Kurt Sørensen

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 survey of current trends in near-surface electrical and electromagnetic methods

ElectricalandelectromagneticE&EMmethodsfornearsurface investigations have undergone rapid improvements over the past few decades. Besides the traditional applications in groundwater investigations, natural-resource exploration, and geological mapping, a number of new applications have appeared. These include hazardous-waste characterizationstudies,precision-agricultureapplications,archeological surveys, and geotechnical investigations. The inclusion of microprocessors in survey instruments, development ofnewinterpretationalgorithms,andeasyaccesstopowerful computers have supported innovation throughout the geophysical community and the E&EM community is no exception. Most notable are development of continuous-measurement systems that generate large, dense data sets efficiently. These have contributed significantly to the usefulness of E&EM methods by allowing measurements over wide areas without sacrificing lateral resolution. The availability of theseluxuriantdatasetsinturnspurreddevelopmentofinterpretation algorithms, including: Laterally constrained 1D inversionaswellasinnovative2D-and3D-inversionmethods. Taken together, these developments can be expected to improve the resolution and usefulness of E&EM methods and permit them to be applied economically. The trend is clearly towarddensesurveyingoverlargerareas,followedbyhighly automated, post-acquisition processing and interpretation to provide improved resolution of the shallow subsurface in a cost-effectivemanner.

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.

Nitrate reduction in geologically heterogeneous catchments--a framework for assessing the scale of predictive capability of hydrological models.

In order to fulfil the requirements of the EU Water Framework Directive nitrate load from agricultural areas to surface water in Denmark needs to be reduced by about 40%. The regulations imposed until now have been uniform, i.e. the same restrictions for all areas independent of the subsurface conditions. Studies have shown that on a national basis about 2/3 of the nitrate leaching from the root zone is reduced naturally, through denitrification, in the subsurface before reaching the streams. Therefore, it is more cost-effective to identify robust areas, where nitrate leaching through the root zone is reduced in the saturated zone before reaching the streams, and vulnerable areas, where no subsurface reduction takes place, and then only impose regulations/restrictions on the vulnerable areas. Distributed hydrological models can make predictions at grid scale, i.e. at much smaller scale than the entire catchment. However, as distributed models often do not include local scale hydrogeological heterogeneities, they are typically not able to make accurate predictions at scales smaller than they are calibrated. We present a framework for assessing nitrate reduction in the subsurface and for assessing at which spatial scales modelling tools have predictive capabilities. A new instrument has been developed for airborne geophysical measurements, Mini-SkyTEM, dedicated to identifying geological structures and heterogeneities with horizontal and lateral resolutions of 30-50 m and 2m, respectively, in the upper 30 m. The geological heterogeneity and uncertainty are further analysed by use of the geostatistical software TProGS by generating stochastic geological realisations that are soft conditioned against the geophysical data. Finally, the flow paths within the catchment are simulated by use of the MIKE SHE hydrological modelling system for each of the geological models generated by TProGS and the prediction uncertainty is characterised by the variance between the predictions of the different models.

Deep groundwater and potential subsurface habitats beneath an Antarctic dry valley

The occurrence of groundwater in Antarctica, particularly in the ice-free regions and along the coastal margins is poorly understood. Here we use an airborne transient electromagnetic (AEM) sensor to produce extensive imagery of resistivity beneath Taylor Valley. Regional-scale zones of low subsurface resistivity were detected that are inconsistent with the high resistivity of glacier ice or dry permafrost in this region. We interpret these results as an indication that liquid, with sufficiently high solute content, exists at temperatures well below freezing and considered within the range suitable for microbial life. These inferred brines are widespread within permafrost and extend below glaciers and lakes. One system emanates from below Taylor Glacier into Lake Bonney and a second system connects the ocean with the eastern 18 km of the valley. A connection between these two basins was not detected to the depth limitation of the AEM survey (∼350 m).

Mutually and laterally constrained inversion of CVES and TEM data: a case study

Mutually constrained inversion in combination with laterally constrained inversion (MCI-LCI) between transient electromagnetic (TEM) and direct current (DC) resistivity methods was successfully used to characterize a buried valley structure. Although both methods measure, in some sense, the electrical resistivity, or conductivity, of the subsurface, they sample different volumes and have different sensitivities, which are exploited with mutually and laterally constrained inversion of combined, coincident profile data sets. The output models incorporate the information from both data sets to obtain optimum layered 1D models, fitting both data sets and constraints. The set-up of constraints contains three parts. First, we constrain the individual data sets along their profile using lateral constraints producing a chain of TEM data and a chain of DC data. Next, we merge the information from these two chains by setting up mutual constraints between the TEM and the DC models. Finally, we adjust the mutual constraints to resemble the increasing sampling volumes with depth, i.e. wide constraints at large depths and short constraints at shallow depths. All data sets are inverted simultaneously; a common objective function is minimized, and the number of output models is equal to the number of 1D soundings. The lateral and mutual constraints are part of the inversion, and consequently the output models are balanced between the constraints and the data-model fit. Information from one model will spread to the neighbouring models through the constraints, helping to resolve parameters that are poorly resolved by any of the individual data sets. A field example illustrates that MCI-LCI allows the governing information from each method to dominate the inversion process. Thus, the model resolution in both the shallow and the deeper parts of the model is significantly enhanced. This could not be obtained by inverting the two data sets separately with a subsequent comparison of the output models. Our results are confirmed by drill-hole data.

