Modelling and Inversion

As a result of the rapidly evolving measuring equipment arises the necessity to develop analysis algorithms. More and more data of increasing accuracy have to be handled by powerful computers. In almost all geophysical methods a three-dimensional analysis is state-of-the-art. Hence we need efficient numerical algorithms. The development in the section is mainly concentrated on modelling and inversion algorithms for DC or EM resistivity measurements. Moreover other measureing technologies such as transient electromagnetics (TEM) or magnetic resonance sounding (MRS) are incorporated.

Numerical algorithms for resistivity methods

Numerical modelling

The development of numerical algorithms moved from Finite Differences to Finite Element based discretisations (Rücker et al., 2006). The latter allow, by the use of unstructured triangular or tetrahedral meshes, for computation on any geometry and furthermore for incorporation of structural information from seismics or boreholes. Due to the ability of local refinement and the use of higher order shape functions an improved accuracy can achieved. Moreover, modern equation solvers and reordering schemes result in moderate run-times even for big models.

All this is implemented into the free library DCFEMLib, which was created by Carsten Rücker (University of Leipzig). As a novelty we are able to use electrodes of finite extend and contact impedance by using the complete electrode model (CEM).

Inversion methods

Modern inversion algorithms are based on Gauss-Newton type minimisation with smoothness constrained regularisation. Consequently, we also use triangles and tetrahedrons as parameters (Günther et al., 2006). By doing so we can reconstruct resistivity distributions on arbitrary geometries and incorporate structural information from seismics and boreholes into the inversion. These techniques are implemented in the software package BERT (boundless electrical resistivity tomography) on basis of DCFEMLib. Resolution analysis (Günther, 2004) is finally used to appraise the results and to optimize experimental design.

Time-lapse inversion

Resistivity methods are well suited to trace dynamic processes such as water infiltration and contaminant transport. Special algorithms were developed to calculate even relatively small resistivity changes. For applications see also the monitoring project.

Spatially Constrained Inversion of Airborne-electromagnetic Data

The Laterally Constrained Inversion is a technique where data sets of adjacent survey sites are combined in one inversion scheme. Using lateral constraints, information can be propagated horizontally to adjacent models and it is possible to resolve layers which are locally poorly resolved.
The Spatially Constrained Inversion was originally developed for SkyTEM data (Viezzoli, 2008) and then was adapted to HEM data (Steuer, 2009).

Structural joint inversion of different tomographic methods

The combined interpretation of different methods is a basic principle of geophysics and helps to reduce the ambiguity of tomographic methods by providing subsurface information based on different physical principles. If the physical parameters, e.g. seismic velocity and resistivity, are not connected by petrophysical relations, we can only structurally combine it. We developed an algorithm based on robust processing techniques within the library GIMLi. Together with cluster analysis it is able to produce a unified multi-parameter subsurface model.

A typical application is the combination of dc resistivity and refraction seismics. For theses purposes we also developed a combined measuring technology.

References

Günther, T. (2004). Inversion Methods and Resolution Analysis for the 2D/3D Reconstruction of Resistivity structures from DC Measurements. PhD Thesis, University of Mining and Technology, Freiberg.
Günther, T., Rücker, C., and Spitzer, K. (2006). 3-d modeling and inversion of dc resistivity data incorporating topography - part II: Inversion. Geophys. J. Int., 166(2): 506-517.
Rücker, C., Günther, T., and Spitzer, K. (2006). 3-d modeling and inversion of dc resistivity data incorporating topography - part I: Modelling. Geophys. J. Int., 166(2): 495-405.
Steuer, A., Joint application of ground-based transient electromagnetics and airborne electromagnetics, PhD thesis, University Köln, 2009.
Viezzoli, A., A. Christiansen, E. Auken and K. Sørensen, Quasi-3D modeling of airborne TEM data by spatially constrained inversion, Geophysics, 73, F105–F113, 2008.