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This paper presents the results of airborne electromagnetic induced polarisation inversions using the Maximum Phase Angle (MPA) model for a helicopter time domain survey in the Quadrilátero Ferrífero area, Minas Gerais State (MG), Brazil. The inversions were conducted using a laterally constrained robust scheme, in order to decrease the difficulties to recover the multi-parametric model in a very ill-posed inverse problem, often found in induced polarisation studies. A set of six flight lines over the Lamego gold mine mineralised structure were inverted using the MPA re-parameterisation of the Cole–Cole model and also the classical resistivity-only parameterisation, in order to understand the implications of the induced polarisation effect in the data and, consequently, in the resistivity model. A synthetic study was also conducted, seeking to understand what to expect from the resistivity-only inversions in the real data. According to borehole lithological data and previous structural knowledge from the literature, the results from the Maximum Phase Angle approach indicate an important chargeable body that seems to be in good agreement with a sulfide enriched carbonaceous/graphite and altered mafic unities, which are important markers for the gold mineralisation.

The signal level and shape of induced polarization responses are significantly affected by the current pulse duration and waveform. If not accounted for, this data dependency on the current will propagate trough the inversion to results rendering unquantifiable subsurface models. While this problem has been addressed in full-response induced polarization modelling, questions remain as to how to accurately retrieve quantitative induced polarization inversion models from the types of apparent integral chargeability data often used in data interpretation. Although several methodologies have been proposed for handling and inverting apparent resistivity and integral chargeability, these cannot compensate for the data dependency on the current waveform and pulse duration. This paper presents a novel inversion method for such data. The method considers current waveform and receiver transfer functions for retrieving quantitative IP models unbiased by transmitter waveform. The method uses the constant phase angle model, expressed in terms of the medium resistivity and phase. Specifically, four field data sets for the same profile but with different 100 per cent duty cycle pulse durations (4, 2, 1 and 0.5 s) serve as examples of data sets giving models dependant on current waveform when inverted with standard approaches. The novel inversion method presented here gives quantifiable models independent on the current waveform and pulse duration. These results resemble models retrieved with existing, full-response induced polarization inversions. The results still contain some degree of uncertainty in relation to underlying assumptions and parametrizations. Managing this source of uncertainty is considered in terms of full-response induced polarization inversions with constant phase angle and maximum phase angle inversions.

Inversion of large-scale time-domain electromagnetic surveys are computationally expensive and time consuming. Deterministic or probabilistic inversion schemes usually require calculations of forward responses, and often thousands to millions of forward responses are computed. We propose a machine learning based forward modelling approach as a computationally feasible alternative to approximate numerical forward modelling where a neural network is employed to model the relationship between the resistivity models and corresponding forward responses. For training of the neural network, we generated forward responses using conventional numerical algorithm for 93,500 resistivity models derived from different surveys conducted in Denmark representing typical resistivities of sedimentary geological layers. The input resistivity models and the network target outputs, i.e. forward responses, are scaled using a novel normalization strategy to ensure each gate is equally prioritized. The performance of the network is evaluated on two test datasets consisting of 8942 resistivity models by comparing the forward responses generated by the neural network and the conventional algorithm. We also measure the performance for the time derivatives of forward responses, i.e. dB/dt, by incorporating a system response. The results show that the proposed strategy is at least 13 times faster than commonly used accurate modelling methods and achieves an accuracy of 98% within 3% relative error, which is comparable to data uncertainty. Additional experiments on surveys from two other continents show that the results generalize in similar geological settings. Thus, under certain geological constraints, the proposed methodology may be incorporated into the pre-existing inversion structures, allowing for significantly faster inversion of large datasets.

One of the primary shortcomings of the standard surface nuclear magnetic resonance (NMR) measurement, called the free-induction decay (FID), is the uncertainty about the link between the signal’s time dependence and the geometry of the pore space. Ideally, the FID signal’s time dependence, described by the parameter T2*, carries an intimate link to the geometry of the pore space allowing robust estimation of pore-size and permeability. However, T2* can also be strongly influenced by background magnetic field (B0) inhomogeneity, which can mask the link to pore geometry. To improve the utility of surface NMR FID measurements, we investigate whether complex inversion of surface NMR data can be used to provide insight into the link between T2* and T2 (the parameter carrying the link to pore geometry). Synthetic and field measurements are presented to demonstrate that an alternative forward modelling approach that involves direct modelling of relaxation during pulse (RDP) effects can help constrain the relationship between T2* and T2. Complex inversions are performed using forward models that include RDP for varying magnitudes of B0 inhomogeneity (consistent with observed T2* values) and it is observed that satisfactory data fits can only be obtained given reliable T2 estimates. Thus providing insight into the T2*-T2 relationship. We aim to demonstrate that an alternative forward modelling approach may help improve the utility of FID measurements for estimation of pore-scale properties.

The principle of equivalence is known to cause nonuniqueness in interpretations of direct current (DC) resistivity data. Low- or high-resistivity equivalences arise when a thin geologic layer with a low/high resistivity is embedded in a relative high-/low-resistivity background formation causing strong resistivity-thickness correlations. The equivalences often make it impossible to resolve embedded layers. We found that the equivalence problem could be significantly reduced by combining the DC data with full-decay time-domain induced polarization (IP) measurements. We applied a 1D Markov chain Monte Carlo algorithm to invert synthetic DC data of models with low- and high-resistivity equivalences. By applying this inversion method, it is possible to study the space of equivalent models that have an acceptable fit to the observed data, and to make a full sensitivity analysis of the model parameters. Then, we include a contrast in chargeability into the model, modeled in terms of spectral Cole-Cole IP parameters, and invert the DC and IP data in combination. The results show that the addition of IP data largely resolves the DC equivalences. Furthermore, we present a field example in which DC and IP data were measured on a sand formation with an embedded clay layer known from a borehole drilling. Inversion results show that the DC data alone do not resolve the clay layer due to equivalence problems, but by adding the IP data to the inversion, the layer is resolved.

