Niels B. Christensen

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.

A generic 1-D imaging method for transient electromagnetic data

This paper presents a fast approximate 1-D inversion algorithm for transient electromagnetic (EM) data that can be applied for all measuring configurations and transmitter waveforms and for all field components. The inversion is based on an approximate forward mapping in the adaptive Born approximation. The generality is obtained through a separation of the forward problem into a configuration-independent part, mapping layer conductivities into apparent conductivity, and a configuration-dependent part, the half-space step response. The EM response from any waveform can then be found by a convolution with the time derivative of the waveform. The approach does not involve inherently unstable deconvolution computations or nonunique transformations, and it is about 100 times faster than ordinary nonlinear inversion. Nonlinear model responses of the models obtained through the approximate inversion fit the data typically within 5%.

1D inversion and resolution analysis of marine CSEM data

We present results from an investigation into 1D inversion of controlled-source electromagnetic (CSEM) data. Based on inspection of a data set, we formulate a simple empirical noise model described by a few pragmatically determined parameters. We also investigate the effects of transmitter height above the seafloor and include the data uncertainty resulting from varying transmitter height in our noise model. Based on the noise model and assumptions about the available data, we analyze model parameter uncertainty estimates derived from the a posteriori model covariance matrix for a resistive layer buried at depth. We find that the layer parameters uncertainty primarily depends on the depth of burial and the thickness of the layer. We then formulate quantitative bounds for these parameters, within which we have a small uncertainty of the parameters of the resistive layer. The depth of burial and the transverse resistance of the layer become better determined the higher its resistance. We invert a field data...

A quantitative appraisal of airborne and ground-based transient electromagnetic (TEM) measurements in Denmark

The last decade has seen growing use of ground-based transient electromagnetic (TEM) methods in Denmark for hydrogeological purposes. Due to an intensified mapping campaign, airborne TEM methods were proposed as a possible tool for mapping large areas. The first test flights were flown in June 2000 using the GEOTEM system. Traditional approximate interpretation tools for airborne data are insufficient in hydrogeological investigations where a quantitative model specifying model parameter reliability is needed. We have carried out full nonlinear one-dimensional inversion on the field amplitude of airborne synthetic and field data and compared the airborne method with the traditional ground-based PROTEM 47 system that has found extensive use in Denmark. An improved measuring procedure for airborne systems is suggested to facilitate the estimation of noise that is necessary in a quantitative inversion. The analyses of synthetic data demonstrate the differences in resolution capability between ground-based and airborne data. Ground-based data typically resolve three- or four-layer models and occasionally up to five layers. Airborne data resolve three layers as a maximum, one or two layers being common. The airborne GEOTEM system detects layers to depths of more than 300 m, bearing only little information about the top 50‐ 70 m. The ground-based PROTEM 47 system has a maximum penetration of approximately 170 m, with higher resolution capabilities in the top 100 m. Coupling to man-made conductors is a serious problem for all TEM methods in densely populated areas and results in distorted data. Coupling influences the airborne data from Denmark on two-thirds of the area covered. These data must be eliminated to avoid misinterpretation.

1D Imaging of Central Loop Transient Electromagnetic Soundings

The success of geophysical investigations in general is to a large extent determined by the density of the measurements and the quality of the interpretations. The development in geophysical data acquisition has gone in the direction of covering larger and larger areas with more and more dense grids of measurements. This development has been especially pronounced in the field of transient electromagnetic data acquisition (TEM) for mineral prospecting, where airborne systems collect large volumes of data, and also in the field of environmental geophysics, where dense measurements of transient soundings have proved very useful in connection with hydrogeological investigations.An ordinary 1D least squares iterative inversion of TEM sounding, data requires that the interpreter supply an initial model, and the computation time is not at all negligible even on present‐day computing platforms. With a large daily production of soundings this procedure is slow, and there is need for fast approximate ways of interp...

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...

