| 1. |
- Buntin, Laura M., et al.
(author)
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Improved accuracy of plane-wave electromagnetic modelling by application of the total and scattered field decomposition and perfectly matched layers
- 2023
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In: Geophysical Journal International. - : Oxford University Press (OUP). - 0956-540X .- 1365-246X. ; 235:2, s. 1201-1217
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Journal article (peer-reviewed)abstract
- In 2-D magnetotelluric modelling, the standard application of Dirichlet boundary conditions (BC) may severely diminish the solution accuracy, because the unknown scattered part of the electromagnetic field is erroneously reflected at the domain boundary. Therefore, we adapt the total and scattered field decomposition (TSFD) to geophysical modelling, enabling the application of fully absorbing boundary methods, here perfectly matched layers (PML), to the scattered field. Our novel TSFD divides the modelling domain into two regions. In the total-field region containing the area of interest, the solution is computed for the total field. In the scattered-field region containing the boundaries, the solution is obtained for the scattered field, which is fully absorbed by PML at the boundaries. The plane-wave source is excited at the TSFD interface between both regions. Thus, boundary reflections are eradicated leading to superior solution accuracy, and boundaries can be placed closer to the receivers, shrinking the computational problem. Especially for challenging models with strong lateral changes, the solution accuracy of the TSFD is superior to that of the standard Dirichlet approach. Owing to the linearity of Maxwell's equations, the inaccuracy introduced to the electric and magnetic fields by using Dirichlet BC can be expected to partly cancel out in the magnetotelluric transfer functions, for example the impedance tensor. In this work, we quantify this cancellation effect. The inaccuracy is less than typical measurement errors in the vast majority of apparent resistivity and phase data, even, when the primary fields are strongly inaccurate.
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| 2. |
- Chen, Chaojian, et al.
(author)
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Exact solutions of the vertical gravitational anomaly for a polyhedral prism with vertical polynomial density contrast of arbitrary orders
- 2018
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In: Geophysical Journal International. - : Oxford University Press. - 0956-540X .- 1365-246X. ; 214:3, s. 2115-2132
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Journal article (peer-reviewed)abstract
- We present general closed-form solutions for the vertical gravitational anomaly caused by a polyhedral prism with mass density contrast varying with depth. Our equations are the first ones to implement a polynomial vertical mass density contrast of arbitrary order. Singularities in the gravity field which arise when the observation site is close to or in the anomalous polyhedral prism are removed in our analytic expressions. Therefore, the observation site can be located outside, on the faces of or inside the anomalous mass bodies. A simple prismatic body of anomalous density is adopted to test the accuracy of our newly developed closed-form solution. Cases of constant, linear, quadratic, cubic and quartic polynomial orders of mass density contrast are tested. For cases of constant, linear, quadratic and cubic polynomial orders, the relative errors between our results and other published exact solutions are less than 10(-11)%. For the case of quartic polynomial order, relative errors less than 10(-10)% are obtained between our solutions and those computed by a high-order Gaussian quadrature rule (512 x 512 x 512 = 134 217 728 quadrature points), where our new analytic solution needs significantly less computational time (0.0009 versus 31.106 s). These numerical experiments not only verified the accuracy of our new formula but also demonstrated their potential in computing exact gravity anomalies for complicated mass density distributions in the Earth.
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| 3. |
- Kalscheuer, Thomas, et al.
(author)
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A non-linear truncated SVD variance and resolution analysis of two-dimensional magnetotelluric models
- 2007
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In: Geophysical Journal International. - 0956-540X .- 1365-246X. ; 169:2, s. 435-447
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Journal article (peer-reviewed)abstract
- A novel approach to assess variance and resolution properties of 2-D models of electrical resistivity derived from magnetotelluric measurements is presented. Based on a truncated singular value decomposition (TSVD) scheme on a local subspace, it partly takes the non-linearity of the inverse problem into account. The TSVD resolution and variance analysis is performed on a single cell at a time. A variance threshold is selected and the resulting model resolution is determined. As an improvement over existing schemes, non-linear semi-axes are introduced to describe the non-linear confidence surface in the directions of the model eigenvectors and they replace the inverse singular values entering into the standard expression of model variances. The model variance of the cell considered is estimated from the sum of squares of the non-linear semi-axes up to the given variance threshold. This, in turn, gives the truncation level of the TSVD and the row of the model resolution matrix belonging to the considered cell can be computed from the model eigenvectors of the TSVD. The information contained in the resolution matrix is condensed to easily comprehensible measures like the centre of resolution and horizontal and vertical resolution lengths.The validity of our non-linear model variance and resolution estimates is tested with a most-squares technique which gives an improved estimate of model variability.A synthetic model with a conductive block in a homogenous half-space is analysed. TSVD analyses for model cells on the upper edge of the block and outside the block illustrate how the truncation process works. Typically, the linear and non-linear semi-axes are almost equal up to a certain singular value number, after which the non-linear semi-axes increase much less than the linear semi-axes. This important result indicates that the resolution of 2-D magnetotelluric models is significantly better than previously suggested by linear schemes for the computation of model variance and resolution properties. A field example from the Skediga area (Sweden) shows that the electrical resistivity distribution of sand and gravel formations which are only laterally bounded by conductive clay lenses is relatively well resolved whereas there is little resolution for the transition between the sand and gravel layer and the basement under a clay cover.
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| 4. |
- Kalscheuer, Thomas, et al.
