By L. L. Vanyan
10.------------------------, 10.------------------------. N ::IE ~ w ~ '" "'0.1 \~ zero M z part VIEW PLAN VIEW 0.01 LI --'---'---LLL-'---LLLlI ~-L---"---LLL..ll..L.LJ'-':';;' 0.01 1 a hundred 10 a hundred fr Fig. 1. The habit of the magnetic and electrical fields from a vertical magnetic dipole resource on the floor of the earth (after Wait [1951,1955]). earth, the experimental curve so plotted must have an analogous form as a element of the ap propriate theoretical curve, yet with the ordinates and abscissas shifted by way of an quantity depending on the resistivity. The conductivity should be decided from the quantity of shift among the sphere information and the theoretical curve. an in depth description of the curve matching approach is located in a textual content by means of Keller and Frischknecht (1966). The curve matching process, even though used, has a number of risks. Measurements has to be remodeled a diagnostic component to the theoretical curve, one within which there's a few curvature, in order that the quantity of shift required to make a fit might be decided uniquely. which means the approximate conductivity of the earth has to be recognized while measurements are made. Secondly, choice of a unmarried price of conductivity calls for measurements revamped quite a lot of frequencies. this might seem to be wasteful of knowledge, inasmuch because the equations point out unmarried dimension at a unmarried frequency might be sufficient to de termine conductivity.
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Therefore, the boundary conditions may be said to require continuity of EWp(W) and BE~p(W) /Bz. ) 11 (mr)dm, and similarly. in evaluating ap and b p ' we require continuity of Bzp(w) and BBzp(w)/Bz at all boundaries except the earth's surface where the source is located. Here, the magnetic field is continuous, but its vertical derivative has a discontinuity, So ~ I(IJJ)fJil . ~sme. 2m 2J) (mr)dm. 25 PHYSICAL AND MATHEMATICAL FOUNDATION OF METHOD Obviously we must take b o = 0 in the upper half-space (z::; 0) as well as no = m.
A block diagram of receiving equipment, containing elements for detecting, amplifying, and recording signals developed in the magnetic transient method is shown in Fig. 8. An ungrounded loop lying in the horizontal plane is used as a detector. The magnitude of the signal voltage induced in the ungrounded loop commonly is no more than a few tens of microvolts. Therefore, the amplifiers must have a low input noise - no more than one microvolt. § 4. 5-57 . These generators have been deSignated as standard equipment for use in direct-current soundings with the Schlumberger and dipole methods.
Consequently, as T 1/h 1- 0, PT I P1 ~ 1. Let us now show that the apparent resistivity approaches a left-hand asymptote of one uniformly. To do this, we must show that PTI P1 increases for-Q2 < 0 and decreases for Q2 > 0, or that a(p T I P1)/a (T 1/h 1) < 0 for Q2 < 0 and that a(p T I P1)/a (Tt/h1) > 0 for Q2 > o. From equation (31) we may show that: (35) where y == /h 1 • 47rT 1 For Q2 > 0, all the terms in the summation in equation (35) are positive, and therefore, O. Similarly, we may show that P T lp1 decreases uniformly over Q2 > O.