Piecewise 1D laterally constrained inversion of resistivity data

Abstract

A B S T R A C TIn a sedimentary environment, layered models are often capable of representing the actual geology more accurately than smooth minimum structure models. Furthermore, interval thicknesses and resistivities are often the parameters to which nongeophysicist experts can relate and base decisions on when using them in waste site remediation, groundwater modelling and physical planning.We present a laterally constrained inversion scheme for continuous resistivity data based on a layered earth model (1D). All 1D data sets and models are inverted as one system, producing layered sections with lateral smooth transitions. The models are regularized through laterally equal constraints that tie interface depths and resistivities of adjacent layers. Prior information, e.g. originating from electric logs, migrates through the lateral constraints to the adjacent models, making resolution of equivalences possible to some extent. Information from areas with well-resolved parameters will migrate through the constraints in a similar way to help resolve the poorly constrained parameters. The estimated model is complemented by a full sensitivity analysis of the model parameters, supporting quantitative evaluation of the inversion result.Examples from synthetic 2D models show that the model recognition of a sublayered 2D wedge model is improved using the laterally constrained inversion approach when compared with a section of combined 1D models and when compared with a 2D minimum structure inversion. Case histories with data from two different continuous DC systems support the conclusions drawn from the synthetic example.

Application of time domain induced polarization to the mapping of lithotypes in a landfill site

“…For each profile the whole dataset was inverted following Fiandaca et al (2012), where the time domain forward response is computed via a Hankel transform of the frequency domain response for a layered medium. Then, inversion is carried out with a 1-D-LCI implementation (Auken et al, 2005) to retrieve the four Cole-Cole parameters for each layer. In the 1-D-LCI inversion algorithm, the model is composed of a set of laterally constrained 1-D models aligned along a profile (Auken et al, 2005).…”

Stretching AEM near-surface resolution limits related to low- and very high resistivity contrasts

“…The raw data were processed using Aarhus Workbench (www.aarhusgeosoftware.dk) and inverted using both smooth and layered laterally constrained inversion (LCI) (Auken et al, 2005). When running inversions without system response the range of time windows used is 10 µs to 8.9 ms, while when system response is applied times as early as 0.515 µs is used.…”

Quasi-3D inversion of full size AEM datasets

“…In particular, AarhusInv supports airborne TEM data and FEM data (Siemon et al, 2009) and several ground based methods, i.e. EM (Christiansen et al, 2007), DC (Auken et al, 2005;Auken and Christiansen, 2004), Induced Polarization (Fiandaca et al, 2012;Fiandaca et al, 2013), Nuclear Magnetic Resonance (Behroozmand et al, 2012b;Behroozmand et al, 2012a), Surface waves (Wisén and Christiansen, 2005) and magnetotellurics (Christiansen and Auken, 2009). …”

“…Inversion of electromagnetic data has developed from single site inversions, over profile oriented inversion using lateral constraints (Auken et al, 2005) to inversions including entire surveys using spatial constraints (Viezzoli et al, 2008). In these inversion methods the model domain is linked to the actual observation points and for e.g.…”