# An overview of a highly versatile forward and stable inverse algorithm for airborne, ground-based and borehole electromagnetic and electric data

Esben Auken^{1}

^{8}Anders Vest Christiansen

^{1}Casper Kirkegaard

^{1}Gianluca Fiandaca

^{1}Cyril Schamper

^{2}Ahmad Ali Behroozmand

^{1}

^{7}Andrew Binley

^{3}Emil Nielsen

^{4}Flemming Effersø

^{5}Niels Bøie Christensen

^{1}Kurt Sørensen

^{1}

^{5}Nikolaj Foged

^{1}Giulio Vignoli

^{1}

^{6}

^{1} Department of Earth Sciences, Aarhus University, C.F. Møllers Allé 4, DK-8000 Aarhus C, Denmark.

^{2} Sorbonne Universités, UPMC Univ Paris 06, 4 Place Jussieu, 75005 Paris, France.

^{3} Lancaster University, Bailrigg, Lancaster LA1 4YW, UK.

^{4} Danish Technical University, Anker Engelunds Vej 1, Bygning 101A 2800 Kgs. Lyngby, Denmark.

^{5} SkyTEM Surveys, Dyssen 2, DK-8200 Aarhus N, Denmark.

^{6} Geological Survey of Denmark and Greenland (GEUS), Lyseng Allé 1, 8270 Højbjer, Denmark.

^{7} School of Earth Sciences, Stanford University, 397 Panama Mall, Mitchell Building, Suite 101, Stanford, CA 94305-2210, USA.

^{8} Corresponding author. Email: esben.auken@geo.au.dk

*Exploration Geophysics* 46(3) 223-235 https://doi.org/10.1071/EG13097

Submitted: 28 November 2013 Accepted: 26 May 2014 Published: 29 July 2014

## Abstract

We present an overview of a mature, robust and general algorithm providing a single framework for the inversion of most electromagnetic and electrical data types and instrument geometries. The implementation mainly uses a 1D earth formulation for electromagnetics and magnetic resonance sounding (MRS) responses, while the geoelectric responses are both 1D and 2D and the sheet’s response models a 3D conductive sheet in a conductive host with an overburden of varying thickness and resistivity. In all cases, the focus is placed on delivering full system forward modelling across all supported types of data. Our implementation is modular, meaning that the bulk of the algorithm is independent of data type, making it easy to add support for new types. Having implemented forward response routines and file I/O for a given data type provides access to a robust and general inversion engine. This engine includes support for mixed data types, arbitrary model parameter constraints, integration of prior information and calculation of both model parameter sensitivity analysis and depth of investigation. We present a review of our implementation and methodology and show four different examples illustrating the versatility of the algorithm. The first example is a laterally constrained joint inversion (LCI) of surface time domain induced polarisation (TDIP) data and borehole TDIP data. The second example shows a spatially constrained inversion (SCI) of airborne transient electromagnetic (AEM) data. The third example is an inversion and sensitivity analysis of MRS data, where the electrical structure is constrained with AEM data. The fourth example is an inversion of AEM data, where the model is described by a 3D sheet in a layered conductive host.

**Key words:** airborne electromagnetic, frequency domain electromagnetic, geoelectric, inversion, magnetic resonance sounding, transient electromagnetic.

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