P. Schmoldt, PhD - MTNet - DIAS

10. Data inversion
tigation is usually limited to forward modelling or a small number of inversion steps.
This study uses the algorithm wsinv3d by Siripunvaraporn et al. [2005a], which reduces
computational load and time by conducting inversions in the data space and calculating
only an approximation of the sensitivity matrix during the forward modelling (cf. Sec.
6.3). The wsinv3d algorithm could therefore, in principle, be run on a PC [Siripunvaraporn
et al., 2005a]; however, in order to obtain results within a reasonable time, in this
study inversions are carried out using a parallel version of the wsinv3d algorithm and 30
processors on a cluster of the Irish Centre for High-End Computing (ICHEC).
The 3D modelling program of the WinGLink software package [WinGLink, 2005] is
used to create the 3D meshes and starting models. The horizontal mesh size of the central
area is as small as 2.5 km, with eight cells used for horizontal padding outside the
central area increasing in horizontal size by a factor of 1.5. Vertical mesh size is 50 m at
the surface, constantly increasing downwards by a factor 1.2. A model with irregularly
increasing vertical mesh size was also appraised, containing a particularly small cell size
at the depth range 100 – 140 km (assumed eLAB depth), but the resulting inversion model
exhibited inversion artefacts at the respective region due to insufficient resolution at this
depth range. Thus, smoothly increasing mesh size is employed for deriving models of
the Tajo Basin subsurface. The final model has 21 × 97 × 48 cells in E-W, N-S, and zdirection
(plus an additional 10 air layers), respectively; resulting in a total mesh size of
approximately 380 × 570 × 474 km. The bottom two layers are fixed at values of 1 Ωm
(last layer) and 100 Ωm (second last layer), which is not representative of the true Earth
but to ensure that boundary conditions on the base of the model are met. Starting models
comprise either a (a) homogeneous 100 Ωm halfspace or (b) a layered structure with a
100 Ωm crust (≤30 km), a 1000 Ωm lithospheric-mantle (30 – 110 km), and a 100 Ωm asthenosphere
(≥100 km). The whole impedance tensor with eight degrees of freedom (four
complex values) per period is used for the computation; therein only 30 periods from the
range 10−3 – 105 s are selected in order to reduce computation time. Following the recommendations
by W. Siripunvaraporn [2008, unpublished] 5% of a normalised off-diagonal
impedance element magnitude is used as error floor, i.e.
Error floor = 5% · Zxy · Zyx. (10.3)
As 3D inversion is computational expensive, after five initial inversion steps models
from the two different starting models are compared in order to infer to what degree
they are affected by the starting model and which model to use for further inversion.
For each iteration step the wsinv3d algorithm yields a range of inversion models (for
this initial sequence up to four) with different smoothing parameters 6 (cf. Fig. 10.23).
Therefore, inversion results can be investigated for a range of models with different degree
of smoothness and model misfit. In Figure 10.23, the typical trade-off between model fit
6 For sake of consistency with notation in Section 6.3 (Eqs. 6.31 and subsequent forms), in here τ is used
as smoothness parameters instead of λ (used by the authors [Siripunvaraporn et al., 2005a,b]).
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