In a sedimentary environment, quasi-layered models often can represent the actual geology more accurately than smooth minimum-structure models. We present a 2D inversion scheme with lateral constraints and sharp boundaries (LCI) for continuous resistivity data. All data and models are inverted as one system, producing layered solutions with laterally smooth transitions. The models are regularized through lateral constraints that tie interface depths or thicknesses and resistivities of adjacent layers. A priori information, used to resolve ambiguities and to add, for example, geological information, can be added at any point of the profile and migrates through the lateral constraints to parameters at adjacent sites. Similarly, information from areas with well-resolved parameters migrates through the constraints to help resolve areas with poorly constrained parameters. The estimated model is complemented by a full sensitivity analysis of the model parameters supporting quantitative evaluation of the inversion result. A simple synthetic model proves the need for a quasi-layered, 2D inversion when compared with a traditional 2D minimum-structure inversion. A 2D minimum-structure inversion produces models with spatially smooth resistivity transitions, making identification of layer boundaries difficult. A continuous vertical electrical sounding field example from Sweden with a depression in the depth to bedrock supports the conclusions drawn from the synthetic example. A till layer on top of the bedrock, hidden in the traditional inversion result, is identified using the 2D LCI scheme. Furthermore, the depth to the bedrock surface is easily identified for most of the profile with the 2D LCI model, which is not the case with the model from the traditional minimum-structure inversion.

We present a new methodology, spatially constrained inversion (SCI), that produces quasi-3D conductivity modeling of electromagnetic (EM) data using a 1D forward solution. Spatial constraints are set between the model parameters of nearest neighboring soundings. Data sets, models, and spatial constraints are inverted as one system. The constraints are built using Delaunay triangulation, which ensures automatic adaptation to data density variations. Model parameter information migrates horizontally through spatial constraints, increasing the resolution of layers that would be poorly resolved locally. SCI produces laterally smooth results with sharp layer boundaries that respect the 3D geological variations of sedimentary settings. SCI also suppresses the elongated artifacts commonly seen in interpretation results of profile-oriented data sets. In this study, SCI is applied to airborne time-domain EM data, but it can also be implemented with other ground-based or airborne data types.

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.

We tested a new robust concept for the calculation of depth of investigation (DOI) that is valid for any 1D electromagnetic (EM) geophysical model. A good estimate of DOI is crucial when building geologic and hydrological models from EM data sets because the validity of the models varies strongly with data noise and the resistivity of the layers themselves. For diffusive methods, such as ground-based and airborne electromagnetic, it is not possible to define an unambiguous depth below which there is no information on the resistivity structure and a measure of DOI is therefore to what depth the model can be considered reliable. The method we presented is based on the actual model output from the inversion process and we used the actual system response, contrary to assuming, e.g., planar waves over a homogeneous half-space, the widely used skin depth calculation. Equally important, the data noise and the number of data points are integrated into the calculation. Our methodology is based on a recalculated sensitivity (Jacobian) matrix of the final model and thus it can be used on any model type for which a sensitivity matrix can be calculated. Unlike other sensitivity matrix methods, we defined a global and absolute threshold value contrary to defining a relative (such as 5%), sensitivity limit. The threshold value will apply to all 1D inverted data and will thus produce comparable numbers of DOI.