The application of time-domain induced polarization (TDIP) is increasing with advances in acquisition techniques, data processing and spectral inversion schemes. An inversion of TDIP data for the spectral Cole-Cole parameters is a non-linear problem, but by applying a 1-D Markov Chain Monte Carlo (MCMC) inversion algorithm, a full non-linear uncertainty analysis of the parameters and the parameter correlations can be accessed. This is essential to understand to what degree the spectral Cole-Cole parameters can be resolved from TDIP data. MCMC inversions of synthetic TDIP data, which show bell-shaped probability distributions with a single maximum, show that the Cole-Cole parameters can be resolved from TDIP data if an acquisition range above two decades in time is applied. Linear correlations between the Cole-Cole parameters are observed and by decreasing the acquisitions ranges, the correlations increase and become non-linear. It is further investigated how waveform and parameter values influence the resolution of the Cole-Cole parameters. A limiting factor is the value of the frequency exponent, C. As C decreases, the resolution of all the Cole-Cole parameters decreases and the results become increasingly non-linear. While the values of the time constant, tau, must be in the acquisition range to resolve the parameters well, the choice between a 50 per cent and a 100 per cent duty cycle for the current injection does not have an influence on the parameter resolution. The limits of resolution and linearity are also studied in a comparison between the MCMC and a linearized gradient-based inversion approach. The two methods are consistent for resolved models, but the linearized approach tends to underestimate the uncertainties for poorly resolved parameters due to the corresponding non-linear features. Finally, an MCMC inversion of 1-D field data verifies that spectral Cole-Cole parameters can also be resolved from TD field measurements.

Surface nuclear magnetic resonance is a geophysical technique providing non-invasive aquifer characterization. Two approaches are commonly used to invert surface nuclear magnetic resonance data: (1) inversions involving many depth layers of fixed thickness and (2) few-layer inversions without predetermined layer thicknesses. The advantage of the many-layer approach is that it requires little a priori knowledge. However, the many-layer inversion is extremely ill-posed and regularisation must be used to produce a reliable result. For optimal performance, the selected regularisation scheme must reflect all available a priori information. The standard regularisation scheme for many-layer surface nuclear magnetic resonance inversions employs an L2 smoothness stabiliser, which results in subsurface models with smoothly varying parameters. Such a stabiliser struggles to reproduce sharp contrasts in subsurface properties, like those present in a layered subsurface (a common near-surface hydrogeological environment). To investigate if alternative stabilisers can be used to improve the performance of the many-layer inversion in layered environments, the performance of the standard smoothness stabiliser is compared against two alternative stabilisers: (1) a stabiliser employing the L1-norm and (2) a minimum gradient support stabiliser. Synthetic results are presented to compare the performance of the many-layer inversion for different stabiliser functions. The minimum gradient support stabiliser is observed to improve the performance of the many-layer inversion for a layered subsurface, being able to reproduce both smooth and sharp vertical variations of the model parameters. Implementation of the alternative stabilisers into existing surface nuclear magnetic resonance inversion software is straightforward and requires little modification to existing codes.

We describe a new approach for modelling airborne transient electromagnetic (TEM) data which combines the use of on- and off-time data for inversion. Specifically, the response is modelled using system response convolution both during and after transmitter ramp-down. High near-surface sensitivity can be achieved through a combination of fast transmitter ramp-down, broad receiver system bandwidth, efficient suppression or explanation of the primary field, and by combining the use of on-time gates with accurate knowledge of the system response. The system response can either be calculated based on the transfer function of the individual system components (i.e. receiver coil, amplifiers, low-pass filters and current waveform) or it can be measured at high altitude. The latter approach has the advantage of avoiding the specific modelling of individual system components. By comparing model parameter uncertainty when the on-time gates are included in the inversion versus when they are not, we show that a significant improvement in near-surface sensitivity is obtained. The method is used to invert both synthetic and field data. In the inversion of synthetic data, we see clear improvements in the determination of thin shallow layers, especially when they are resistive. This is confirmed by inversion of field data where we observe more pronounced structures with better definition of layer boundaries and layer resistivities.

Recently, the interest in the induced polarization (IP) phenomenon in airborne time-domain electromagnetic (ATEM) data has increased considerably. IP may affect the ATEM data significantly and mask underlying geologic structures. To simulate 2D airborne IP data, a 2D finite-element forward-modeling algorithm has been developed with the dispersive conductivity described by the well-known Cole-Cole model. We verify our algorithm by comparison with the 1D solution of the AarhusInv code. Two-dimensional forward responses on six synthetic models, mimicking archetypal 2D conductive and chargeable anomalies, have been generated, and the results indicate that 2D IP affects the data significantly. Differences between the 2D IP responses and the 1D IP responses are evident above the 2D anomalies and at their edges. These differences are similar to what is found when comparing 2D and 1D forward responses over conductive 2D anomalies without considering IP. We evaluate an effective robust inversion scheme to recover the 2D IP parameters using the 1D laterally constrained inversion (LCI) scheme. The inversion of the synthetic data using the robust scheme indicates that not only can the IP parameters be recovered, but also the IP inversions can provide more accurate resistivity sections than a resistivity-only inversion, in terms of resistivity values and anomaly thickness/depth. The field example from Hope Bay area in Canada is even more valuable, considering that part of the profile consists of only negative data, which cannot be inverted with a resistivity-only scheme. Furthermore, the edge effects at the anomaly boundaries are less pronounced in the IP parameters than in the resistivity parameter on the synthetic models with more conductive backgrounds.

Envelope detection is an integral step of the surface NMR data processing workflow to estimate these parameters. We present a new method for retrieving NMR signal envelopes using spectral analysis and the subsequent inversion scheme with the new data space. By exploiting the fact that the spectral magnitude at the Larmor frequency is proportional to the product of the initial amplitude and relaxation time, a high-SNR complex envelope can be extracted by Fourier transform for a number of sliding windows. However, SA estimated envelopes are weighted by the NMR relaxation time during processing and the envelopes have units of volt-seconds. We propose to modify the surface NMR forward model such that it predicts data directly in the voltage-time data space. Field data inversions are presented to demonstrate advantages of pairing the SA envelope detection scheme with a forward model that works in the voltage-time data space.

Surface nuclear magnetic resonance (NMR) data are sensitive to key hydrogeological parameters including water content and pore size. The measured data are modelled as a complex sinusoidal exponential decay where the phase is a function of the physics of the experiment and instrumental factors, parameters that are difficult to decouple. When inverting surface NMR data, practitioners typically account for these phases either by considering only the amplitudes of the complex signals, thus eliminating the influence of the phase, or by iteratively rotating the complex data during inversion so the data phase matches the theoretical phase generated during forward modelling. Each of these approaches assumes the user has an accurate forward model; if not, the data will be incorrectly rotated and forced to fit an erroneous forward model. Additionally, this rotation will artificially reduce the total data misfit, thus masking the effect of the erroneous forward model. We demonstrate the pitfalls of using inverse methods that correct for the phase by inverting synthetic data with three types of deliberate modelling errors that may occur during a surface NMR experiment: errors in the offset between the Larmor and transmit frequencies, errors in the subsurface resistivity model, and errors in the relative positioning of a separated transmitter-receiver coil pair. The inverted water content profiles show that the modelling errors can introduce inversion artifacts. However, the amplitude inversions and complex inversions with iterative phase correction frequently produce χ2 misfit values close to unity, showing that these inverse methods will fail to “raise the alarm” when an incorrect forward model is implemented.

