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.
Summary Sensitivity, resolution, and data quality are important parameters to consider when designing an ERT cross-borehole survey. We present an open-source algorithm for computing 2D and 3D sensitivity patterns of any borehole setup and use this to compare single-borehole and different cross-borehole electrode configurations, which both show complex patterns. To study the resolution capability of an entire survey, the model resolution matrix is computed for a field dataset. The dataset is split into different electrode configurations and the model resolution matrices of the different configuration are compared. The results show that the sensitivity and resolution decreases very quickly away from the electrodes, especially for the single-borehole configurations. In the studied field case, this means cross-borehole configurations are needed to correctly image the area between the boreholes, even though the cross-borehole data often are associated with a lower signal-to-noise ratio due to near-zero potential measurements and generally more outliers. The study concludes that in a production mode, where acquisition time and thus the number of possible data points are limited, the combination of electrode configurations must be carefully considered and a trade-off between resolution and data quality must be evaluated.
SUMMARY Electrical and electromagnetic methods are well suited for mapping the top 100 m of the subsurface, particularly electrical resistivity tomography (ERT) and Traseint electromagnetic (TEM). Both methods can provide comparable resolution and depth of investigation for generating continuous 2-D resistivity profiles. TEM measurements taken continuously from moving platforms, whether towed on the ground or airborne, can generate 2-D-like resistivity sections similar to those produced by ERT profiling. However, despite the fact that both ERT and TEM can map the electrical resistivity of the subsurface, their results differ due to fundamental differences in physical principles, sensitivity, system geometry and instrumentation. The main objective of this paper is to provide a one-on-one comparison of the newly developed towed TEM system, tTEM, against ERT and airborne TEM, in our case a SkyTEM system. First, we performed the comparison in terms of model resolution using synthetic data and models. For all methods, synthetic data were generated using a 1-D forward response, and inversions were carried out using smooth layered models in a laterally constrained inversion framework. Overall, the inversion results are comparable across the three methods, and they all capture the key features of the synthetic models. The ERT and tTEM cross-sections from two field cases show very comparable results even in the top 5 m where thin resistive layers (∼60 Ω·m) are clearly mapped by both methods. However, the resistivity of the resistive layer is better resolved using ERT than tTEM because of the high sensitivity close to the surface in the ERT case. In the deeper part of the section, tTEM tends to resolve the boundaries of conductive layers (resistivity < 10 Ω·m) better than the ERT method. Compared to SkyTEM, tTEM has a better vertical and horizontal resolution especially in the top 20 m. The better tTEM resolution compared to SkyTEM is primarily due to a smaller footprint and denser data sampling. Depth of investigation-wise the SkyTEM system is superior compared to tTEM due to its larger magnetic moment.
<p>Cable bacteria are multicellular microorganisms that are capable of long distance electron transport (LDET) along their length. This electron transport is the result of oxidation of hydrogen Sulfide (H2S) in the sulfidic sediment layer where electrons are conducted up through cable filament aided by cell-to-cell transfer in the oxic layer thus reducing oxygen by gaining electrons. Cable bacteria behave as dipoles where anaerobic zones interfere with oxic zones for example oil/tar pollution site and can generate enough natural SP fields as a function of redox mechanism that can be measured on the surface. This study focuses on the theoretical analysis of Self-Potential (SP) signals resulting due to the presence of dipole current source under different conductivity structures in the subsurface. To investigate the behavior of SP signals, four different types of forward models are synthesized by varying resistivity of subsurface layers and changing the depth of the dipole beneath the surface. The dipole has a default current density of 20 mA/m<sup>2</sup>. In the first model, a rectangular pollution patch carrying a dipole of the same shape is placed between two homogeneous layers where the top layer resistivity is swept from 10-1000 ohm-m while keeping the resistivity of bottom layer constant. In the second model, the pollution patch is placed between an inhomogeneous layer with low, intermediate, and high resistivity contrasts and a homogeneous layer. In this model, half of the patch lies in lower conducting region whereas the other part is in the high conductivity region. The third model is an extension of the second one, where the inhomogeneous layer is sandwiched between two homogeneous layers. In the last model, the pollution patch was moved beneath the surface to a depth where the SP signal cannot be observed at the surface. In this model, the depth is observed for three different pollution sources with current density values equal to 2, 20 and 200 mA/m<sup>2</sup> respectively. The results showed that SP anomaly caused by the patch when the conductivity of upper layer is high is smaller as compared to the anomaly due to the less conducting upper layer. Next two models with inhomogeneous layer, correlate well with the first model showing high SP anomaly caused by dipole when it is present in the lower conducting region and low values when in high conducting region. Fourth model demonstrates when the depth of pollution patch is increased beneath the surface, SP signal decreases and is not observed beneath a depth of around 10 m, even when the source has current density value as high as 200 mA/m<sup>2</sup>. This study explicitly demonstrates the behavior of SP anomaly and will help in improved interpretation of SP technique where inhomogeneity will be present beneath the surface.</p>
Summary We present a flexible algorithm for modelling of 3D direct current (DC) resistivity and time-domain induced polarization (IP) data. A structured model mesh allows easy implantation of constrains, whereas the finite-element forward algorithm is based on unstructured tetrahedral meshes and therefore handles both topography, arbitrary shaped boundaries and local refinement. This, together with modelling of the secondary potential field for singularity removal around the sources, ensures high accuracy. Electrodes may be placed on the boundaries or arbitrarily in the subsurface thus allowing both surface and cross-borehole applications. The forward response is computed in frequency-domain and then transformed to time-domain using the Hankel Transform, taking into account the current waveform and system filters for a quantitative IP modelling of either full-decay IP responses or integral chargeability allowing the IP phenomenon to be parameterised using any IP parameterization. An accuracy test of the forward response shows the advantages of the singularity removal (computing primary and secondary potential fields separately) as it decreases the relative deviation to the analytic solution significantly compared to computing the total field.
