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layers of the resistiive lithosphere. Due to severe galvanic screening, the sensitiv-
ity of the TM-mode is too poor for this task. So, the TE-mode with its higher
sensitivity to buried conductors is the only contributor of useful information. The
situation is paradoxical. We have to abandon the TM-mode with its high accuracy
of 2D-approximation, and instead to harness the less-accurate TE-mode. But there
is no way to the necessary information except by using the TE-mode with all trou-
bles arising from the 2D-approximation errors and the 3D-static effects that cannot
be reproduced by two-dimensional modeling. It is better to get rough (maybe even
qualitative) information than no information. Thus, we have to use the TE-mode and
try to control the errors of its two-dimensional inversion by means of a posteriori
3D-estimates.
In closing, we state that in the general case the most comprehensive and reli-
able information on the Earth's conductivity can be derived by means of bimodal
inversion, using the TE- and TM-modes (tippers, magnetic tensors, longitudinal and
transverse MT-curves).
12.5 Two Approaches to Multicriterion Inverse Problem
Solution to an inverse problem, constrained by the interpretation model, is chosen
using criteria of the minimal misfits. These criteria ensure the agreement between
the solution and the observation data. The number of criteria is determined by the
number of the response functions in use (real and imaginary or amplitude and face
functions). If the inversion envolves a few response functions, the problem is multi-
criterion.
The two-dimensional integrated interpretation of magnetovariational and mag-
netotelluric data belongs to the class of multicriterion problems. The electric con-
ductivity of the Earth can be usually inferred from the TE-mode with the response
functions Re
W
and Im
W
(real and imaginary tippers, longitudinal appar-
ent resistivities and phases of longitudinal impedances) and the TM-mode with
the response functions
,
and
⊥
(transverse apparent resistivities and phases of
transverse impedances). These functions differ in the sensitivity to target geoelectric
structures, in the robustness to 3D effects, in the susceptibility to near-surface static
distortions. The TE-mode is more sensitive to deep structures and less sensitive to
the resistance of the lithosphere, whereas the TM-mode is less sensitive to deep
structures and more sensitive to the resistance of the lithosphere. On the other hand,
the apparent resistivities may suffer from the near-surface static distortions, whereas
the low-frequency tippers and impedance phases are immune to these troubles. An
algorithm of the 2D bimodal inversion should be constructed so that the different
response functions support and complement each other. When inverting the differ-
ent response functions, one should give priority to the most reliable elements of the
solution and suppress the least reliable ones.
The following two approaches are possible in solving multicriterion inverse prob-
lems: (1)
parallel inversion
of all response functions taking part in the interpretation,
and (2)
successive partial inversion
of each of the response functions.
⊥
and