Conventional regularized nonlinear inversion methods for estimating electrical conductivity from observed electromagnetic data seek to find a single model that fits the data while minimizing a user-imposed model regularization norm. By contrast, Bayesian sampling techniques produce a large suite of models, all of which fit the data adequately, providing a wealth of statistical information about the model parameters. Importantly, this includes quantitative uncertainty estimates as well as any statistical property of interest. In this work, we apply a Bayesian trans-dimensional Markov chain Monte Carlo scheme to recover subsurface conductivity from airborne transient electromagnetic (TEM) data collected over Taylor Glacier, Antarctica, to image subglacial hydrologic structure. We provide a synthetic model study, followed by inversions of real soundings. Our results identify a zone of conductive, wet sediments beneath the glacier, corroborating interpretations from previous studies that used regularized, smooth inversions. Our results provide, however, the opportunity to examine a rich suite of additional information, including uncertainty estimates on the conductivity within the conductive subglacial layer as well as quantitative estimates of its total conductance. We apply principles of Bayesian information theory for estimating the depth of investigation of the airborne TEM data and apply it to this data set. Additionally, we use themodel ensemble to derive estimates of pore fluid resistivity within the conductive layer, with associated uncertainties. Finally, we use Bayesian model studies to explore the range of ice thicknesses and conductive layer thicknesses that could be resolved with ground or airborne TEM data if they had one to two orders of magnitude lower noise levels.

In many cases, inversion in 2D gives a better description of the subsurface compared with 1D inversion, but, computationally, 2D inversion is expensive, and it can be hard to use for large-scale surveys. We have developed an efficient hybrid 2D airborne frequency-domain electromagnetic inversion algorithm. Our hybrid scheme combines 1D and 2D inversions in a three-stage process, in which each step is progressively more accurate and computationally more expensive than the previous one. This results in an approximately [Formula: see text] speedup compared with full 2D inversions, and with only minor changes to the inversion results. Our inversion structure is based on a regular grid, in which each sounding is discretized individually. The 1D modeling code uses layered models with derivatives derived through the finite-difference method, whereas our 2D modeling code uses an adaptive finite-element mesh, and it uses the adjoint-state method to calculate the derivatives. By incorporating the inversion grid structure into the 2D finite-element mesh, interpolation between the different meshes becomes trivial. Large surveys are handled by using local meshing to split large surveys into small sections, which retains the 2D information. The algorithm is heavily optimized and parallelized over the frequencies and sections, with good scalability even on nonuniform memory architecture systems, on which it is generally hard to achieve a satisfactory scaling. The algorithm has been tested successfully with various synthetic studies as well as field examples, of which results from two synthetic studies and a field example are shown.

Surface nuclear magnetic resonance is a technique capable of providing insight into subsurface aquifer properties. To produce estimates of aquifer properties (such as the spatial distribution of water content and parameters controlling the duration of the nuclear magnetic resonance signal), an inversion is required. Essential to the reliable interpretation of the estimated subsurface models is an understanding of the uncertainty and correlation between the parameters in the estimated models. To quantify parameter uncertainty and correlation in the surface nuclear magnetic resonance inversion, a Markov chain Monte Carlo approach is demonstrated. Markov chain Monte Carlo approaches have been previously employed to invert surface nuclear magnetic resonance data, but the primary focus has been on quantifying parameter uncertainty. The focus of this paper is to further investigate whether the parameters in the estimated models exhibit correlation with one another; equally important to building a reliable interpretation of the subsurface is an understanding of the parameter uncertainty. The utility of the Markov chain Monte Carlo approach is demonstrated through the investigation of three questions. The first question investigates whether the parameters describing the water content and thickness of a layer exhibit a strong correlation. This question stems from applying concepts known to electromagnetic surveys (that the layer thickness and layer resistivity parameters are strongly correlated) to the surface nuclear magnetic resonance inversion. A water content–layer thickness correlation in surface nuclear magnetic resonance would not have large effects for quantifying total water content but would affect the ability to identify layer boundaries. The second question examines whether the parameter controlling the duration of the nuclear magnetic resonance signal exhibits a correlation with the water content and layer thickness parameters. The resolution of surface nuclear magnetic resonance typically does not consider the duration of the signal and focuses primarily on the distribution of current amplitudes that form the suite of transmit pulses. It is common to treat regions with short-duration signal with greater uncertainty, but it is important to understand whether the signal duration controls resolution for medium to long duration signals as well. The third question explores if the parameter uncertainty produced by the Markov chain Monte Carlo approach is consistent with that produced by an alternative approach based upon the posterior covariance matrix (for the linearised inversion). The ability of the Markov chain Monte Carlo approach to more thoroughly explore the model space provides a means to improve the reliability of surface nuclear magnetic resonance aquifer characterisations by quantifying parameter uncertainty and correlation.

Modern airborne transient electromagnetic surveys typically produce datasets of thousands of line kilometres, requiring careful data processing in order to extract as much and as reliable information as possible. When surveys are flown in populated areas, data processing becomes particularly time consuming since the acquired data are contaminated by couplings to man-made conductors (power lines, fences, pipes, etc.). Coupled soundings must be removed from the dataset prior to inversion, and this is a process that is difficult to automate. The signature of couplings can be both subtle and difficult to describe in mathematical terms, rendering removal of couplings mostly an expensive manual task for an experienced geophysicist. Here, we try to automate the process of removing couplings by means of an artificial neural network. We train an artificial neural network to recognize coupled soundings in manually processed reference data, and we use this network to identify couplings in other data. The approach provides a significant reduction in the time required for data processing since one can directly apply the network to the raw data. We describe the neural network put to use and present the inputs and normalizations required for maximizing its effectiveness. We further demonstrate and assess the training state and performance of the network before finally comparing inversions based on unprocessed data, manually processed data, and artificial neural network automatically processed data. The results show that a well-trained network can produce high-quality processing of airborne transient electromagnetic data, which is either ready for inversion or in need of minimal manual processing. We conclude that the use of artificial neural network scan significantly reduce the processing time and its costs by as much as 50%.

