LIAG / Research / Methods / Numerical Methods / Modelling and Inversion 

Modelling and Inversion

The research area "Modelling and Inversion" of the department 2 deals with the numerical modelling of partial differential equations, particularly Maxwell's equations and electric/hydraulic continuity equations. Additionally we develop modern inversion algorithm that are able to reconstruct realistic subsurface images from the measured data and additional information.


Physical fields are usually described by partial differential equations. In order to simulate those fields one has to solve boundary value problems using appropriate approximations and discretizations. Typical methods are Finite Elements (FE), Finite Volume (FV) and Finiten Differences (FD). FE (mainly for Maxwell's equations) and FV (mainly for flow and transport) can be used on irregular meshes that are able to incorporate arbitrary geometries, such as topography or anomalous bodies. Therefore they are increasingly used in inverse problems when it comes to using prior information.


Most methods in Applied Geophysics lead to the task of computing a subsurface image (1D, 2D or 3D) of one or more parameters from the measured data and their errors, i.e. an inverse problem has to be solved. Particular challenges are the incorporation of prior information, e.g. lithological boundaries from boreholes or seismic reflections, point measurements from the lab or in boreholes, or geostatistic distributions. To this end, dedicated regularization methods are applied, i.e. by using local smoothness decoupling or geostatistic operators. An interesting approach is the joint inversion of different data sets to improve resolution and to decrease ambiguity in the interpretation, e.g. by structurally coupling. An increasingly important field are coupled methods like electric-hydraulic inversion and temporally (monitoring) or spectrally (IP) coupled inversion.

Software development

All our efforts follow the paradigm of reproducible science: all published results from synthetic studies or analysed field data can be reproduced by the readers. Besides freely releasing the underlying scripts and data this includes also publishing the used software. Together with colleagues from other institutes we develop different open-source software packages that are distributed over platforms like github/gitlab and use continuous integration/deployment cycles, mostly in the Python language:

  • pyGIMLi (Python Geophysical Modelling and Inversion Library) is the general core of many detailed developments providing the infrastructure for modelling, inversion, meshing and visualization tasks (Rücker et al., 2017). It can use geostatistical constraints (Jordi et al. 2018), incorporate structural information (Jiang et al. 2020), perform structurally coupled inversion (Jordi et al. 2020, Skibbe et al. 2018, Ronczka et al. 2017, Hellman et al. 2017) or petrophysical joint inversion (Wagner et al. 2019).
  • BERT (Boundless Electrical Resistivity Tomography) is a package for analysing direct current resistivity and induced polarization data on arbitrary geometries by flexible control of the inversion, particularly for spectral IP in time or frequency domain (Günther & Martin 2016, Martin et al. 2020)
  • MRSmatlab: A Matlab-toolbox forprocessing, 1D modeling and inversion of surface-NMR data (Müller-Petke et al., 2016)
  • custEM (customizable ElectroMagnetics) is a Python library for modelling electromagnetic data (CSEM) based on the open-source FE library FEniCS, developed in the project DESMEX (Rochlitz et al. 2019)
  • COMET (COupled Magnetic resonance and Electrical resistivity Tomography) is a Python library for (1D/2D/3D) modelling and inversion of surface NMR data (Skibbe et al. 2020), particularly for structurally coupling MRT with ERT for improved hydrogeophysical characterazation, in the project COMET

Current projects

    Deep Electromagnetic Soundings for Mineral EXploration - IV Modelling and Inversion
  • Sirius-B
    Simple and rapid imaging of groundwater using magnetic resonance using grounded bipoles
    COupled Magnetic Resonance and Electrical Resistivity Tomography
    Strukturally coupled inversion of surface NMR using GPR data
  • Joint Inversion
    of different methods by using structural or petrophysical coupling

Selected publications