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Two efficient implementations of 3D and 2.5D modeling and inversion are presented to be applicable to large-scale transient electromagnetic (TEM) method explorations. The key novel features are (1) forward response and Jacobian calculations are implemented using the octree-based finite-element method, (2) a mirror approach is used to build a 2.5D inversion scheme for further efficiency, and (3) a flexible link between the forward mesh and inversion model is applied on 3D and 2.5D schemes based on the voxel formulation. We compare the performance of the new implementations with 3D modeling using tetrahedral meshes, with respect to speed and memory requirements. The 3D octree algorithm requires less than 1/3 of the computational time compared with a 3D tetrahedral scheme for equivalent accuracy. The 2.5D octree algorithm further speeds up the process by reducing the computational time by another factor of two. The inversion uses the Levenberg-Marquart approach minimizing the least-squares criterion of the objective function. We determine the utility of our inversion approach on a synthetic example and a field example. In the synthetic example, the 3D octree inversion result finds superior resolution of a 3D anomaly compared with a 1D result, whereas the 2.5D inversion result is, expectedly, between the 1D and 3D results, but with favorable computational expenses compared with the full 3D solution. The field data set contains 200 soundings, and we perform a 3D inversion on the full survey. A 24-sounding section is then selected for the 2.5D inversion. The 2.5D inversion result finds resistivity features similar to the 3D inversion result at the selected profile. Hence, we conclude that the presented implementations are capable of handling relatively large TEM surveys on modern computational platforms. This could be smaller subsets of production-size surveys where 2D and 3D effects are pronounced.

Airborne time-domain electromagnetic surveys produce extremely large data sets with thousands of line kilometers of data and millions of possible models to explain the data. Inversion of such data sets to obtain the resistivity structures of the subsurface is computationally intensive and involves calculation of a significant number of forward and derivative responses for solving the least-squares inverse problem. The flight altitude of the airborne system needs to be included in the modeling, which adds further complexity. We propose to integrate neural networks in a damped iterative least-squares inversion framework to expedite the inversion process. We train two separate neural networks to predict the forward responses and partial derivatives independently for a broad range of resistivity structures and flight altitudes. Data inversion is not only used for producing the final subsurface models but also used during data processing, or to produce intermediate results during a survey. With these purposes in mind, we provide three inversion schemes with a tunable balance between computational time and modeling accuracy: (1) numerical forward responses used initially in combination with neural network derivatives, and the derivatives switched to a numerical solution in final iterations, (2) numerical forward responses in combination with neural network derivatives used throughout the inversion, and (3) only neural network forward responses and derivatives used in inversion. Experiments on field data find that we improve inversion speed without any loss in modeling accuracy with our first approach, whereas the second scheme gives a significant speedup at the cost of minor and often acceptable deviations in the inversion results from the conventional nonlinear inversion. The last approach is the fastest and captures the overall resistivity structures quite well. Therefore, depending on the modeling accuracy, inversion speedup factors of up to 50 are realized by using the proposed schemes.

Surface nuclear magnetic resonance (NMR) is emerging as a competitive method for aquifer exploration due to its direct sensitivity to subsurface water, but the method still has several shortcomings, for example, a signal-to-noise ratio that is often poor, long survey times, and bulky equipment. We have developed Apsu, a new surface NMR system designed for near-surface groundwater investigations. It provides several features such as a compact transmitter unit, separated, small receiver coils, wireless connections between multiple receivers, quasi-zero dead time, and robust phase determination. The transmitter unit is powered by a lightweight generator, and it drives a triangular current in an untuned [Formula: see text] transmitter coil. The peak current of the triangular waveform is up to 145 A, with an effective peak current of 105 A at a Larmor frequency of 2 kHz, corresponding to a 30 m depth of investigation. The frequency and amplitude in each half-oscillation of the transmit pulses can be modulated independently, which gives great flexibility in the pulse design. The receiver uses low-noise preamplifiers and multiple receivers linked to a central unit through Wi-Fi. The use of small receiver coils and wireless connections to multichannel receivers greatly improves the layout configuration flexibility and survey efficiency. The performance of the system under field conditions is demonstrated with high-quality data collected near Silkeborg, Denmark, using on-resonance and numerically optimized modulation pulses.

