P. Schmoldt, PhD - MTNet - DIAS

8.3. Inversion of 3D model data
parameter τ and a resistivity gradient regularisation (instead of a laplacian regularisation)
for the objective function of the inversion process (cf. Fig. 8.18). The misfit for the inversion
models, obtained through inversion with different smoothing parameters, is generally
low (RMS misfit ≤ 2 for phases with a 5% error floor and apparent resistivities with a
10% error floor) and its distribution within the TE and TM mode responses varies between
inversion models with different parameters; cf. plots of apparent resistivity and
phase misfit in Figure 8.17 and in the respective figures in Section A.3.2.
For the 3D-crust profile with stations that represent the PICASSO Phase I recording
sites generally a good agreement with the true subsurface is achieved and the results
can be reproduced for other profiles and datasets from different stations (cf. Fig. 8.19).
However, the selection of inversion parameters is tailored to the characteristics of the 3D
model and its very localised changes of electric resistivity (e.g. from 50 Ωm to 1000 Ωm
in the northern region of the model). Thus, for the case of real subsurface, with unknown
distribution of electric resistivity, using a higher degree of smoothing may proof more
appropriate.
In order to test robustness of the anisotropic 2D inversion approach, inversion of the
3D-crust profile is repeated for data with low, medium, and high amount of noise. For
that purpose 1%, 3%, and 10% random noise is added to the dataset and inversion is
carried out according to the second approach, with resistivity gradient regularisation and
low smoothing (τ = 6). Inversion results for the three noise levels indicate that synthetic
model structures can be resolved for low and medium amount of noise, whereas for higher
amount of noise the vertical resistivity interface at mantle is not well reproduced (cf. Fig.
8.20). For subsurface cases that are more complex than the synthetic model used in this
study responses will be affected by noise as well as by additional geological features
(e.g. small-scale bodies). Therefore, a smaller amount of noise may already result in a
significant corruption of the data.
Anisotropic 2D inversion is capable of recovering the electric resistivity distribution
for a profile over a 3D subsurface to a certain degree. Lateral changes of resistivity in the
model are reproduced at crustal and mantle depth, however, sharpness and apparent lateral
location of the interface at mantle depth are subject to the choice of smoothing parameters.
Moreover, values of the resistive mantle region are less constrained and may significantly
exceed values of the synthetic model without adequate inversion constraints. For the 3D
model and parameter range used in this study, a combination of low smoothing parameter
(τ = 1) and resistivity gradient regularisation yields an optimal model. As the synthetic
model is a (simplified) representation of predicted Tajo Basin subsurface characteristics,
anisotropic 2D inversion has the potential to yield a model of the local electric resistivity
distribution that is superior to the results of isotropic 2D inversion without the need for
costly 3D inversion (presuming low or medium amount of noise in the data); cf. Section
A.2.4 for a comparison of computational time for the different inversion approaches.
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