Robust 1D inversion and analysis of helicopter electromagnetic (HEM) data

Ground-based electrical and electromagnetic methods are used systematically for quantitative hydrogeologic investigations in Denmark. In recent years, a desire for faster and more cost-efficient methods has led to growing interest in the possibility of using airborne systems, and in 2001 a number of test flights were performed using a frequency-domain, helicopter-borne electromagnetic (HEM) system. We perform a theoretical examination of the resolution capabilities of the applied system. Quantitative model parameter analyses show that the system only weakly resolves conductive, near-surface layers but can resolve layer boundary to a depth of more than 100 m. Modeling experiments also show that the effect of altimeter errors on the inversion results is serious. We suggest a new interpretation scheme for HEM data founded solely on full nonlinear 1D inversion and providing layered-earth models supported by data misfit parameters and a quantitative model-parameter analysis. The backbone of the scheme is the removal of cultural coupling effects followed by a multilayer inversion that in turn provides reliable starting models for a subsequent few-layer inversion. A new procedure for correlation in the model space ensures model sections with slow lateral variations in resistivity, normally assumed in sedimentary environments. A field example from a Danish survey demonstrates that the interpretation scheme can produce satisfactory results within the limitations of the system.

Sensitivity functions of frequency-domain magnetic dipole-dipole systems

The resolution capabilities of airborne electromagnetic AEM frequency-domain systems are traditionally analyzed in terms of the footprint, which provides a simple measure of the lateral extent of the earth volume involved in a given measurement. However, considerably more detailed insight into the system resolution capabilities can be obtained by studying the 3D sensitivity distribution as defined by the Frechet derivatives. A qualitativeanalysisofthe3Dsensitivitydistributionsforsixtypical magnetic dipole-dipole configurations demonstrates that the spatial resolution characteristics differ widely and that the optimalcoilconfigurationforpracticalinvestigationsdependsonthe expected target characteristics. For all six coil configurations, the 3D sensitivity distributions reveal significant sign changes downwardsandoutwardsfromthecenter,stressingthenecessity ofreliablestartingmodelsforsuccessfulinversionoffrequencydomain AEM data. Likewise, the central zone of sensitivity for the in-phase component is always larger than for the quadrature, indicating an inferior lateral resolution of the former.Anew sensitivity footprint is defined, based on the at-surface behavior of thesensitivitydistribution,simplyastheareawherethesensitivity is at least 10% of its maximum value. For the vertical coaxial VCA coil configuration, the size of the sensitivity footprint in they-directionperpendiculartotheflightpathisapproximately a factor of two larger than in the x-direction along the flight path, while there is virtually no difference for the horizontal coplanar HCP coil configuration. The ratio of the HCP to VCA sensitivityfootprintexceedsoneinbothx-andy-directions,suggesting that the VCA coil configuration has the best lateral resolution.

Rapid inversion of 2-D geoelectrical data by multichannel deconvolution

Modern geoelectrical data acquisition systems can record more than 100 000 data values per field day. Despite the growth in computer power and the development of more efficient numerical algorithms, interpreting such data volumes remains a nontrivial computational task. We present a 2-D one-pass inversion procedure formulated as a multichannel deconvolution. It is based on the equation for the electrical potential linearized under the Born approximation, and it makes use of the 2-D form of the Fr ´ echet derivatives evaluated for the homogeneous half-space. The inversion is formulated in the wavenumber domain so that the 2-D spatial problem decouples into many small 1-D problems. The resulting multichannel deconvolution algorithm is very fast and memory efficient. The inversion scheme is stabilized through covariance matrices representing the stochastic properties of the earth resistivity and data errors. The earth resistivity distribution is assumed to have the statistical characteristics of a two-parameter, selfaffine fractal. The local apparent amplitude and fractal dimension of the earth resistivity are estimated directly from geoelectrical observations. A nonlinearity error covariance matrix is added to the conventional measurement error covariance matrix. The stochastic model for the dependence of nonlinearity error on electrode configuration as well as resistivity amplitude and fractal dimension is determined pragmatically through nonlinear simulation experiments. Tests on synthetic examples and field cases including well control support the conclusion that for long data profiles this method automatically produces linearized resistivity estimates which faithfully resolve the main model features.