There is a growing need for detailed investigation of the top 30–50 m of the subsurface, which is critical for infrastructure, water supply, aquifer storage and recovery, farming, waste deposits, and construction. Existing geophysical methods are capable of imaging this zone; however, they have limited efficiency when it comes to creating full 3D images with high resolution over dozens to hundreds of hectares. We have developed a new and highly efficient towed transient electromagnetic (tTEM) system, which is capable of imaging the subsurface up to depth of 70 m at a high resolution, horizontally and vertically. Towed by an all-terrain vehicle, the system uses a [Formula: see text] transmitter coil and has a [Formula: see text]-component receiver placed at 9 m offset from the transmitter. The tTEM uses dual transmitter moment (low and high moment) measurement sequence to obtain the early and late time gates corresponding to shallow and deep information about the subsurface layers. The first bias-free gate is as early as [Formula: see text] from beginning of the ramp ([Formula: see text] after end of ramp). Data are processed and inverted using methods directly adopted from airborne electromagnetics. The system has been successfully used in Denmark for various purposes, e.g., mapping raw materials, investigating contaminated sites, and assessing aquifer vulnerability. We have also used the tTEM system in the Central Valley of California (United States) for locating artificial recharge sites and in the Mississippi Delta region, to map complex subsurface geology in great detail for building hydrogeologic models.

Adiabatic half-passage (AHP) pulses show great promise for significantly enhancing the signal-to-noise ratio of the surface nuclear magnetic resonance (NMR) free-induction decay measurement. Performing an AHP requires that the frequency sweep terminates when the transmit frequency is equal to the Larmor frequency, a condition that demands accurate knowledge of the true Larmor frequency. If the frequency sweep is terminated at an incorrect frequency, i.e., with an unknown offset between the transmit and Larmor frequency at the end of the pulse, the net excitation is affected and it can differ from that predicted by modeling that assumes a 0 Hz offset at the end of the sweep. Surface NMR surveys using a traditional single-frequency pulse have previously been shown to display degraded performance in the presence of an uncertain Larmor frequency estimate; the AHP pulse is also likely susceptible to such degraded performance. To ensure that reliable results can be produced by AHP pulses in the presence of an uncertain Larmor frequency estimate, we have developed an approach that adapts the frequency-cycling scheme for use with AHP pulses. We hypothesize that data collected using two similar AHP pulses, each with the exact same frequency sweep but where one sweeps toward the Larmor frequency from higher frequencies and the other from lower frequencies, can be stacked in such a manner that the impact of an unknown frequency offset is significantly reduced. We present synthetic and field results to demonstrate that frequency-cycling AHP pulse surface NMR data can ensure reliable performance even in the presence of an uncertain Larmor frequency estimate.

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 nuclear magnetic resonance sounding (MRS) method is used increasingly as a tool for hydrological investigations. Compared to other geophysical methods, the advantage of MRS is that it is directly sensitive to the presence of water in the subsurface. Data interpretations can also be used to get information about the subsurface pore structures, which under special conditions can be related to hydraulic properties such as aquifer transmissivity. However, to broaden the usage of this information in hydrological modeling, the uncertainties related to these transmissivity estimates must be determined. Otherwise, properly balanced weights cannot be given to the prior information obtained from MRS transmissivity estimates as compared to the hydrological data sets when used for groundwater model calibration. We have developed a methodology to estimate the uncertainties of MRS-based transmissivity estimates. Compared to previous studies, the methodology is well defined, and it takes into account important factors such as the uncertainties of the hydraulically estimated transmissivities, the uncertainty of the correlation factor in the petrophysical relation, and the uncertainties and correlations of the geophysically estimated parameters. We have determined the correlations and uncertainties of the geophysical parameters using a linear and a nonlinear method, and we find that the results are comparable.