Airborne electromagnetic (AEM) data is used throughout the world for mapping of mineral targets and groundwater resources. The development of technology and inversion algorithms has been tremendously over the last decade and results from these surveys are high-resolution images of the subsurface. In this keynote talk, we discuss an effective inversion algorithm, which is both subjected to intense research and development as well as production. This is the well know Laterally Constrained Inversion (LCI) and Spatial Constrained Inversion algorithm. The same algorithm is also used in a voxel setup (3D model) and for sheet inversions. An integral part of these different model discretization is an accurate modelling of the system transfer function and of auxiliary parameters like flight altitude, bird pitch, etc.

We present a 2D inversion code for frequency-domain HEM data designed for inverting field scale surveys on normal desktop computers. The fundamental algorithm is a 2.5D algorithm with field separation into primary and secondary fields. Due to limited memory, as well as performance concerns, sectioning is introduced for splitting large surveys into smaller sections. Sectioning is only done when calculating the 2D forward and derivatives, and it is done with a sufficient overlap, such that vital 2D information is preserved. The algorithm uses a hybrid scheme which i) starts with 1D forward and inverse calculations, ii) then switches to 2D forward calculations and 1D derivatives, and iii) finally ends with full 2D calculations. The result of this is a code which produces results like a 2D code, but with a substantially shorter computational time.

Time-domain electromagnetic data are conveniently inverted by using smoothly varying 1D models with fixed vertical discretization. The vertical smoothness of the obtained models stems from the application of Occam-type regularization constraints, which are meant to address the ill-posedness of the problem. An important side effect of such regularization, however, is that horizontal layer boundaries can no longer be accurately reproduced as the model is required to be smooth. This issue can be overcome by inverting for fewer layers with variable thicknesses; nevertheless, to decide on a particular and constant number of layers for the parameterization of a large survey inversion can be equally problematic. Here, we present a focusing regularization technique to obtain the best of both methodologies. The new focusing approach allows for accurate reconstruction of resistivity distributions using a fixed vertical discretization while preserving the capability to reproduce horizontal boundaries. The formulation is flexible and can be coupled with traditional lateral/spatial smoothness constraints in order to resolve interfaces in stratified soils with no additional hypothesis about the number of layers. The method relies on minimizing the number of layers of non-vanishing resistivity gradient, instead of minimizing the norm of the model variation itself. This approach ensures that the results are consistent with the measured data while favouring, at the same time, the retrieval of horizontal abrupt changes. In addition, the focusing regularization can also be applied in the horizontal direction in order to promote the reconstruction of lateral boundaries such as faults. We present the theoretical framework of our regularization methodology and illustrate its capabilities by means of both synthetic and field data sets. We further demonstrate how the concept has been integrated in our existing spatially constrained inversion formalism and show its application to large-scale time-domain electromagnetic data inversions.

Over the past decade the typical size of airborne electromagnetic data sets has been growing rapidly, along with an emerging need for highly accurate modelling. Onedimensional approximate inversions or data transform techniques have previously been employed for very large-scale studies of quasi-layered settings but these techniques fail to provide the consistent accuracy needed by many modern applications such as aquifer and geological mapping, uranium exploration, oil sands and integrated modelling. In these cases the use of more time-consuming 1D forward and inverse modelling provide the only acceptable solution that is also computationally feasible. When target structures are known to be quasi layered and spatially coherent it is beneficial to incorporate this assumption directly into the inversion. This implies inverting multiple soundings at a time in larger constrained problems, which allows for resolving geological layers that are undetectable using simple independent inversions. Ideally, entire surveys should be inverted at a time in huge constrained problems but poor scaling properties of the underlying algorithms typically make this challenging. Here, we document how we optimized an inversion code for very large-scale constrained airborne electromagnetic problems. Most importantly, we describe how we solve linear systems using an iterative method that scales linearly with the size of the data set in terms of both solution time and memory consumption. We also describe how we parallelized the core region of the code, in order to obtain almost ideal strong parallel scaling on current 4-socket shared memory computers. We further show how model parameter uncertainty estimates can be efficiently obtained in linear time and we demonstrate the capabilities of the full implementation by inverting a 3327 line km SkyTEM survey overnight. Performance and scaling properties are discussed based on the timings of the field example and we describe the criteria that must be fulfilled in order to adapt our methodology for similar type problems.

The possibility of extracting IP information from AEM data never stopped being of inetrest to the sceintific community and industry. We apply to this old problem the proven approach of the Laterally and Spatially Constrained Inversion. By applying constraints in the model space, we improve the resolvability of model parameters in the ill posed inversion problem. We present a synthetic study where the model the IP response over a layered earth using the Cole Cole model. We simulate both an environmental and an exploration target. Results show that, as expected, in some cases, some of the Cole Cole parameters can be resolved better using the LCI-SCI than by using stitched together inversions. They also provide useful insight into different ranges/combinations of resolvable parameters. Limitations of the approach are those of the SCI-LCI; In presence of strong 3D varitaions, the dimensionality of the forward response produces inaccuracies in the recovered models. Nonetheless, we argue that this approach can be applied satisfactorily to a number of real cases.We aim at presenting at the conference results also from real dataset.

Increasingly, electromagnetic induction methods (EMI) are being used within the area of archaeological prospecting for mapping soil structures or for studying paleo-landscapes. Recent hardware developments have made fast data acquisition, combined with precise positioning, possible, thus providing interesting possibilities for archaeological prospecting. However, it is commonly assumed that the instrument operates in what is referred to as Low Induction Number, or LIN. Here, we detail the problems of the approximations while discussing a best practice for EMI measurements, data processing, and inversion for understanding a paleo-landscape at an Iron Age human bone depositional site (Alken Enge) in Denmark. On synthetic as well as field data we show that soil mapping based on EMI instruments can be improved by applying data processing methodologies from adjacent scientific fields. Data from a 10 hectare study site was collected with a line spacing of 1-4 m, resulting in roughly 13,000 processed soundings, which were inverted with a full non-linear algorithm. The models had higher dynamic range in the retrieved resistivity values, as well as sharper contrasts between structural elements than we could obtain by looking at data alone. We show that the pre-excavation EMI mapping facilitated an archaeological prospecting where traditional trenching could be replaced by a few test pits at selected sites, hereby increasing the chance of finding human bones. In a general context we show that (1) dedicated processing of EMI data is necessary to remove coupling from anthropogenic structures (fences, phone cables, paved roads, etc.), and (2) that carrying out a dedicated full non-linear inversion with spatial coherency constraints improves the accuracy of resistivities and structures over using the data as they are or using the Low Induction Number (LIN) approximation.

