P. Schmoldt, PhD - MTNet - DIAS

6. Using magnetotellurics to gain information about the Earth
and Mackie, 2001; Siripunvaraporn and Egbert, 2007]. The different computation results
in a significant reduction of the computational cost [e.g. Siripunvaraporn, 2010]. GN-CG
inversion is divided into two loops: the outer inversion loop, and the inner CG loop replacing
the direct solver (e.g. LU-factorisation [Smith and Booker, 1991]). The efficiency
of the GN-CG method is controlled by the number of CG iterations (NCG) [Avdeev, 2005;
Siripunvaraporn and Egbert, 2007; Siripunvaraporn and Sarakorn, 2010], which in turn
is anti-proportional to the smoothing parameter τ [Siripunvaraporn and Egbert, 2007;
Siripunvaraporn and Sarakorn, 2010]. A pre-conditioner, such as the QN method, can be
included to reduce the inversion time by speeding up the CG solver [Haber et al., 2005].
In the nonlinear conjugate gradient inversion (NLCG) method the computation of H
is replaced by a line search determining the step length parameter in the CG approach.
The direction for the CG iteration step is usually derived using either the Fletcher-Reeves
[Fletcher and Reeves, 1964] or the Polyak-Ribiere [Polyak and Ribiere, 1969] methods.
Computational requirements of the NLCG method are similar to the QN method and are
dominated by the computation of ∇ T m and the line search [Newman and Alumbaugh,
2000; Rodi and Mackie, 2001]. The efficiency of the NLCG method is controlled by
the number of NLCG iterations and the line search step, the former can be significantly
reduced using a pre-conditioner [Newman and Alumbaugh, 2000; Rodi and Mackie, 2001;
Newman and Boggs, 2004]. The overall CPU time is in the order of the model space GN-
CG method [Rodi and Mackie, 2001].
Inversion programs for MT data
A list of commonly-used, freely-available inversion programs for MT data is given in Table
6.3, with most of the programs being accessible via the MTNet website. Whereas
a range of 1D and 2D inversion programs is today easily obtainable, only one noncommercial
3D inversion code (WSINV3DMT) is available at present. Even though the
WSINV3DMT program is based on model space Occam’s inversion (cf. Sec. 6.3.3) it is
computationally still very expensive, making inversion of larger datasets with a high resolution
virtually impossible. Full 3D investigations of the subsurface with MT data are
therefore presently limited to forward modelling processes. Further 3D inversion programs
are under development, e.g. MCMT3DID [Miensopust, 2010], which will hopefully
allow 3D inversion to become a common tool of MT investigation in the future. The
MCMT3DID program has the advantage that it is set up to include the effects of distortion;
however, because the algorithm uses a FE forward solver and the Gauss-Newton method
for inversion it is computational very expensive. Therefore, faster and more powerful
computing machines are required to facilitate detailed 3D inversion of MT data. One
solution to the problem of required computational power might be parallelisation of the
algorithms and intensive employment of cluster computers, carried out, among others, by
Ritter et al. [1998]; Newman and Alumbaugh [2000]; Newman et al. [2003].
In principle, inversion programs can also be applied to cases of lower dimensionality
investigation, such as 3D inversion of 2D MT profile data [e.g. Siripunvaraporn et al.,
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