Description: Various electromagnetic (EM) measuring techniques were developed to fulfil the requirements in diverse earth or resources explorations, such as the long-offset transient electromagnetic (LOTEM) and the semi-airborne EM methods. The novel semi-airborne frequency-domain electromagnetic system takes advantages of both ground and airborne techniques by combining ground-based high power sources with large scale and spatially dense covered data. However, its signal-to-noise ratio is still smaller in comparison with the ground-based method like LOTEM due to the limited stacking time. From the perspective of inversion, the data of different EM methods have distinct resolutions towards the subsurface resistivity structures and therefore they can provide complementary earth information. However, these distinct resolutions could also lead to different inversion results if each dataset is inverted individually, which may introduce confusions to the following interpretations. To reduce the ambiguities and parameter uncertainties, joint inversion algorithms are developed to couple spatially dense sampled semi-airborne data and horizontal electric fields (Ex) measured using LOTEM. Nevertheless, the 1D joint inversion faces convergence problems due to 2D effects in the field data. The synthetic modelling suggests that the 2D effects in different datasets lead to distinct artificial structures in the 1D inversion, which makes the 1D joint inversion unfeasible. Therefore, a 2D joint inversion algorithm was further developed for the frequency-domain semi-airborne EM data and the LOTEM transient electric fields. With its application, the newly developed 2D joint inversion of the semi-airborne and LOTEM Ex field data acquired in eastern Thuringia,Germany, converged successfully and a 2D conductivity model could be derived for the survey area. In the consequent 2D synthetic modelling studies, it is demonstrated that part of the discrepancies between the individual inversion result of each field dataset can be explained by the resolution differences leaded by the different observed quantities and by the measurement configurations, and the 2D joint inversion result of field data is validated to be one effective equivalent model.

Description: The inversion of magnetotelluric data into subsurface electrical conductivity poses an ill-posed problem. Smoothing constraints are widely employed to estimate a regularized solution. Here, we present an alternative inversion scheme that estimates a sparse representation of the model in a wavelet basis. The objective of the inversion is to determine the few non-zero wavelet coefficients which are required to fit the data. This approach falls into the class of sparsity constrained inversion schemes and minimizes the combination of the data misfit in a least-squares 2 sense and of a model coefficient norm in an 1 sense ( 2 - 1 minimization). The 1 coefficient norm renders the solution sparse in a suitable representation such as the multiresolution wavelet basis, but does not impose explicit structural penalties on the model as it is the case for 2 regularization. The presented numerical algorithm solves the mixed 2 - 1 norm minimization problem for the nonlinear magnetotelluric inverse problem. We demonstrate the feasibility of our algorithm on synthetic 2-D MT data as well as on a real data example. We found that sparse models can be estimated by inversion and that the spatial distribution of non-vanishing coefficients indicates regions in the model which are resolved.

Description: Magnetotelluric (MT) responses in complex, 3-D terrains are in general characterized by (i) elliptical polarization states of horizontal electric and magnetic fields; (ii) the non-orthogonality of electric and magnetic fields and (iii) a coupling of the anomalous tangential-electric (TE) and tangential-magnetic (TM) modes, giving rise to a mode-mixed anomalous electric field at the surface. These 3-D effects are propagated into theMTimpedance tensor, which is derived from horizontal electric and magnetic fields, recorded at the earth’s surface. The 2 × 2 impedance tensor is in general fully occupied, and each of its elements is a mode-mixed quantity. To study 3-D effects of MT (impedance) data, the TE and TM mode contributions must be separated. This becomes possible with the inclusion of the single-mode vertical magnetic transfer function (the ratio of vertical to horizontal magnetic fields). Then, the individual modes can be resolved without prior knowledge of the underlying 3-D conductivity structure. For this purpose, we consider (i) the spatial relations between electromagnetic field components recorded in an array of sites (Faraday’s law) and (ii) that the magnetic TE mode and electric TM mode fields are potential fields within the insulating air half-space above the earth’s surface. Based on these two dependencies, it is possible to reconstruct the entire electromagnetic field from (measured) mixed-mode impedances and vertical magnetic transfer functions and to separate it into TE and TM modes, and into normal and anomalous parts. Hereby, we cannot only study the contribution of the two modes on the observed impedance tensor but also quantify the influence of 3-D effects at each location and frequency of a particular data set. Results of a modelling study suggest, that (i) none of the elements of a 3-D impedances tensor can be regarded as favourable for a 2-D interpretation (only 3-D models can explain 3-D data), (ii) a heterogeneous crust can strongly obscure identification of responses originating from the lower crust or upper mantle even at very long periods and (iii) the TE mode magnetic transfer functions are most important for sensing deep anomalies.