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.

Helicopter borne time domain EM systems historically measure only the Z-component of the secondary field, whereas fixed wing systems often measure all field components. For the latter systems the X-component is often used to map discrete conductors, whereas it finds little use in the mapping of layered settings. Measuring the horizontal X-component with an offset loop helicopter system probes the earth with a complementary sensitivity function that is very different from that of the Z-component, and could potentially be used for improving resolution of layered structures in one dimensional modeling. This area is largely unexplored in terms of quantitative results in the literature, since measuring and inverting X-component data from a helicopter system is not straightforward: The signal strength is low, the noise level is high, the signal is very sensitive to the instrument pitch and the sensitivity function also has a complex lateral behavior. The basis of our study is a state of the art inversion scheme, using a local 1D forward model description, in combination with experiences gathered from extending the SkyTEM system to measure the X component. By means of a 1D sensitivity analysis we motivate that in principle resolution of layered structures can be improved by including an X-component signal in a 1D inversion, given the prerequisite that a low-pass filter of suitably low cut-off frequency can be employed. In presenting our practical experiences with modifying the SkyTEM system we discuss why this prerequisite unfortunately can be very difficult to fulfill in practice. Having discussed instrumental limitations we show what can be obtained in practice using actual field data. Here, we demonstrate how the issue of high sensitivity towards instrument pitch can be overcome by including the pitch angle as an inversion parameter and how joint inversion of the Z- and X-components produces virtually the same model result as for the Z-component alone. We conclude that adding helicopter system X-component to a 1D inversion can be used to facilitate higher confidence in the layered result, as the requirements for fitting the data into a 1D model envelope becomes more stringent and the model result thus less prone to misinterpretation.

International audience; We develop a technique allowing 3D gridding of large sets of 1D resistivity models obtained after inversion of extensive airborne EM surveys. The method is based on the assumption of a layered-earth model. 2D kriging is used for interpolation of geophysical model parameters and their corresponding uncertainties. The 3D grid is created from the interpolated data, its structure accurately follows the geophysical model, providing a lightweight file for a good rendering. Propagation of errors is tracked through the quantification of uncertainties from both inversion and interpolation procedures. The 3D grid is exported to a portable standard, which allows flexible visualization and volumetric computations, and improves interpretation. The method is validated and illustrated by a case-study on Santa Cruz Island, in the Galapagos Archipelago.

Being able to recover accurate and quantitative descriptions of the subsurface electrical conductivity structure from airborne electromagnetic data is becoming more and more crucial in many 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 airborne TEM system was studied in detail. The data were inverted and the consequences of inaccurate modeling of the system transfer function were studied inthe model space. Errors in the description of the transfer function 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 the late time gates. Depth of investigation is highly model dependent, but in general the early times hold information on the shallower parts of the model and the late times hold information on the deeper parts of the model. Amplitude, gain, and current variations 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 airborne TEM 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 fitted within noise level.

The combination of in situ geotechnical testing and continuously measured geophysical data can be a powerful tool in geotechnical site investigation. In two cases from Sweden and one case from Denmark electric resistivity surveys are used successfully in geotechnical site investigations. The main contribution of resistivity results is the possibility to interpret continuous geological models. An improved methodology combines two-dimensional (2D) smooth inversion and 2D laterally constrained inversion (2D-LCI) to significantly increase interpretability. The 2D smooth inversion has high horizontal resolution and 2D-LCI high vertical resolution. The possibility to add a priori information from, for example, drill log data to constrain the 2D-LCI increases the confidence in the inverted model and limits ambiguity. In a site investigation for a railway trench in southern Sweden a geotechnical data set is used as a priori data to increase the reliability of the inversion of the resistivity data. From this combined survey a complex Quaternary geology is described in detail. A slope stability study from south of Stockholm, Sweden, employed resistivity data together with refraction seismic and geotechnical drill log data. The result gives necessary geometrical information for the important geological units, for example for stability calculations. Both these surveys were performed with a multielectrode system. In the third case a pulled array resistivity survey was used to map the uppermost 15-20 m to estimate the distribution of the geological formations for freeway construction in Denmark. The result enables a more accurate estimate of the total freeway construction costs.

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.

Airborne transient electromagnetic (TEM) methods target a range of applications that all rely on analysis ofextremely large datasets, but with widely varying requirements with regard to accuracy and computing time. Certainapplications have larger intrinsic tolerances with regard to modelling inaccuracy, and there can be varying degrees of tolerancethroughout different phases of interpretation. It is thus desirable to be able to tune a custom balance between accuracy andcompute time when modelling of airborne datasets. This balance, however, is not necessarily easy to obtain in practice.Typically, a significant reduction in computational time can only be obtained by moving to a much simpler physicaldescription of the system, e.g. by employing a simpler forward model. This will often lead to a significant loss of accuracy,without an indication of computational precision.We demonstrate a tuneable method for significantly speeding up inversion of airborne TEM data with little to no lossof modelling accuracy. Our approach introduces an approximation only in the calculation of the partial derivatives usedfor minimising the objective function, rather than in the evaluation of the objective function itself. This methodologicaldifference is important, as it introduces no further approximation in the physical description of the system, but only in theprocess of iteratively guiding the inversion algorithm towards the solution. By means of a synthetic study, we demonstratehow our new hybrid approach provides inversion speed-up factors ranging from ~3 to 7, depending on the degree ofapproximation. We conclude that the results are near identical in both model and data space. A field case confirms theconclusions from the synthetic examples: that there is very little difference between the full nonlinear solution and the hybridversions, whereas an inversion with approximate derivatives and an approximate forward mapping differs significantly fromthe other results.

Traditional approaches to surveying well catchments usually involve investigations at two quite different spatial scales: very high resolution borehole-based studies and low resolution tracer and pump tests. In recent years, various researchers have attempted to fill the wide gap between the two scales of acquired data by using a variety of geophysical tools that have high-to-medium resolution capabilities. Although geophysical surveying may be relatively straightforward at many locations, there are numerous regions where topography, the presence of ubiquitous metal objects and/or a lack of suitably placed boreholes cause the acquisition, processing, inversion and interpretation of certain types of geophysical data to be extremely challenging. It was neces- sary for us to address such problems in an investigation of an active well catchment near Zurich, Switzerland. The principal goals of our project were to determine the geometries and physical properties of the shallow sedimentary layers, with emphasis on a key water-bearing gravel unit. To achieve these goals, four different geophysical methods were employed. In a first step, frequency-domain electromagnetic measurements allowed the locations of buried metal pipes to be established. A 2D tomographic seismic refraction survey then provided information on the interface between the low-velocity surface loamy topsoil and underlying high-velocity morainal material. The high electrical resistivity of the important gravel unit allowed its upper boundary to be outlined in 2D models derived from geoelectric data and its lower boundary to be deline- ated in models based on 1D linked inversions of geoelectric and transient electromagnetic data.

