Inverse modeling

The main responsibility of the LIAG in DESMEX II was the implementation of flexible, multidimensional inversion routines for semi-airborne CSEM data. We aim to test different inversion techniques suitable to build upon the forward modeling solver custEM and the inversion framework pyGIMLi which are both developed at the LIAG. The goal is to include the real topographic information of our survey areas and invert magnetic field data, measured with the helicopter- or UAV-towed receivers, together with magnetic and electric field data from surface stations.

A suited possibility based on forward solutions with a direct solver is to re-use the already computed factorization of the system matrix to calculate the sensitivity matrix explicitly, which requires affordable computational effort due to the exploitation of comparatively cheap back-substitutions for this task. It is convenient to define the inversion domains as crowds of tetrahedral, e.g., by building a tetrahedral mesh by subdividing larger blocks or prisms, corresponding to the inversion domains, into multiple tetrahedra for an accurate forward solution. As an example, we used about 750 prisms with +-500 m elongation in y-direction for discretizing a mesh to invert synthetic data of a shallow 2D dipping plate model (Figure 5).

The method was eventually published by Rochlitz et al. (2023) and meets all requirement. It is therefore superior regarding the flexibility, but also competes in terms of performance.  Besides synthetic models, the approach was applied to field data from five transmitters in Schleiz (DESMEX I). It has been successfully applied to large-scale exploration of the field data from the graphite deposit Kropfmühl (Mörbe et al., 2024) and is particularly important for data analysis of the flight campains in the Upper Harz (DESMEX-REAL). Moreover, it is used for data analysis from UAV-based semi-airborne flights measurements

In a similar manner, this procedure can be extended to build meshes for 3D inversions with thousands of domains. This is work in progress before applying our developed tools on real survey data. We expect computation times of about than 1 day for simpler 3D inversion setups with our approach based on explicit Jacobian calculations. For more complex models, we are going to consider alternative or approximative techniques for obtaining the sensitivities to keep the computational efforts manageable.