Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet
Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet
is calculated as function of frequency and location. It is converted into an apparent CAGKIARD resistivity and phase: or alternatively into the depth of a perfect substitute con.ductor and a modified apparent resistivity : which'can be combined'into a local depth versus apparent resj-sti- x X vity profile p (z,, , y). 11 If the magnetic variation anomaly rather than the geoelectric field has been observed, the anomalous part of El! can be derived by integration over the anomaly of the vertical magnetic varia-tions, w11il.e the normal part of E,, is calculated from the normal impedance outside of the anomaly or derived theoretically for a hypothetical normal resistivity model: or in terms of transfer functions with respect to H n l ' using for the transfer function of H the nota-tj.ons of page 113. az Magnetotelluric and geomagne-tic depth sounding data along a profi1.e are in this way readily converted either into CAGNIARD r~esistivity ,and phase-contours in frequency--distance coordina.i-es , 'if into lines of , depth-of-penetration z at a gi.ven frequency, % or into modified apparent-resis.tivi-ty- contours in a z -distance cposs-section Either one of these plots will outline the frequency range, respectively the depth range, i.11 which the source of the anomaly can be expected to lie, and provide a rough idea about the resistivities like1.y to occur within the anona1.ous zone,
Single frequency -- interpretation by perfect conductors - at -- variable depth Geomagne-tic variations anomalies show frequc.ntly nearly zero phase with respect to the normal field, the transfer functions which connect the cbmponents of H and fin being real func-tions -a of frequency and locations. This applies in particular .to two. types of anomalies. Firstly to those which arise from a non- uniform surf ace layer, thin enough to allow -the 'ltl~in-sl~ee~t" approxima-tion of the previous sec-t:ion with predominant .i.nduction within the sheet (ns>>l), Secondly, it applies to anomalies above a highly conductive subsurface layer at variab1.e dfpth benea-th an effectively non-conducting cover. In the first case En will be in-phase with Hn, in the second case out-of-phase (cf .Sec.9.1). But it is important to note that the anomalous variation field H wi1.l be in either casc roughly a in-phase -. with Hn.
- 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 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
Single frequency -- interpretation by perfect conductors - at<br />
--<br />
variable depth<br />
Geomagne-tic variations anomalies show frequc.ntly nearly zero<br />
phase with respect to the normal field, the transfer functions<br />
which connect the cbmponents of H and fin being real func-tions<br />
-a<br />
of frequency and locations. This applies in particular .to two.<br />
types of anomalies. Firstly to those which arise from a non-<br />
uniform surf ace layer, thin enough to allow -the 'ltl~in-sl~ee~t"<br />
approxima-tion of the previous sec-t:ion with predominant .i.nduction<br />
within the sheet (ns>>l), Secondly, it applies to anomalies<br />
above a highly conductive subsurface layer at variab1.e dfpth<br />
benea-th an effectively non-conducting cover.<br />
In the first case En will be in-phase with Hn, in the second<br />
case out-of-phase (cf .Sec.9.1). But it is important to note that<br />
the anomalous variation field H wi1.l be in either casc roughly<br />
a<br />
in-phase -. with Hn.
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