Wilson, A.J.S.

English

The equivalent wavefield concept relates diffusive electromagnetic propagation to non-diffusive
propagation, provided equivalent source and boundary conditions are satisfied. This well-known
concept is a special case of a more general theorem, proven here, relating the solutions of two
systems of partial differential equations that have the same spatial, but different temporal
derivatives. In the case we consider, the velocity of the equivalent wavefield is proportional
to the square root of the resistivity of the diffusive electromagnetic medium. The use of the
concept has two advantages: first, analytical results may be derived more easily in the equivalent
wavefield domain; second, interpretation of data is easier after mapping to the equivalent
wavefield domain.

In general, electromagnetic fields have an irrotational component that is equivalent to Pwave
propagation, and a solenoidal component that is equivalent to S-wave propagation. Using
a moment tensor and a dipole moment to represent electromagnetic dipole sources allows
comparison with seismic sources. For example, the equivalent wavefield of the magnetic field
generated by an electric current dipole in a whole space is generated by a point source of torque,
generating shear waves only.

The electric field generated by a switch-off electric current dipole at the surface of a halfspace
has an equivalent wavefield at the interface equal to a triangle with origin at the switch-off
time, peak at the arrival time and zero thereafter. When graphed as a function of space versus
time, arrivals in the equivalent wavefield lie on straight lines and can be interpreted using
straightforward concepts from the seismic refraction method.

Diffusive to propagative mapping of numerical data requires regularisation to stabilise whatever
numerical inversion procedure is used. Approaches include matrix inversion and a new algorithm
which uses deconvolution in log time. The latter approach is computationally inexpensive
and permits analysis of the distortion of the recovered waveform which is caused by regularisation.
Both approaches successfully extract several arrivals when these are well-resolved in
the original diffusive synthetic. Diffusive to propagative mapping applied to synthetic electromagnetic
responses calculated for a horizontal electric current dipole source over a uniform
half-space or simple layered-Earth models yields equivalent wavefields which are interpretable
after calibration for waveform regularisation

Wilson, Andrew J. S.

Edinburgh Research Archive

The equivalent wavefield concept in multichannel transient electromagnetic surveying

https://era.ed.ac.uk/bitstream/1842/7101/1/516379.pdf

The equivalent wavefield concept in multichannel transient electromagnetic surveying.

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