EMMA - a geophysical training and education tool for electromagnetic modeling and analysis

An interactive modeling and analysis program with a user-friendly graphical interface, for students and professionals in the field of exploration geophysics, has been developed. The ElectroMagnetic Modeling and Analysis program—EMMA—is capable of modeling one-dimensional responses for most electrical and electromagnetic methods and array configurations, including the time-domain, frequency-domain, resistivity, magnetotelluric and borehole methods. EMMA is available on-line, at no charge, from http:∕∕www.hgg.au.dk. An innovation of EMMA is the calculation of the model sensitivity analysis, a feature that is usually only present in inversion codes. The variance of the model parameters depends on the variance of the measured data and the way in which an error is mapped from the data to the model parameters. The measurement situation is realized by ascribing data noise to the model response. This facilitates the calculation of a realistic model parameter analysis. For time-domain data, piece-wise linear wavef...

Coil response inversion for very early time modelling of helicopter‐borne time‐domain electromagnetic data and mapping of near‐surface geological layers

Very early times in the order of 2–3 μs from the end of the turn-off ramp for time-domain electromagnetic systems are crucial for obtaining a detailed resolution of the near-surface geology in the depth interval 0–20 m. For transient electromagnetic systems working in the off time, an electric current is abruptly turned off in a large transmitter loop causing a secondary electromagnetic field to be generated by the eddy currents induced in the ground. Often, however, there is still a residual primary field generated by remaining slowly decaying currents in the transmitter loop. The decay disturbs or biases the earth response data at the very early times. These biased data must be culled, or some specific processing must be applied in order to compensate or remove the residual primary field. As the bias response can be attributed to decaying currents with its time constantly controlled by the geometry of the transmitter loop, we denote it the ‘Coil Response’. The modelling of a helicopter-borne time-domain system by an equivalent electronic circuit shows that the time decay of the coil response remains identical whatever the position of the receiver loop, which is confirmed by field measurements. The modelling also shows that the coil response has a theoretical zero location and positioning the receiver coil at the zero location eliminates the coil response completely. However, spatial variations of the coil response around the zero location are not insignificant and even a few cm deformation of the carrier frame will introduce a small coil response. Here we present an approach for subtracting the coil response from the data by measuring it at high altitudes and then including an extra shift factor into the inversion scheme. The scheme is successfully applied to data from the SkyTEM system and enables the use of very early time gates, as early as 2–3 μs from the end of the ramp, or 5–6 μs from the beginning of the ramp. Applied to a large-scale airborne electromagnetic survey, the coil response compensation provides airborne electromagnetic methods with a hitherto unseen good resolution of shallow geological layers in the depth interval 0–20 m. This is proved by comparing results from the airborne electromagnetic survey to more than 100 km of Electrical Resistivity Tomography measured with 5 m electrode spacing.

Mutually Constrained Inversion (MCI) of Electrical and Electromagnetic Data

Summary Mutually constrained inversion (MCI) is a process in which two distinct data sets are inverted to produce two closely related models. Time domain electromagnetic (TEM) and electrical resistivity are two methods, that measure the same fundamental property, resistivity, but have different sensitivity and will not necessarily respond to the earth in the same manner. MCI has many of the properties of joint inversion, the process where two datasets are inverted to produce one model. Poorly resolved parameters are enhanced and invisible layers can be seen. However MCI is more robust, the two resulting models can be independently evaluated, and the best resolved parameters used in the interpretation. The approach is illustrated first on synthetic data. The MCI is used to resolve incompatibilities produced when the resistivity sounding is distorted with near surface inhomogeneities, a static shift, without the need of a special parameter that cannot be measured. A field study demonstrates how a resistive layer, which is important in aquifer characterization, that is either inconsistently detected or unresolved in the separate time domain and resistivity datasets, is well delineated with the MCI.

The fields from a finite electrical dipole; a new computational approach

Controlled‐source, frequency‐domain, and time‐domain electromagnetic methods require accurate, fast, and reliable methods of computing the electric and magnetic fields from the source configurations used. Except for small magnetic dipole sources, all electric and magnetic sources are composed of lengths of straight wire, which may be grounded. If the source‐receiver separation is large enough, the composite electrical dipoles may be considered to be infinitely small, and in a 1-D earth model the fields are expressed as Hankel transforms of an input function, which depends only on the model parameters. The Hankel transforms can be evaluated using the digital filter theory of fast Hankel transforms. However, the approximation of the infinitely small dipole is not always valid, and fields from a finite electrical dipole must be calculated. Traditionally, this is done by numerical integration of the fields from an infinitesimal dipole, thus increasing computation time considerably. The fields from the finite ...