Anders Vest Christiansen

Layered and laterally constrained 2D inversion of resistivity data

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 quasilayered, 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 minimumstructure inversion.

Quasi-3D modeling of airborne TEM data by spatially constrained 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.

A review of helicopter-borne electromagnetic methods for groundwater exploration

For about three decades, airborne electromagnetic (AEM) systems have been used for groundwater exploration purposes. Airborne systems are appropriate for large-scale and efficient groundwater surveying. Due to the dependency of the electrical conductivity on both the clay content of the host material and the mineralization of the water, electromagnetic systems are suitable for providing information about the aquifer structures and water quality, respectively. More helicopter than fixed-wing systems are used in airborne groundwater surveys. Helicopter-borne frequency-domain electromagnetic (HEM) systems use a towed rigid-boom. Helicopter-borne time-domain (HTEM) systems, which use a large transmitter loop and a small receiver within or above the transmitter, are generally designed for mineral exploration purposes but recent developments have made some of these systems usable for groundwater purposes as well. The quantity measured, the secondary magnetic field, depends on the subsurface conductivity distribution. Due to the skin-effect, the penetration depths of the AEM fields depend on the system characteristics used: high-frequency data/early-time channels describe the shallower parts of the conducting subsurface and the low-frequency data/late-time channels the deeper parts. Typical investigation depths range from some ten metres (conductive grounds) to several hundred metres (resistive grounds), where the HEM systems are appropriate for shallow to medium deep (about 1–100 m) and the HTEM systems for medium deep to deep (about 10–400 m) investigations. Generally, the secondary field values are inverted into resistivities and depths using homogeneous or layered half-space models. As the footprint of AEM systems is rather small, one-dimensional interpretation of AEM data is sufficient in most cases and single-site inversion procedures are widely used. Laterally constrained inversion of AEM data often improves the stability of the inversion models, particularly for noisy data. Higher dimensional inversion is still not possible for standard-size surveys. Based on typical field examples the advantages as well as the limitations of AEM surveys compared to long-established ground-based geophysical methods used in groundwater surveys are discussed. In a case history from a German island an airborne frequency-domain system is used to successfully locate freshwater lenses on top of saltwater. An example from Denmark shows how a time-domain system is used to locate large-scale buried structures forming ideal groundwater aquifers.

An integrated processing scheme for high-resolution airborne electromagnetic surveys, the SkyTEM system

The SkyTEM helicopter-borne transient electromagnetic system was developed in 2004. The system yields unbiased data from 10 to 12 μs after transmitter current turn-off. The system is equipped with several devices enabling a complete modelling of the movement of the system in the air, facilitating excellent high-resolution images of the subsurface. An integrated processing and inversion system for SkyTEM data is discussed. While the authors apply this system with SkyTEM data, most of the techniques are applicable for airborne electromagnetic data in general. Altitude data are processed using a simple recursive filtering technique that efficiently removes reflections from trees. The technique is completely general and can be used to filter altitude data from any airborne system. Raw voltage data that are influenced by electromagnetic coupling to man-made structures are culled from the dataset to avoid uncoupled data being distorted by coupled data, and geometrical corrections are applied to correct for pitch and roll of the transmitter frame. Data are de-spiked and averaged using trapezoid-shaped filter kernels. A Laterally Constrained Inversion using smooth models is actively used to evaluate the processing, and the final inversion is tightly connected to the processing procedures.

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

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 present an overview of a mature and general algorithm for inversion of most electromagnetic and geoelectrical data, ground-based and airborne. The implementation uses a 1D formulation for electromagnetics and MRS responses, geoelectric responses are 1D and 2D, and the 3D sheet’s response implements an overburden of varying thickness and resistivity.

Quantification of modeling errors in airborne TEM caused by inaccurate system description

Beingabletorecoveraccurateandquantitativedescriptionsof the subsurface electrical conductivity structure from airborne electromagneticdataisbecomingmoreandmorecrucialinmany applications such as hydrogeophysical and environmental mapping, but also for mining exploration. The effect on the inverted models of inaccurate system description in the 1D forward modeling of helicopter time-domain electromagnetic TEM data was studied. The most important system parameters needed for accurate description of the subsurface conductivity were quantified using a nominal airborne TEM system and three different reference models to ensure the generality of the conclusions. By calculating forward responses, the effect of changing the system transfer function of the nominal airborneTEM system was studied in detail. The data were inverted and the consequences of inaccuratemodelingofthesystemtransferfunctionwerestudiedin themodelspace.Errorsinthedescriptionofthetransferfunction influence the inverted model differently. The low-pass filters, current turn-off, and receiver-transmitter Rx-Tx timing issues primarily influenced the early time gates. The waveform repetition, gate integration, altitude, and geometry mainly influenced thelatetimegates.Depthofinvestigationishighlymodeldependent, but in general the early times hold information on the shallower parts of the model and the late times hold information on thedeeperpartsofthemodel.Amplitude,gain,andcurrentvariations affect the entire sounding and therefore the entire model. The results showed that all of these parameters should be measured and modeled accurately during inversion of airborneTEM data. If not, the output model can differ quite dramatically from the true model. Layer boundaries can be inaccurate by tens of meters, and layer resistivities by as much as an order of magnitude. In the worst cases, the measured data simply cannot be fittedwithinnoiselevel.

