Schmucker, 1970 (Scripps) - MTNet
Schmucker, 1970 (Scripps) - MTNet Schmucker, 1970 (Scripps) - MTNet
76 Bulletin, Scripps Institution of Oceanography The induction in a plane sheet-substratum model is governed by very similar relations. Considering a wave component with the wave number k we have in analogy to (5.60) l/E = i T'J/ (1 + i 11t) l/E = Sc(k)/(l + i 1\) 2TIWT[ ] T'J t = -k-. - 1 - Sc(k) • exp(- 2kh) (5.65) where h denotes the depth of the substratum and T'J t the pertinent induction parameter. In the case of a highly conducting substratum at shallow depth (k • h « 1) we may insert for Sdk) the approximation (5.52) and obtain for 1'1 t the same approximation (5.62) as for the spherical parameter 11 s.
6, ELEOTROMAGNErrIO INDUOTION IN NONUNIFORM OONDUOTORS 6.1 Introduction This chapter deals with the effect of lateral nonuniformities upon the induced surface field of geomagnetic variations. The arising induction problem has been considered by various authors, beginning with Ertel's (1932) and Price's (1949) basic articles on this subject. Further references can be found in Rikitake's (1966) monograph. The following treatment is restricted to 2 -dimensional nonuniformities and the curvature of the earth's surface is neglected within the range of the anomaly of geomagnetic variations. Let this surface be the horizontal plane z ::;; 6 ··of Cartesian coordinates, z down and y perpendicular to grad 0-. The x- and z-component of the internal eddy currents will not contribute to the induction anomaly of the poloidal magnetic mode (cf. sec. 1.2). Hence, no anomalous behavior will be associated with the y-component of the normal variation field. Denoting the llOrizontal x-component of the transient magnetic field vector with H and its vertical component with Z we express their anomalous parts throughout this chapter in the standard form H ::;;h·H+h .2 a -rI Z z::;;z ·B+z·2 a H Z (6.1) with exp (i w t) as time factor On both sides. Each frequency component of the induction anomaly will be considered separately. We distinguish three types of anomalies as shown schematically in figure 35. Surface anomalies are due to superficial conductivity variations above the crystalline basement, including the outstanding conductivity contrast of seawater and rock formations on land. Deep anomalies reflect conductivity imbalances in the upper mantle, and intermediate anomalies are connected with insulated conductors in the high-resistivity zone of the earth's crust and uppermost mantle. Intermediate anomalies are the most unlikely type to occur as shown in section 6.4. Hence, those anomalies which are not explicable as surface effects on the basis of a probable near-surface conductivity distribution are presumably of deep origin. 77
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6, ELEOTROMAGNErrIO INDUOTION IN<br />
NONUNIFORM OONDUOTORS<br />
6.1 Introduction<br />
This chapter deals with the effect of lateral nonuniformities upon the induced<br />
surface field of geomagnetic variations. The arising induction problem has<br />
been considered by various authors, beginning with Ertel's (1932) and Price's<br />
(1949) basic articles on this subject. Further references can be found in<br />
Rikitake's (1966) monograph.<br />
The following treatment is restricted to 2 -dimensional nonuniformities<br />
and the curvature of the earth's surface is neglected within the range of the<br />
anomaly of geomagnetic variations. Let this surface be the horizontal plane<br />
z ::;; 6 ··of Cartesian coordinates, z down and y perpendicular to grad 0-. The<br />
x- and z-component of the internal eddy currents will not contribute to the<br />
induction anomaly of the poloidal magnetic mode (cf. sec. 1.2). Hence, no<br />
anomalous behavior will be associated with the y-component of the normal<br />
variation field.<br />
Denoting the llOrizontal x-component of the transient magnetic field vector<br />
with H and its vertical component with Z we express their anomalous parts<br />
throughout this chapter in the standard form<br />
H ::;;h·H+h .2<br />
a -rI Z<br />
z::;;z ·B+z·2<br />
a H Z<br />
(6.1)<br />
with exp (i w t) as time factor On both sides. Each frequency component of the<br />
induction anomaly will be considered separately.<br />
We distinguish three types of anomalies as shown schematically in figure<br />
35. Surface anomalies are due to superficial conductivity variations above<br />
the crystalline basement, including the outstanding conductivity contrast of<br />
seawater and rock formations on land. Deep anomalies reflect conductivity<br />
imbalances in the upper mantle, and intermediate anomalies are connected<br />
with insulated conductors in the high-resistivity zone of the earth's crust and<br />
uppermost mantle.<br />
Intermediate anomalies are the most unlikely type to occur as shown in<br />
section 6.4. Hence, those anomalies which are not explicable as surface<br />
effects on the basis of a probable near-surface conductivity distribution are<br />
presumably of deep origin.<br />
77
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