SUMMARY Airborne systems collecting transient electromagnetic data are able to gather large amounts of data over large areas in a very short time. These data are most often interpreted through 1-D inversions, due to the availability of robust, fast and efficient codes. However, in areas where the subsurface contains complex structures or large conductivity contrasts, 1-D inversions may introduce artefacts into the models, which may prevent correct interpretation of the results. In these cases, 2-D or 3-D inversion should be used. Here, we present a 2.5-D inversion code using 3-D forward modelling combined with a 2-D model grid. A 2.5-D inversion is useful where the flight lines are spaced far apart, in which case a 3-D inversion would not add value in relation to the added computational cost and complexity. By exploiting the symmetry of the transmitter and receiver system we are able to perform forward calculations on a reduced 3-D mesh using only half the domain transecting the centre of the transmitter and receiver system. The forward responses and sensitivities from the reduced 3-D mesh are projected onto a structured 2-D model grid following the flight direction. The difference in forward calculations is within 1.4 per cent using the reduced mesh compared to a full 3-D solution. The inversion code is tested on a synthetic example constructed with complex geology and high conductivity contrasts and the results are compared to a 1-D inversion. We find that the 2.5-D inversion recovers both the conductivity values and shape of the true model with a significantly higher accuracy than the 1-D inversion. Finally, the results are supported by a field case using airborne TEM data from the island of Mayotte. The inverted flight line consisted of 418 soundings, and the inversion spent an average of 6750 s per iteration, converging in 16 iterations with a peak memory usage of 97 GB, using 18 logical processors. In general, the total time of the 2-D inversions compared to a full 3-D inversion is reduced by a factor of 2.5 while the memory consumption was reduced by a factor of 2, reflecting the half-mesh approach.
Summary Electrical resistivity tomography (ERT) and time domain electromagnetic (TEM) are two widely adopted geophysical methods for near surface resistivity mapping. However, the results produced by the two may differ due to fundamental differences in physical principles, sensitivity, system geometry. The main objective of this paper is to provide a one-to-one comparison of ERT against a newly developed towed TEM system tTEM and comparison of tTEM against its airborne counterpart SkyTEM. We compare three methods using both synthetic as well as field data. Overall, we found that inversion results are comparable across the three methods. They all capture the prominent features of synthetic models. The ERT and tTEM inversion of field data show very comparable results even in the top 5 m where both can image thin resistive layers. However, the resistivity of the thin resistive layer is better resolved using ERT because of its high sensitivity close to the surface. In deeper part of the profile, tTEM tends to produce better resolved boundaries compared to the ERT method. Comparing the SkyTEM inversion results against the tTEM, shows that tTEM has a better vertical and horizontal resolution in the top 20 m.
Summary The principle of equivalence is known to cause non-uniqueness in interpretations of direct current (DC) resistivity data. Here, we show that these equivalences can be significantly reduced by combining DC data with time-domain induced polarization (IP) measurements. An understanding of model equivalences requires a comprehensive investigation for each model when using gradient-based inversion methods. Instead, we apply a 1D Monte Carlo inversion that makes it possible to investigate the space of equivalent models. We invert synthetic DC data of a model with low-resistivity equivalences. We then include a contrast in chargeability, modelled in terms of spectral Cole-Cole IP parameters, and invert the DC and IP data together. The results show that the inclusion of IP data resolves the equivalences. The degree of resolution depends on the contrast in the chargeability and/or the other IP parameters. The contrasts required are easily expected in the field, which is justified with a field example where DC and IP data are measured on a sand formation with an embedded clay layer. Inversion results show that the resistivity data alone does not resolve the clay layer due to equivalence problems, but by adding the IP data to the inversion, the layer is resolved.
ABSTRACT The induced polarization phenomenon, both in time domain and frequency domain, is often parameterised using the empirical Cole–Cole model. To improve the resolution of model parameters and to decrease the parameter correlations in the inversion process of induced polarization data, we suggest here three re‐parameterisations of the Cole–Cole model, namely the maximum phase angle Cole–Cole model, the maximum imaginary conductivity Cole–Cole model, and the minimum imaginary resistivity Cole–Cole model. The maximum phase angle Cole–Cole model uses the maximum phase φ max and the inverse of the phase peak frequency, τ φ , instead of the intrinsic charge‐ability m 0 and the time constant adopted in the classic Cole–Cole model. The maximum imaginary conductivity Cole–Cole model uses the maximum imaginary conductivity instead of m 0 and the time constant τ σ of the Cole–Cole model in its conductivity form. The minimum imaginary resistivity Cole–Cole model uses the minimum imaginary resistivity instead of m 0 and the time constant τ ρ of the Cole–Cole model in its resistivity form. The effects of the three re‐parameterisations have been tested on synthetic time‐domain and frequency‐domain data using a Markov chain Monte Carlo inversion method, which allows for easy quantification of parameter uncertainty, and on field data using 2D gradient‐based inversion. In comparison with the classic Cole–Cole model, it was found that for all the three re‐parameterisations, the model parameters are less correlated with each other and, consequently, better resolved for both time‐domain and frequency‐domain data. The increase in model resolution is particularly significant for models that are poorly resolved using the classic Cole–Cole parameterisation, for instance, for low values of the frequency exponent or with low signal‐to‐noise ratio. In general, this leads to a significantly deeper depth of investigation for the , , and parameters, when compared with the classic m 0 parameter, which is shown with a field example. We believe that the use of re‐parameterisations for inverting field data will contribute to narrow the gap between induced polarization theory, laboratory findings, and field applications.
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