Modern airborne transient electromagnetic surveys typically span thousands of line kilometres requiring careful data processing. When surveys are flown in populated areas, data processing becomes particularly time consuming, since the acquired data is contaminated by couplings to man made conductors (power lines, fences, pipes, etc.). Coupled soundings must be removed from the dataset prior to inversion, but since the signature of couplings can be subtle and difficult to describe in general terms it has so far remained mostly a manual task. We train an artificial neural network to recognize coupled soundings in previously processed data and use this network to identify couplings in other data. The approach provides a dramatic reduction in the time required for data processing, since one can directly apply the network to the raw data. We present the training state and performance of the network and compare inversions based on manually processed data and ANN processed data. The results show that a well trained network can produce a high quality processing of ATEM data, which are either ready for inversion or in need of minimal manual processing. The results are very promising and can significantly reduce the processing time and cost of large ATEM surveys.

While full 2D and 3D inversion schemes are emerging for airborne TEM datasets, the workhorse of large scale surveying still remains the well established 1D forward formulation. Modern airborne TEM surveys typically span several thousand line kilometers of data, which can be very time consuming to invert even within the framework of 1D forward modeling. Here, we present how we have modified our existing inversion code to offload its 1D forward computations to massively parallel Intel Xeon Phi co-processors. A prerequisite for good performance on this type of next generation technology is for a code to provide not only good parallel scaling, but also make efficient use of vector instructions. The latter is not possible without modification to the established framework of 1D forward modeling and we demonstrate how this problem can be overcome in a straight forward manner. We show how the modified algorithm provides virtually ideal parallel scaling and almost ideal use of vector instructions on both multi-core processors and massively parallel Intel Xeon Phi co-processors. The use of vector instructions alone provide a speed-up of almost 8x on the co-processor, allowing for full inversion of several thousand line kilometers of data per hour.

Airborne electromagnetic methods (AEM) have in the last decade undergone immense hardware and software developments. 10 years ago high resolution shallow surveys for geotechnical engineering, aquifer mapping, landslides etc, could only be done by frequency domain methods whereas time domain methods were more suited for deep measurements. Today, the development of the time domain methods has reached a level where the same or even better data from an airborne platform is obtained compared to the best groundbased system. Also, data inversion has changed from being dominated by approximate algorithms to full solutions modelling the complete system characteristics with inversion of thousands of line kilometers of data in one run. These inversions are possible because the algorithms use multithreaded architecture, which efficiently runs on small workstations or severs. In this paper we discuss the newest hardware developments of the SkyTEM system and also how these developments are accompanied by inversion algorithms closely adapted to the hardware. The SkyTEM system, as shown in Figure 1, originally developed at Aarhus University, is now operated and developed by an independent spin-off company, SkyTEM Surveys, while inversion and processing algorithms are developed at Aarhus University. However, there are fruitful collaborations and SkyTEM Surveys identify themselves as a high-tech company with an ambitious research and development (R/D) program.

The transient electromagnetic (TEM) method has been used extensively for hydrogeophysical exploration in Denmark for the past decade. Innovative instrumentation combined with multi-dimensional modelling and interpretational insights based on experience gained through numerous case studies have proven to be a successful strategy. In the case study reported here, the combination revealed an unknown and unexpected buried valley complex. Drill hole data were in good agreement with estimates of both the bearings and depths of valleys defined by the TEM surveys. The Pulled Array Transient Electromagnetic (PATEM) system was built to provide high data density for increased lateral resolution. A High moment Transient Electromagnetic (HiTEM) system was developed for delineation of aquifers to depths up to 300 m. Because both of these systems provide high data density, data quality can be assessed as part of the interpretational strategy. When acquiring TEM measurements in areas as densely populated as the Danish countryside, precautions must be taken to minimize coupling between the TEM system and man-made conductors. Modelling the slope of the flanks of buried valleys has challenged the adequacy of the one-dimensional (1-D) assumption for inversion of TEM data. The study shows that for a valley structure in a low-resistive layer, the 1-D assumption is sufficient to track the presence of rather steep slopes. For a valley structure in a high-resistive layer, however, the insensitivity of the TEM method to resistors makes it difficult to determine a slope with a 1-D inversion, and only the overall structure is defined.

In a sedimentary environment, layered models are often capable of reproducing the actual geology more accurately than smooth minimum structure models. We present and evaluate a 2D inversion scheme with lateral constraints (2D-LCI) and sharp boundaries for continuous profile oriented data sets. Here, we focus on resistivity data. All data and models are inverted as one system, producing layered sections with laterally smooth transitions. The models are regularized through laterally equal constraints that tie interface depths and resistivities of adjacent layers. Prior information, originating from e.g. electrical logs, migrates through the lateral constraints to the adjacent models, making resolution of equivalences possible. Information from areas with well resolved parameters will, in a similar way, migrate through the constraints 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. For evaluation we use broad-banded von Karman covariance functions to create various geological realistic models. We compare results from the 2D-LCI routine with results from the widely used smooth minimum structure program Res2dinv. The comparison is point-to-point on resistivities in the model space. The statistics conclude that the 2D-LCI resolves the true models to the same level as Res2dinv. The clear distinction of separate units and unit boundaries is often critical in hydrogeophysical or geotechnical applications, and hence we suggest using a layered inversion scheme in these cases.

SUMMARY In the computation of the forward response for Time Domain Induced Polarization the incomplete description of the transmitter waveform causes dramatic errors in the estimation of the magnitude and time characteristic of the IP phenomenon. Both the duration of the current pulse and the sequence of pulses used for the stacking procedure have a strong effect in the magnitude and shape of the IP decays. Furthermore, it is important to model low-pass filters of the receiver system, in order to extract all the information contained in the acquired data. For these reasons, a new 1D forward and inversion algorithms have been developed using the full time decay of the IP response and the receiver transfer function to reconstruct the distribution of the four Cole-Cole parameters of the earth. The waveform implementation in the forward response for TDIP is a significant improvement that allows moving from a qualitative interpretation of TDIP data for recognition of anomaly patterns towards a quantitative analysis, able to discriminate soil lithotypes and, if present, some contamination plumes.

