Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet
Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet
. 7. Basic concepts of geomagnetic and magnetotelluric depth sounding . . 7.1. . General characteristics of the method Two types of geophysical surface data can be distinguished to in- vestigate the distribution of some physical property m(g) of matter beneath the Earth's surface. The first type is connected with static or quasi-static phenomena (gravity and magnetic fields), the second type with time-dependent phenomena (seismic wave propagation) or with controlled experiments under vartable experimental con- ditions (DC-geoelectric soundings). Geomagnetic and magnetotellur7ic soundings utilize the skin-effect of transient electromagnetic fields. Their penetration into the Earth represents a time-depen- dent diffusion process, thus the observation of these fields at the surface produces data of the second type. The interpretation of static data y = y(R) ...- is non-unique alld an arbitrary choice can be made among an unlimited number of possible distributions m(r), - explaining y(R) - equally well. The interpretation of transient data is with certain constraints unique in the sense that oniy - one distribution m(r) - can explain the surface data y = y(R,t), basically because opeadditional variable t (time, variable parameter of controlled experiment) is involve?, If the observation of the transient process or the perforrfiance of the experiment is made at .a single site, the data y '= .~(t) permit a vertical sounding of the property m = 'm(z), assumed to be a sole function of depth z beneath that site, If the observations or ex-
'periments are done with profiles or arrays, the data y = y(R,t) permit a structural sounding of the property m = F(z) + Am(r) with particular emphasis on lateral variations Am(2). - . Here m(z) represents either a global or regional mean distribution. It may also be the result of vertical soundings at "normal sLtesn wheqzthe surface data show no indications for lateral variations of m. Since the dependence of y(R,t) - on m(r) - will be non-linear, anomalies Ay(R,t) and - -. = y(R,t) - yn(t) will be dependent on Am - m(z) , i.e. the inierpretation of. second-type -data must proceed on the basis of a known mean or nornlal distribution F(z) consistent with data yn("c at a normal site. It should be noted that in the case of static data of the first type usually no ii~terdependence between Ay and will exist, i.e, the interpretation of their anomalies is gependent of global or regional mean distributions of the relevant property n. Suppose that for data of the second type the lateral variations bm(r) - are small in relation to G(z). Then the results of vertical soundings at many different single sites may be combined to - approximate a structural distribution m = m + Am. For geomagnetic induction data the relevant property, namely the electrical. re- sistivity has usually substantial lateral variations and a one- dimensional intezpretation as in the case of vertical soundings will not be adequate. Instead a truly multi-dimensional inter- pretation of the data is required which is to be based on "normal data" at selected sites (cf. 8.2). Such normal sites are her@ rather the exception than the rule. 7.2 The data and physicai properties of internal matter which are involved The Earth's magnetic field is subject to small fluctuations g(rtt). . They arise from primary sources in the high atmosphere and from seconda-y sources within the Earth. At the Earth's surface their ' r. amplitude is -
- 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 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 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
.<br />
7. Basic concepts of geomagnetic and magnetotelluric depth sounding<br />
.<br />
. 7.1. . General characteristics of the method<br />
Two types of geophysical surface data can be distinguished to in-<br />
vestigate the distribution of some physical property m(g) of matter<br />
beneath the Earth's surface. The first type is connected with<br />
static or quasi-static phenomena (gravity and magnetic fields), the<br />
second type with time-dependent phenomena (seismic wave propagation)<br />
or with controlled experiments under vartable experimental con-<br />
ditions (DC-geoelectric soundings). Geomagnetic and magnetotellur7ic<br />
soundings utilize the skin-effect of transient electromagnetic<br />
fields. Their penetration into the Earth represents a time-depen-<br />
dent diffusion process, thus the observation of these fields at<br />
the surface produces data of the second type.<br />
The interpretation of static data y = y(R) ...- is non-unique alld an<br />
arbitrary choice can be made among an unlimited number of possible<br />
distributions m(r), - explaining y(R) - equally well. The interpretation<br />
of transient data is with certain constraints unique in the<br />
sense that oniy - one distribution m(r) - can explain the surface data<br />
y = y(R,t), basically because opeadditional variable t (time,<br />
variable parameter of controlled experiment) is involve?,<br />
If the observation of the transient process or the perforrfiance of<br />
the experiment is made at .a single site, the data y '= .~(t) permit<br />
a vertical sounding of the property m = 'm(z), assumed to be a sole<br />
function of depth z beneath that site, If the observations or ex-