Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet
Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet
E~~ T r: j = const. or E T + E a r = j = 0. n~ a a This approach has been used by HAACK to obtain a fairly reliable conductance cross-section through the Rhinegraben. In the case of E-pol-arisation a different kind of simplification may be in order: Suppose tHe half-width of the anomaly is sufficiently small in comparison to (W~~T)-' everwhere. Then no significant local self-induction clue to HaZ which produces takes places, i.e. the electric field driving the anomalous current will be the large-scale induced normal field only: Assuming E again to be known, the conductance anomaly is now -n ll derived from the observation of the tangential magnetic var,iation anomaly normal to the trend, In the actual performance with real data all field components may be expressed in terms of their transfer functions W and Z and thus be norrnalised with regard to h+ r1tg' Let T be variable only in one horizontal direction, say, i.n y- dlrec-tion'which. implies that the anomal.ous fj-eld is also variable only in that direction, obeying the field equa-tions CE-polarisation) (H-polarisation) - H+ - 1-1- = H - H.k - ay ay ?ax ax ax - jay with and
Here a denotes the conducti.vity at the top of the substratum 0 and ~a~ the anomalous vertical field at z = d which is responsible for driving currents upwards from the substructure to the sheet and vice versa. The boundary conditions, reflecting the "thin-sheet origin" of the variation anomaly, are (E-polarisation) (H-polarisation) for z = 0: H' = -K x H H+ = 0, a Y az ax - for z = d: H- = LII x Haz E = x Eaz. ay a Y c The kernel function of the convolution integrals - are -n 5 H " ' ~ - K * I ~ ' ~ ~ * 1 r "7 ip H KCy) = - =-> "' = Q ~ Y ) - : ~ Y ~ . ~ - "Y hy? q* c(i) U- +m sin(y k ) -7 LB% HCi; "I 1 LII(w,y) = - I - dk + 't H"b x " oik Y Ha): ! Y Cn~=(W'!C Y 7 ) I L E, Y-,.-r-,--* . ./-: sin(y k ) m' 1 Y LICw,y) = - I - d k . ' LI" Ea; . 2 - . UCLX = -go. "-0 ik ~-(w,k) Y n1 Y {hcifl< s2x.x:,~.c.r := ---- He-e C- n I1 is the response function of the substructure for the anomalous TE-field in the case of E-polarisation and C- the nI response function of the substructure for the anomalous TM-field in the case of H-polarisation. The kernel K is the separation kernel, introduced in Sec.5.1. It i connects K and HaZ in such a manner that the source of the aY anomaly is "internal" wh.cn seen from above the sheet. The kernels L are the Fourier transforms of the response functions, intro- .duced in Sec.7.3, which connect the tangential and horizontal field components above a layered half-space. Their application to the anomalous field at z = d implies that H and E diffuse -a -a downward into tlie substructure antidisappear for z -p a. --- They represent the.inductive coupling of the anomalous field with the substructure .'
- 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 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
E~~ T r: j = const. or E T + E a r = j = 0.<br />
n~ a a<br />
This approach has been used by HAACK to obtain a fairly reliable<br />
conductance cross-section through the Rhinegraben.<br />
In the case of E-pol-arisation a different kind of simplification<br />
may be in order: Suppose tHe half-width of the anomaly is<br />
sufficiently small in comparison to (W~~T)-' everwhere. Then no<br />
significant local self-induction clue to HaZ which produces<br />
takes places, i.e. the electric field driving the anomalous<br />
current will be the large-scale induced normal field only:<br />
Assuming E again to be known, the conductance anomaly is now<br />
-n ll<br />
derived from the observation of the tangential magnetic var,iation<br />
anomaly normal to the trend,<br />
In the actual performance with real data all field components<br />
may be expressed in terms of their transfer functions W and Z<br />
and thus be norrnalised with regard to h+<br />
r1tg'<br />
Let T be variable only in one horizontal direction, say, i.n y-<br />
dlrec-tion'which. implies that the anomal.ous fj-eld is also variable<br />
only in that direction, obeying the field equa-tions<br />
CE-polarisation) (H-polarisation)<br />
-<br />
H+ - 1-1- = H - H.k -<br />
ay ay ?ax ax ax - jay<br />
with<br />
and