The Okavango Delta is a huge alluvial megafan in northwestern Botswana. Despite numerous geologic, geochemical, geophysical, and hydrologic investigations over the past half-century, the sedimentary units underlying the delta are largely unknown. To address this issue, helicopter transient electromagnetic data (HTEM) have been collected across the entire delta and coincident ground-based electrical resistance tomographic (ERT) and transient electromagnetic (TEM) data have been acquired at two locations, one along the delta’s western margin and one in its north-central region. Inversions of the HTEM data have yielded three-layer resistivity models in which a relatively homogeneous conductive layer is sandwiched between two resistive layers. The three-layer HTEM model is reproduced in models obtained from independently and jointly inverting the ground-based data. The conductive layer’s low resistivities and depths to its upper and lower boundaries are practically equal in the HTEM and ground-based models. Resistivities of the upper resistive layer are similar in the various models, with the ground-based estimates being somewhat higher than those of the HTEM model at one site and somewhat lower at the other site. For the basal resistive layer, it can only be concluded that its resistivity must be substantially higher than that of the overlying conductive layer. An interpretation of the HTEM and ground-based resistivity models in the delta’s north-central region, appropriately constrained by the surface geology, high-resolution seismic refraction-reflection models, and borehole logs suggests the following structure: basement overlain at progressively shallower depths by freshwater-saturated sand and gravel that represent the remnants of a Paleo Okavango Megafan, saline-water-saturated sand, and lacustrine clay originally deposited in Paleo Lake Makgadikgadi, and freshwater-saturated megafan and fluvial sediments of the current Okavango Delta.

A newly developed helicopter transient electromagnetic (TEM) system has the ability to measure very early times within just a few μs after the turn off of the primary current. For such a system, careful calibration and accurate modeling of the electromagnetic (EM) response is critical to get true resistivities of the very shallow geologic layers. We discovered that this leads to resolution of the same level or in some cases even better than what can be obtained from airborne frequency EM systems. This allowed a range of important applications where high and accurate resolution is mandatory, e.g., geotechnical applications such as urban planning, railroad and road investigations, landslides or distribution of raw materials, and assessing aquifer vulnerability. We evaluated the results of a pilot survey covering the Norsminde catchment south of Aarhus, Denmark, where we found that near-surface layers (top 30 m) can be mapped with an accuracy of a few meters in a complicated glacial sedimentary environment. The mapping of the geologic layers was assessed by a detailed analysis in which we developed a general methodology for crosschecking the EM and borehole data. This methodology is general and can easily be adapted to other data types and surveys. After rating the quality of the boreholes based on a list of predefined criteria, we concluded that the EM data matched with about three-quarters of the boreholes located within less than 15 m from the closest EM soundings. The remaining quarter of the boreholes fell into two groups in which half of the boreholes were of very poor quality or had inaccurate coordinates. Only eight of all the boreholes could not be reproduced by the data, and we attributed this to be caused by very strong lateral or vertical geologic variations not resolvable by the TEM technique.

Validation and calibration of airborne and ground-based time-domain electromagnetic (TEM) systems are important to obtain high-quality data and thereby reliable and reproducible results. Validation and calibration become even more important when the TEM systems are to be used for low-anomaly groundwater and environmental applications. The recent extension of the Danish TEM test site has made it possible to perform detailed validation of airborne TEM systems and calibrate airborne TEM systems that cannot make hovering measurements. We evaluated the Danish TEM test site and used a test site calibration scheme recommended for ground-based as well as airborne TEM systems. Furthermore, we discovered an extended data set from the airborne TEM system, SkyTEM, from the test site, used for an extensive validation of the SkyTEM system. This validation included repeatability tests at different heights and comparisons with the reference sections obtained with ground-based measurements. The validation and comparison were performed directly on the inversion results and in data space, down to the single data gate values. The extensive validation of the SkyTEM system at the TEM test site revealed a very stable and reliable system. The data repeatability of the SkyTEM system at different heights and directions was, in general, well within the standard deviation (STD) of the data. The agreement between the ground-based reference model sections and the SkyTEM model section from different recording heights was very good. Likewise, the match between the ground-based reference data and the SkyTEM data was good and, in general, within 1.5 times the STD on the data. The positive outcome of the extensive validation also confirmed that data processing and modeling were performed at the highest standard.

