Solving joint inverse problems requires appropriate regularisation and coupling operators. In particular, when the inversion is performed on irregular meshes where cell sizes vary throughout the domain, the operators should be designed to be as independent of the discretisation as possible. We define regularisation operators for inversions on irregular meshes based on a geostatistical correlation model. The same correlation model is combined with a neighbourhood approach for gradient-calculation to produce cross-gradient operators with a geostatistical footprint. We apply geostatistical regularisation operators to a 3D synthetic cross-hole ERT example and show how they can improve the resulting tomogram compared to anisotropic smoothing. In a synthetic study, we show that the geostatistical cross-gradient operators are much less dependent on the discretisation and improve the accuracy of the calculated cross-gradient field. The geostatistical regularisation and cross-gradient operators will be the base for a joint inversion formulation on irregular meshes.


Article metrics loading...

Loading full text...

Full text loading...


  1. Coscia, I., Greenhalgh, S. A., Linde, N., Doetsch, J., Marescot, L., Günther, T., Vogt, T., Green, A. G.
    [2011] 3D crosshole ERT for aquifer characterization and monitoring of infiltrating river water. Geophysics, 76(2), G49–G59.
    [Google Scholar]
  2. Doetsch, J., Linde, N., Coscia, I., Greenhalgh, S. A., Green, A. G.
    [2010]. Zonation for 3D aquifer characterization based on joint inversions of multimethod crosshole geophysical data. Geophysics, 75(6), G53–G64.
    [Google Scholar]
  3. Gallardo, L.A., Meju, M.A.
    [2003] Characterization of heterogeneous near-surface materials by joint 2D inversion of dc resistivity and seismic data. Geophysical Research Letters, 30, 1658.
    [Google Scholar]
  4. Lelièvre, P. G., and FarquharsonC. G.
    , [2013] Gradient and Smoothness Regularization Operators for Geophysical Inversion on Unstructured Meshes. Geophysical Journal International, 178, 623–637
    [Google Scholar]
  5. Linde, N., Binley, A., Tryggvason, A., Pedersen, L. B., Revil, A.
    [2006] Improved hydrogeophysical characterization using joint inversion of cross-hole electrical resistance and ground-penetrating radar traveltime data. Water Resources Research, 42(12).
    [Google Scholar]
  6. Maurer, H., Holliger, K., Boerner, D. E.
    [1998] Stochastic regularization: Smoothness or similarity?. Geophysical Research Letters, 25(15), 2889–2892.
    [Google Scholar]
  7. Rücker, C., Günther, T., Wagner, F.
    [2016] pyGIMLi - An Open Source Python Library for Inversion and Modelling in Geophysics, 8th EAGE Conference and Exhibition - Workshops, Vienna, Austria.
    [Google Scholar]

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error