SUMMARY We present examples of integration of ancillary information to AEM data from different surveys around the world. The data enters the inversion as apriori extra parameter, either from a grid, or from a point source. We use the spatially constrained inversion to migrate the apriori information across the dataset. This approach allows also using the apriori information to re-calibrate the AEM dataset, solving for extra calibration parameters, along the lines of holistic inversion.

Early times are of interest for near-surface surveys and are object of developments during the last decade both in the electronics and the processing domains. The new SkyTEM system, called SkyTEM101, has a very short turn-off of 3 µs which authorizes the use of gates between 3 and 10 µs, and to increase the vertical resolution of the near-surface. However, a reliable monitoring of the Coil Response (CR) is necessary to get these very early time gates usable. For this, a new Coil Response Correction (CRC) has been developed which allows removing the CR in the first early gates before the inversion process. Application of this CRC correction to high altitude and production measurements has shown its efficiency to reduce the CR to the noise level. A new adaptive data filtering has also been developed to maintain the best lateral resolution above different areas like open fields or forests above which the signal to noise ratio varies due to the change of the helicopter altitude. This improvement of the lateral resolution has a great value for environmental surveys where definition of local and shallow heterogeneities is a critical issue.

Precision agriculture applications rely on highly detailed information on variations in soil properties. This demand has led to recent developments in EMI instrumentation, resulting in stable and high data quality. The reliability of the data enables real non-linear inversion providing true formation resistivity with depth. With the aim of mapping soil heterogeneity, an EMI survey has been carried out in the central part of Jutland, Denmark. The collected data were carefully processed prior to inversion in order to remove any couplings from man-made conductors such as buried electrical cables, which can cause errors in the lithological interpretation. The data were subsequently modelled with a 1D layered spatially constrained inversion which takes the entire EMI data geometry into account. The inversion results gives a detailed quasi tree-dimensional image of the survey area, revealing several small scale resistivity variations which corresponds well with existing geological knowledge.

International audience; 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.

SUMMARY While the forefront of AEM research is focusing on the challenges of 3D modelling, the wide AEM community still rely on less sophisticated computational techniques for their calculations. Inversion of large time domain AEM surveys still prove a computational challenge within a 1D formulation, and require much more computational resources than can be delivered by an office workstation. Emerging Monte-Carlo based 1D Bayesian inversion schemes provide another example of applications that are currently limited by the 1D forward modelling rate. In this abstract we describe our research in modifying the AarhusInv AEM inversion code to utilize next generation massively parallel co-processors. While our results are early and based on very little optimization, we still achieve comparable levels of performance (>80%) from a single co-processor and a 48 cpu core server. We estimate that performance on the co-processor can be speeded up by approximately another 4x with a limited amount of code restructuring/rewriting.

SUMMARY We present a new algorithm for quasi-3D inversion of airborne transient electromagnetic data (AEM). The algorithm uses a 3D voxel grid for the model domain while the forward response and derivatives are calculated using interpolated "virtual" 1D models collocated at the AEM measurement points. The algorithm efficiently decouples the model domain from the practical spatial sampling which are often dictated by the landscape, ground installations ect., rather than the optimal model resolution. The algorithm uses sparse storage with efficient solvers and it scales linearly both with the number of CPU's and with the survey size. This means that it can be used to invert entire surveys of thousands of kilometres on small multiprocessor servers priced less than 5000 Euro. The algorithm allows inputting a-priori information from boreholes, joint inversion with groundbased electrical/electromagnetic data and modelling of flight altitude and shift parameters.

Modern airborne transient electromagnetic (ATEM) surveys typically span thousands of line kilometres requireing careful data processing. When surveys are flown in populated areas data processing becomes particularly time consuming, since the acquired data is contaminated by couplings to man made conductors (power lines, fences, pipes, etc). Coupled soundings must be removed from the dataset prior to inversion, but since the signature of couplings can be subtle and difficult to describe in general terms it has so far remained mostly a manual task. Here we train an artificial neural network (ANN) to recognize coupled soundings in previously processed data and use this network to identify couplings in other data. The approach provides a dramatic reduction in the time required for data processing, since one can directly apply the network to the raw data. We describe the neural network we use and present the inputs and normalizations required for maximizing the effectiveness of the network. We present the training state and performance of the network and finally compare inversions based on manually processed data and ANN processed data. The results show that a well trained network can produce a high quality processing of ATEM data, which is either ready for inversion or in need of minimal manual processing. The results are very promising and can significantly reduce the processing time and cost of large ATEM surveys.

One of the main limiting factors to the accuracy of large scale groundwater models is the scarcity of hydraulic data. High-resolution Airborne Electromagnetic Methods (AEM) are capable of mapping the electrical resistivity structure of the subsurface in great detail and covering large areas in short time and on a limited budget. As such, there is great potential in integrating AEM data in groundwater modeling as a supplementing source of an extensive amount of information. We have developed several novel techniques that in combination allows for bringing groundwater and AEM models much closer together, i.e.: (1) a novel, scalable inversion engine that allows the AEM inversion to handle arbitrarily large areas at a time; (2) the spatially-decoupled inversion approach, which decouples the inversion model from the acquisition points and can operate on the same grid/voxel cells as the groundwater model; (3) a custom regularization scheme that allows for producing geophysical models with sharp vertical/horizontal resistivity transitions. In this study we present the very first application of the sharp spatially-decoupled inversion on an AEM survey flown for improving the groundwater model in the Kasted area, in the north of Aarhus (Denmark).

It is shown that the electromagnetic (EM) spectrum is characterized by strong amplitude-modulated transmitters operating in the target bandwidth of transient electromagnetic (TEM) measurements. As these transmitters cause significant noise in TEM soundings, it is mandatory to band-limit the input signals to improve the signal-to-noise ratio and thereby the depth of exploration. Band-limitation will distort the TEM responses, which leads to erroneous inversion results if the applied low-pass filters are not accounted for in the inversion scheme. We incorporate the low-pass filters in the inversion scheme and test the inversion approach on theoretical and field data. Inversion of band-limited theoretical responses results in recovery of erroneous resistivity models if the filters are not included in the inversion scheme. By contrast, inversion of band-limited theoretical and field data, for which the applied low-pass filters are included in the inversion scheme, leads to recovery of similar resistivity models, independent of the applied cut-off frequencies.

