Geoscience Reference
In-Depth Information
fIGURe 21.1
The 1 m horizontal coplanar/perpendicular (HCP/PRP) instrument in sled.
and conductivity of the various layers in the earth. Where the operating frequency of the EM array
is sufficiently low (Wait, 1962), the sensitivity of the array to a layer that occupies a given interval of
depth beneath the array is a simple function of depth. Consequently, the contribution of each layer
to the apparent conductivity is the product of the sensitivity to the layer times the conductivity of the
material in the layer, and apparent conductivity is the sum of these contributions. For the PRP array,
Wait's criterion for low-frequency (Wait, 1962) (i.e., low induction number [LIN]) operation is
|(
i
σμω)
1/2
ρ| < 0.5
(21.1)
where
i
is the square root of −1, σ is the electrical conductivity of the material below the EM array,
μ is the magnetic permeability of the material below the EM array, ω is the angular frequency of
operation of the EM array, and ρ is the horizontal distance between the transmitter and receiver. For
the HCP array, this inequality should be less than 0.16.
Figure 21.1 shows an EM instrument, mounted in a sled, that incorporates both the HCP and
the PRP arrays. The transmitter and receiver separation (ρ) is 1 m, and the operating frequency
(ω/2π) is 9 kHz. For this instrument (H/P-1), the LIN criterion is satisfied where the conductivity of
the earth does not exceed 0.36 S/m for the HCP array, and 3.5 S/m for the PRP array, assuming the
earth has the permeability of free space. For comparisons pertinent to golf-course applications,
the conductivity of native soil seldom exceeds 0.2 S/m, and the conductivity of sand is usually less
than 0.02 S/m (20 mS/m). In environmental conditions typical of golf courses, the H/P-1 pictured in
Figure 21.1 has an accuracy of about 1 mS/m.
21.3 ReSolUtIon of MeASUReMent
In addition to conductivity accuracy, spatial resolution must be finer than the features of interest.
The functions of depth sensitivity for the HCP and PRP arrays indicate the depth resolution of an
LIN instrument. For depth expressed in terms of ρ, the cumulative depth sensitivity of the HCP
array is
C
H
= 1 - 1/(4 ρ
2
+ 1)
1/2
(21.2)