Time-domain-induced polarization has significantly broadenedits field of reference during the last decade, from mineralexploration to environmental geophysics, e.g., for clay and peatidentification and landfill characterization. Though, insufficientmodeling tools have hitherto limited the use of time-domaininducedpolarization for wider purposes. For these reasons, anew forward code and inversion algorithm have been developedusing the full-time decay of the induced polarization response,together with an accurate description of the transmitter waveformand of the receiver transfer function, to reconstruct thedistribution of the Cole-Cole parameters of the earth. The accuratemodeling of the transmitter waveform had a strong influenceon the forward response, and we showed that thedifference between a solution using a step response and a solutionusing the accurate modeling often is above 100%. Furthermore,the presence of low-pass filters in time-domain-inducedpolarization instruments affects the early times of the acquireddecays (typically up to 100 ms) and has to be modeled in theforward response to avoid significant loss of resolution. The developedforward code has been implemented in a 1D laterallyconstrained inversion algorithm that extracts the spectral contentof the induced polarization phenomenon in terms of the Cole-Cole parameters. Synthetic examples and field examples fromDenmark showed a significant improvement in the resolution ofthe parameters that control the induced polarization responsewhen compared to traditional integral chargeability inversion.The quality of the inversion results has been assessed by a completeuncertainty analysis of the model parameters; furthermore,borehole information confirm the outcomes of the field interpretations.With this new accurate code in situ time-domaininducedpolarization measurements give access to new applicationsin environmental and hydrogeophysical investigations,e.g., accurate landfill delineation or on the relation betweenCole-Cole and hydraulic parameters.

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.

We have investigated potential rockslides in Western Norway using a time- and cost-efficient airborne electromagnetic (AEM) survey approach. The study area comprises phyllite, a low-grade metamorphic rock type that tends to be reworked to clay in disturbed zones. Mapping these electrically conductive clay zones was the aim of the AEM survey. Based on indications that precipitation drives the reported rockslide movements, the local municipality and regional hydroelectricity company are evaluating the option of draining the unstable area to a nearby hydropower reservoir using a drainage tunnel of more than 10 km. We conducted the AEM mapping survey to locate the sliding planes and to investigate the tunnel corridor for areas with potential tunneling hazards. Spatially constrained inversion of the data set (250 km) reveals extended conductive zones interpreted as sliding planes and/or gneiss/phyllite interface. Detailed follow-up of these initial results is planned with targeted percussion drilling and ground resistivity surveys.

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.

Electrical and electromagnetic (E&EM) methods for near-surface 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 characterization studies, precision-agriculture applications, archeological surveys, and geotechnical investigations. The inclu-sion of microprocessors in survey instruments, development of new interpretation algorithms, and easy access to powerful 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 these luxuriant data sets in turn spurred development of interpretation algorithms, including: Laterally constrained 1D inversion as well as innovative 2D- and 3D-inversion methods. 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 toward dense surveying over larger areas, followed by highly automated, post-acquisition processing and interpretation to provide improved resolution of the shallow subsurface in a cost-effective manner.

We describe a procedure for rapid characterization of shallow-water, contaminated wetlands. Terrain-conductivity (TC), vertical-magnetic-gradiometry, and surface-water-chemistry data were obtained from a shallow-draft paddleboat operable in as little as [Formula: see text] of water. Measurements were taken every [Formula: see text], with data-acquisition rates exceeding [Formula: see text] of line ([Formula: see text] data points) per 8-hr field day. We applied this procedure to an urban wetland that is affected by point and nonpoint sources of pollution. We used a one-dimensional, laterally constrained inversion algorithm to invert the apparent-conductivity data set obtained from the TC survey and to create a pseudo-2D image of sediment conductivity. The continuously recorded surface-water depth and conductivity values were input as a priori information in the inversion. We used soil chemistry determined for 28 sediment samples collected from the site, as well as lithologic logs from across the wetland, to constrain interpretation of the geophysical data. The inverted sediment conductivity describes a pattern of contamination probably attributable to leachates from adjacent landfills and/or to saltwater ingress from a partial tidal connection that is not obvious in the surface-water data. Magnetic-gradiometry values and the in-phase component of an EM31 response both reflect primarily the distribution of junk metal associated with a legacy of illegal dumping. Historic aerial photographs suggest that this distribution reflects land-use history and defines the maximum previous extent of an adjacent landfill and a pattern of dumping correlated with historic roadways.