Specifications

University of Pretoria etd – Combrinck, M (2006)

forward modeling and is the reason why synthetic data is normally used as a first run to

test new interpretation algorithms.

The third factor proves to be the most difficult – accurately solving Maxwell’s equations.

These equations can only be solved analytically for a few very simple geometrical models

and only if assumptions regarding homogeneity, isotropy, frequency dependence, and

frequency and conductivity ranges are made. Kaufman and Keller (1983) makes use of

asymptotic equations based on even more assumptions and terms like “far away”, “late

time”, “early time” and “large loops” are found extensively in EM literature. Solutions

are calculated for these very special instances of system geometry and conductivity

models, but the results are applied and compared to real earth situations, not complying

with these assumptions. Following this reasoning it is understandable why geophysicists

sometimes experience frustration in terms of knowing that there is a conductive unit but

not being able to say exactly what or where, leading to simply drilling anomalies – also

known as “bump-hunting”.

Accepting that Maxwell’s equations cannot be solved analytically for a general situation,

the next option would be to solve them numerically making use of standard numerical

solutions for differential equations. The complexity of these equations, numerical

instabilities under certain conditions (e.g. high conductivity contrasts), and the very long

computer calculation times, imply that full three dimensional solutions (and especially

inversion) of realistic geological models are not yet reaching industry expectations as an

efficient interpretation tool.

The only option left at this stage is to develop time- and cost efficient algorithms to find

solutions based on some of these assumptions and apply these only to geological settings

and data satisfying those assumptions. An example of this is the mathematical assumption

of one dimensionality of the earth, which is met when horizontally layered geology is

investigated. This approach implies a number of different interpretational procedures

and algorithms to be developed. It is of course possible to apply one algorithm or

procedure to all data acquired over a range of different geological settings, but the

obtained results would only be reliable if the inherent assumptions of the algorithm are

met.