| Summary: | Inversion of measurements from a geophysical electromagnetic survey to produce a
two- or three-dimensional conductivity model of the Earth is computationally demanding.
The classical approach is to linearise the inverse problem and iterate towards the solution.
A typical, modern version of this approach is described in the initial part of this thesis,
and applied to the one-dimensional inversion of time-domain electromagnetic data.
One of the most time-consuming parts of a linearised, iterative inversion procedure is
the generation of the Jacobian matrix of sensitivities. In this thesis, I have developed an
approximate method for generating these sensitivities. The approximation is based on the
adjoint-equation method in which the sensitivities are obtained by integrating, over an
individual cell, the scalar product of an adjoint field (the adjoint Green’s function) with
the electric field produced by the sources for the geophysical survey. Instead of calculating
the adjoint field in the multi-dimensional conductivity model, an approximate adjoint field
is computed in a homogeneous or layered halfspace, or using the Born approximation.
This approximate adjoint field is significantly quicker to compute than the true adjoint
field and leads to considerable reductions in the time required to generate the Jacobian
matrix of sensitivities. The time-differences were found to be of one or two orders of
magnitude for the small examples considered in this thesis, and this saving will further
increase with the size of the problem.
The approximate sensitivities were compared to the accurate sensitivities for two
and three-dimensional conductivity models, and for both artificial sources and the plane
wave source of magnetotellurics. In all the examples considered, the approximate sensi
tivities appeared to be sufficiently accurate to allow an iterative inversion algorithm to
converge to an acceptable model. This was emphasised by the successful inversion, using
approximate sensitivities, of two sets of magnetotelluric data: a synthetic data-set and a
sub-set of the COPROD2 data.
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