Specifications
University of Pretoria etd – Combrinck, M (2006)
the diffusion of the smoke-ring currents (Nabighian and Macnae, 1991) and the
assumptions stated in 2.3 are not valid anymore. This different nature of the inducing field
has two consequences. Firstly, the toroidal vortex (induced) currents will not be as strong
as in the case of a conductor in free space, because of the reduced ∂
B/∂t component
(fields are varying slower with time). Secondly, the smoke-rings will also cause galvanic
currents to flow in the conductor and lead to charge accumulation on the boundaries
between the conductor and the host rock. The smoke-ring electric field will
instantaneously be opposed within the target by the field of this electric charge distribution
created at the target boundaries. A secondary electric field created by these charges will
cause a poloidal current flow that tends to cancel most of the primary electric field (i.e. the
field associated with the smoke-rings) inside the conducting target (Nabighian and Macnae,
1991). This cancellation is more effective for short strike length bodies which, therefore,
have less poloidal (galvanic) current flow than longer bodies. The strength of these
currents depends mainly on the conductivity of the host rock and is only weakly dependent
on the much higher conductivity of the target. As such, the secondary magnetic field will
decay at a rate governed chiefly by the host rock conductivity. Anomalies due to both
poloidal (galvanic) and toroidal (inductive) currents are generally of the same sign and
increase the detectability of a given target according to Nabighian and Macnae (1991).
However, the combined anomaly will be spatially smeared toward longer wavelengths
compared to that of vortex currents alone – leading to erroneous interpretation if modelled
using a conductor in free-space approach. Singh (1973) has calculated the TDEM
response for a conductive sphere in a conducting infinite space and shown that the late
time response can also be presented as an inverse power law that is characteristic of whole-
and half space responses (i.e. straight-line behaviour in the late time on a logarithmic graph
of emf versus time). In the following graphs, h refers to the magnetic field component, the
first subscript 1 to the multi-pole, the second to the spherical component (r, θ, or φ), and
the third to the orientation of the magnetic dipole (r for radial, θ for transverse). The
superscripts v and u refer to the magnetic mode or transverse electric (TE) and electric
mode or transverse magnetic (TM) solutions. In free space (i.e. making the quasi-static
approximation) only TE solutions are generated with a radial magnetic dipole as source
(horizontal loop above sphere). Figures 2.6 to 2.8 show the differences in late time decay
behaviour between a conductive sphere in free space (σ1/σ2=0) and a conductive sphere
in a conducting infinite space for various conductivity contrasts (σ1/σ2=1/10 to 1/100).
The secondary magnetic field component h
v
1rr
(t) in figure 2.6, is equivalent to the vertical
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