Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

More documents

Recommendations

Info

For this interpretation the condition 1 C(O) ( K has to be satisfied on C (w) . An application of (2.87) is given in the following figure* When K increases attenuation is interpreted by geometrical dampping at the expense of electromagnetic damping due to a perfect conductor. .3... M.o.del. .cal.c.ul.at.ions. for. .tw,o-.dimension.al. structures .-- ~- .- ~ ~~ -- - 3. I.' General. 'equations We are considering now induction prbblems, where both the conductivity structure and the inducing field are independent of one horizontal coordinate, say x. Compared with Ch,. 2, the class of inducing fields has become more restricted, hut the class of ad- mitted conductivity structures has been enlarged. For x-independence, Maxwell's equations are split into two disjoint sets
The TE-mode has no vertical electric field, ?he TM-mode has no vertical magnetic field. In the treatment of the;+? modes the use of - - electromagnetic potentials is not necessary since E x and H x can serve as pertinent potentials. For conciseness let - - H: = Hx I E: = Ex (3.4b,a! Then E and H satisfy the equations , In uniform domains both equations. agree. Eq. (3.5b) resembles the equation of heat conduction in a non-unifor15 heat conductor. The continuity of the tangential electric and magnetic field components at conductivity discontinuities leads to the conditions -- .. I -1 E, -- continuous : an TE (3.6a) H, - 1 - aH continuous : TM a - (3.613) an - a is the derivative in direction to the normal of the discontinuity. an The E- and H-polarization - shores very different patterns. From (3.lb), (3.2b) follows that Ex is constant in the air half-space (u=o). Hence the Tbl-mode admits only a quasi.-uniform inducing magnetic field. In contrast in the TE-mode any two-dimensional inducing magnetic field is allowed. Hence, t17.e source terms to he added on the PJKS of (3. I a, b) are je(y1z) and Ho 6 (z+h), -
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: 1 2 3 4 CPD 1 2 3 4 CPD - g) Depend
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 -
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 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 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 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
show all

Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

Create successful ePaper yourself

Delete template?

Save as template?