Anisotropic Inversion of Induced Polarisation (IP) Data

Induced polarisation (IP) data recorded at the field scale are usually interpreted using techniques based on isotropic electrical properties, despite the common occurrence of anisotropy in the subsurface. We propose an anisotropic IP inversion algorithm to overcome this limitation. Our approach is based on the established code CRTomo, which supports the inversion of isotropic complex conductivities (magnitude and phase) from 2D frequency-domain IP data. In order to extend this algorithm for the support of anisotropic complex conductivities, we modified the underlying forward modelling, sensitivity and model update implementations. The extended Finite Element modelling allows for anisotropic complex conductivities assuming the three principal directions x, y and z. The basis for the iterative model update are sensitivities with respect to the complex conductivities in the different directions, which we simply refer to as anisotropic sensitivities. We outline the calculation of these anisotropic sensitivities and highlight their characteristics in comparison with the isotropic analogues. The iterative model update algorithm is extended to account for the three principal directions of anisotropy. Here, we introduce a coupling parameter between the complex conductivities in the different directions, which is used to impose a bias on anisotropy for regularization purposes. As a this first approach, we favour isotropic models by imposing a penalty on anisotropy. The balancing between the usual spatial smoothness constraint and the newly introduced isotropy constraint can be adjusted by a weighting parameter. We demonstrate the effectiveness of the new anisotropic complex conductivity inversion scheme by means of synthetic examples representing different setups and measurement configurations, and we highlight benefits and drawbacks of an anisotropic inversion approach.