A method for cognitive 3D geological voxel modelling of AEM data

Airborne electromagnetic (AEM) data have proven successful for the purpose of near-surface geological mapping and are increasingly being collected worldwide. However, conversion of data from measured resistivity to lithology is not a straightforward task. Therefore, it is still challenging to make full use of these data. Many limitations must be considered before a successful geological interpretation can be performed and a reasonable 3D geological model constructed. In this paper, we propose a method for 3D geological modelling of AEM data in which the limitations are jointly considered together with a cognitive and knowledge-driven data interpretation. The modelling is performed iteratively by using voxel modelling techniques with tools developed for this exact purpose. Based on 3D resistivity grids, the tools allow the geologist to select voxel groups that define any desirable volumetric shape in the 3D model. Recent developments in octree modelling ensure exact modelling with a limited number of voxels.

Mapping of landfills using time-domain spectral induced polarization data: the Eskelund case study

This study uses time-domain induced polarization data for the delineation and characterization of the former landfill site at Eskelund, Denmark. With optimized acquisition parameters combined with a new inversion algorithm, we use the full content of the decay curve and retrieve spectral information from time-domain IP data. Thirteen IP/DC profiles were collected in the area, supplemented by el-log drilling for accurate correlation between the geophysics and the lithology. The data were inverted using a laterally constrained 1D inversion considering the full decay curves to retrieve the four Cole-Cole parameters. For all profiles, the results reveal a highly chargeable unit that shows a very good agreement to the findings from 15 boreholes covering the area, where the extent of the waste deposits was measured. The thickness and depth of surface measurements were furthermore validated by el-log measurements giving in situ values, for which the Cole-Cole parameters were computed. The 3D shape of the waste body was pinpointed and well-defined. The inversion of the IP data also shows a strong correlation with the initial stage of the waste dump and its composition combining an aerial map with acquired results.

Integrated management and utilization of hydrogeophysical data on a national scale

Development of more time-efficient and airborne geophysical data acquisition systems during the past decades have made large-scale mapping attractive and affordable in the planning and administration of e.g., groundwater resources or raw material deposits. The handling and optimized use of large geophysical data sets covering large geographic areas requires a system that allows data to be easily stored, extracted, interpreted, combined and used one time after another with different purposes. Such an integrated system for management and utilization of hydrogeophysical data on a national scale has been developed during the past decade in Denmark. This data handling system includes a comprehensive national geophysical data base (the GERDA data base), a national data base for borehole information (the Jupiter data base), a program package for processing, interpretation and visualization of electrical and electromagnetic data as well as preparation of these data for upload to the geophysical data base (the Aarhus Workbench) and finally a 3D visualization and modelling tool used for geological modelling and data quality control. The Aarhus Workbench program package allows visualization and analysis of subsets of data from the geophysical data base, which may include data from many individual mapping campaigns. The 3D visualization and modelling tool uses data from the geophysical and the borehole data bases directly; moreover, it handles maps and grids produced in the Aarhus Workbench. The integrated system for management of hydrogeophysical data allows management of large amounts of data collected over several years in different mapping campaigns, of different consultant companies and with different geophysical methods and instrumentation. It is now used by all partners involved in the groundwater mapping in Denmark. The system promotes reuse of geophysical data and models in future mapping projects, as well as easing and promoting the use of geophysical data in the geological modelling. The integrated system secures transfer of documentation all the way from data acquisition over processing and inversion of the geophysical data to geological modelling through storage of data acquisition parameters, data processing parameters, inversion parameters and uncertainties on data and models in the geophysical data base. The benefits of the large amount of geophysical data gathered in the national geophysical data base and utilized by the two program packages are invaluable for all future groundwater planning and administration.

Laterally and mutually constrained inversion of surface wave seismic data and resistivity data

The laterally and mutually constrained inversion (LCI and MCI) techniques allow for the combined inversion of multiple geophysical datasets and provide a sensitivity analysis of all model parameters. The LCI and MCI work with few-layered models, and are restricted to quasi-layered geological environments. LCI is used successfully for inversion of surface wave (SW) seismic data and MCI for combined inversion of SW data and continuous vertical electrical sounding (CVES) data. The primary model parameters are resistivity or shear wave velocity and thickness, and depth to layer interfaces is included as a secondary model parameter. The advantages and limitations of LCI and MCI are evaluated on synthetic SW data. The main conclusions are: Depth to a high velocity halfspace is generally well-resolved even if thicknesses of overlaying layers and the velocity of the halfspace are unresolved; Applying lateral constraints (LCI) between individual SW soundings improves model resolution, particularly for velocities and depths, and; Adding mutual constraints (MCI) to resistivity data improves model resolution of all parameters in the shear wave velocity model. When applied to field data, model resolution improves significantly when LCI or MCI is used, and resistivity and velocity models correlate structurally with better correlation to lithological interfaces identified in drill logs.