Geostatistical Regularization and Cross-gradients Operators for Joint Inverse Problems on Irregular Meshes
C. Jordi, J. Doetsch, T. Günther, C. Schmelzbach and J.O.A. Robertsson
Event name: 23rd European Meeting of Environmental and Engineering Geophysics
Session: Modelling and Inversion in Near-surface Geophysics II
Publication date: 03 September 2017
Info: Extended abstract, PDF ( 1.17Mb )
Price: € 20
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.