SUMMARY Field-based time domain (TD) induced polarization (IP) surveys are usually modelled by taking into account only the integral chargeability, thus disregarding spectral content. Furthermore, the effect of the transmitted waveform is commonly neglected, biasing inversion results. Given these limitations of conventional approaches, a new 2-D inversion algorithm has been developed using the full voltage decay of the IP response, together with an accurate description of the transmitter waveform and receiver transfer function. This allows reconstruction of the spectral information contained in the TD decay series. The inversion algorithm is based around a 2-D complex conductivity kernel that is computed over a range of frequencies and converted to the TD through a fast Hankel transform. Two key points in the implementation ensure that computation times are minimized. First, the speed of the Jacobian computation, time transformed from frequency domain through the same transformation adopted for the forward response is optimized. Secondly, the reduction of the number of frequencies where the forward response and Jacobian are calculated: cubic splines are used to interpolate the responses to the frequency sampling necessary in the fast Hankel transform. These features, together with parallel computation, ensure inversion times comparable with those of direct current algorithms. The algorithm has been developed in a laterally constrained inversion scheme, and handles both smooth and layered inversions; the latter being helpful in sedimentary environments, where quasi-layered models often represent the actual geology more accurately than smooth minimum-structure models. In the layered inversion approach, a general method to derive the thickness derivative from the complex conductivity Jacobian is also proposed. One synthetic example of layered inversion and one field example of smooth inversion show the capability of the algorithm and illustrates a complete uncertainty analysis of the model parameters. With this new algorithm, in situ TD IP measurements give access to the spectral content of the polarization processes, opening up new applications in environmental and hydrogeophysical investigations. Key words: Inverse theory; Electrical properties; Hydrogeophysics

We present a comparison between two different regularisation schemes for multi-layer inversion of the MRS data. The two regularizations consist of the norm (Occam’s inversion) and the support (focused inversion) of the variation of the water content and relaxation time. The focused regularization provides a sharp inversion as it minimizes the area (the support) where the variations of the model parameters occur, and not the (L2) norm of the variations. Clearly, when sharp vertical transitions of the inversion parameters are present, the focused inversion retrieves the interfaces with higher precision and reconstructs more effectively the physical property values as well. This is a quite common situation in hydrogeophysics, e.g. in correspondence with the water table and/or at the boundary between aquifers and aquitards.

Increasingly, ground-based and airborne geophysical datasets are used to inform groundwater models. Recent research focuses on establishing coupling relationships between geophysical and groundwater parameters. To fully exploit such information, this paper presents and compares a joint hydrogeophysical inversion (JHI) approach and sequential hydrogeophysical inversion (SHI) approach to inform a field-scale groundwater model with Time Domain Electromagnetic (TDEM) and Electrical Resistivity Tomography (ERT) data. The implemented SHI coupled inverted geophysical models with groundwater parameters, where the strength of the coupling was based on geophysical parameter resolution. To test whether the implemented SHI over- or underestimated the coupling strength between groundwater and geophysical model, we compared its results with a JHI in which a geophysical model is simultaneously inverted with a groundwater model using additional coupling constraints that explicitly account for an established petrophysical relationship and its accuracy. The first set of simulations for a synthetic groundwater model and TDEM data, employing a high-quality petrophysical and geometric relationship, showed improved estimates for groundwater model parameters that were coupled to relative well-resolved geophysical parameters. Compared to a SHI these improvements were insignificant and geophysical parameter estimates became slightly worse. In a second set of simulations, employing a low-quality petrophysical relationship, groundwater parameter improved less for both the SHI and JHI, where the SHI performed slightly better. For a real-world groundwater model and ERT data, different parameter estimates were obtained with a JHI and SHI. Parameter uncertainty was reduced but was similar for the SHI and JHI. The geometric constraint showed little impact while the petrophysical constraint showed significant changes in geophysical and groundwater parameters. For both cases investigated in this paper, the SHI seems favorable, taking in account parameter error, data fit and the complexity of implementing a JHI in combination with its larger computational burden.

We present a geophysical inversion algorithm working directly in a voxel grid disconnected from the actual measuring points, which allows for straightforward integration of different data types in joint inversion, for informing geological/hydrogeological models directly and for easier incorporation of prior information. Inversion of geophysical data usually refers to a model space being linked to the actual observation points. For airborne surveys the spatial discretization of the model space reflects the flight lines. Often airborne surveys are carried out in areas where other ground-based geophysical data are available. The model space of geophysical inversions is usually referred to the positions of the measurements, and ground-based model positions do not generally coincide with the airborne model positions. Consequently, a model space based on the measuring points is not well suited for jointly inverting airborne and ground-based geophysical data. Furthermore, geological and groundwater models most often refer to a regular voxel grid not correlated to the geophysical model space, and incorporating the geophysical data into the geological/hydrological modelling grids is problematic. We present a voxel grid inversion routine that overcomes these problems and we discuss in detail the algorithm implementation.

We developed a new scheme for joint and laterally constrained inversion (LCI) of magnetic resonance sounding (MRS) data and transient electromagnetic (TEM) data, which greatly improves the estimation of the MRS model parameters. During the last few decades, electrical and electromagnetic methods have been widely used for groundwater investigation, but they suffer from some inherent limitations; for example, equivalent layer sequences. Furthermore, the water content information is only empirically correlated to resistivity of the formation. MRS is a noninvasive geophysical technique that directly quantifies the water content distribution from surface measurements. The resistivity information of the subsurface is obtained from a complementary geophysical method such as TEM or DC resistivity methods. The conventional inversion of MRS data assumes the resulting resistivity structure to be correct and considers a constant MRS kernel through the inversion. We found that this assumption may introduce an error to the forward modeling and consequently could result in erroneous parameter estimations in the inversion process. We investigated the advantage of TEM for the joint inversion compared to DC resistivity. A fast and numerically efficient MRS forward routine made it possible to invert the MRS and TEM data sets simultaneously along profiles. Furthermore, by application of lateral constraints on the model parameters, lateral smooth 2D model sections could be be obtained. The simultaneous inversion for resistivity and MRS parameters led to a more reliable and robust estimation of all parameters, and the MRS data diminished the range of equivalent resistivity models. We examined the approach through synthetic data and a field example in Denmark where good agreement with borehole data was demonstrated with clear correlation between the relaxation time [Formula: see text] and the grain size distribution of a sandy aquifer.