = - tanh(~z) K it is transformed into in such a way that remains unchanged. Hence any C can first be interpreted by a uni- - - form external field (K=o) and the result @(z) is then transformed to the true conductivity by - -1 1 o(z) = sech4 (ez) .a (- tan11 (KZ) ) K (2.87) -
- 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: where L is a positively oriented cl
- 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 and 42: The RHS i.s a closed line integral
- 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 -
1 2 3 4 CPD 1 2 3 4 CPD<br />
-<br />
g) Dependence of interpretation - on wave-ru~S7er<br />
The fundamental equation is<br />
By the transformations - 1<br />
z = - tanh(~z)<br />
K<br />
it is transformed into<br />
in such a way that<br />
remains unchanged. Hence any C can first be interpreted by a uni-<br />
- -<br />
form external field (K=o) and the result @(z) is then transformed<br />
to the true conductivity by<br />
- -1 1<br />
o(z) = sech4 (ez) .a (- tan11 (KZ) )<br />
K (2.87)<br />
-
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