(author)
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Joint inversions of three types of electromagnetic data explicitly constrained by seismic observations : results from the central Okavango Delta, Botswana
- 2015
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In: Geophysical Journal International. - : Oxford University Press (OUP). - 0956-540X .- 1365-246X. ; 202:3, s. 1429-1452
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Journal article (peer-reviewed)abstract
- The Okavango Delta of northern Botswana is one of the world’s largest inland deltas or megafans. To obtain information on the character of sediments and basement depths, audio-magnetotelluric (AMT), controlled-source audiomagnetotelluric (CSAMT) and central-loop transient electromagnetic (TEM) data were collected on the largest island within the delta. The data were inverted individually and jointly for 1-D models of electric resistivity. Distortion effects in the AMT and CSAMT data were accounted for by including galvanic distortion tensors as free parameters in the inversions. By employing Marquardt–Levenberg inversion, we found that a 3-layer model comprising a resistive layer overlying sequentially a conductive layer and a deeper resistive layer was sufficient to explain all of the electromagnetic data. However, the top of the basal resistive layer from electromagnetic-only inversions was much shallower than the well-determined basement depth observed in high-quality seismic reflection images and seismic refraction velocity tomograms. To resolve this discrepancy, we jointly inverted the electromagnetic data for 4-layer models by including seismic depths to an interface between sedimentary units and to basement as explicit a priori constraints. We have also estimated the interconnected porosities, clay contents and pore-fluid resistivities of the sedimentary units from their electrical resistivities and seismic P-wave velocities using appropriate petrophysical models. In the interpretation of our preferred model, a shallow ∼40 m thick freshwater sandy aquifer with 85–100 Ohmm resistivity, 10–32 per cent interconnected porosity and <13 per cent clay content overlies a 105–115 m thick conductive sequence of clay and intercalated salt-water-saturated sands with 15–20 Ohmm total resistivity, 1−27 per cent interconnected porosity and 15–60 per cent clay content. A third ∼60 m thick sandy layer with 40–50 Ohmm resistivity, 10–33 per cent interconnected porosity and <15 per cent clay content is underlain by the basement with 3200–4000 Ohmm total resistivity. According to an interpretation of helicopter TEM data that cover the entire Okavango Delta and borehole logs, the second and third layers may represent lacustrine sediments from Paleo Lake Makgadikgadi and a moderately resistive freshwater aquifer comprising sediments of the recently proposed Paleo Okavango Megafan, respectively.
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| 5. |
- Kalscheuer, Thomas, et al.
(author)
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Non-linear model error and resolution properties from two-dimensional single and joint inversions of direct current resistivity and radiomagnetotelluric data
- 2010
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In: Geophysical Journal International. - 0956-540X .- 1365-246X. ; 182:3, s. 1174-1188
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Journal article (peer-reviewed)abstract
- P>For the first time, a comparative analysis of the resolution and variance properties of 2-D models of electrical resistivity derived from single and joint inversions of dc resistivity (DCR) and radiomagnetotelluric (RMT) measurements is presented. DCR and RMT data are inverted with a smoothness-constrained 2-D scheme. Model resolution, model variance and data resolution analyses are performed both with a classical linearized scheme that employs the smoothness-constrained generalized inverse and a non-linear truncated singular value decomposition (TSVD). In the latter method, the model regularization used in the inversion is avoided and non-linear semi-axes give an approximate description of the non-linear confidence surface in the directions of the model eigenvectors. Hence, this method analyses the constraints that can be provided by the data. Model error estimates are checked against improved and independent estimates of model variability from most-squares inversions. For single and joint inverse models of synthetic data sets, the smoothness-constrained scheme suggests relatively small model errors (typically up to 30 to 40 per cent) and resolving kernels that are spread over several cells in the vicinity of the investigated cell. Linearized smoothness-constrained errors are in good agreement with the corresponding most-squares errors. The variability of the RMT model as estimated from non-linear semi-axes is confirmed by TSVD-based most-squares inversions for most model cells within the depth range of investigation. In contrast to this, most-squares errors of the DCR model are consistently larger than errors estimated from non-linear semi-axes except for the smallest truncation levels. The model analyses confirm previous studies that DCR data can constrain resistive and conductive structures equally well while RMT data provide superior constraints for conductive structures. The joint inversion can improve error and resolution of structures which are within the depth ranges of exploration of both methods. In such parts of the model which are outside the depth range of exploration for one method, error and resolution of the joint inverse model are close to those of the best single inversion result subject to an appropriate weighting of the different data sets.
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| 6. |
- Kalscheuer, Thomas, et al.
(author)
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Radiomagnetotelluric two-dimensional forward and inverse modelling accounting for displacement currents
- 2008
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In: Geophysical Journal International. - 0956-540X .- 1365-246X. ; 175:2, s. 486-514
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Journal article (peer-reviewed)abstract
- Electromagnetic surface measurements with the radiomagnetotelluric (RMT) method in the frequency range between 10 and 300 kHz are typically interpreted in the quasi-static approximation, that is, assuming displacement currents are negligible. In this paper, the dielectric effect of displacement currents on RMT responses over resistive subsurface models is studied with a two-dimensional (2-D) forward and inverse scheme, that can operate both in the quasi-static approximation and including displacement currents.Forward computations of simple models exemplify how responses that allow for displacements currents deviate from responses computed in the quasi-static approximation. The differences become most obvious for highly resistive subsurface models of about 3000 Ohm*m and more and at high frequencies. For such cases, the apparent resistivities and phases of the transverse magnetic (TM) and transverse electric (TE) modes are significantly smaller than in the quasi-static approximation. Along profiles traversing 2-D subsurface models, sign reversals in the real part of the vertical magnetic transfer function (VMT) are often more pronounced than in the quasi-static approximation. On both sides of such sign reversals, the responses computed including displacement currents are larger than typical measurement errors.The 2-D inversion of synthetic data computed including displacement currents demonstrates that serious misinterpretations in the form of artefacts in inverse models can be made if displacement currents are neglected during the inversion. Hence, the inclusion of the dielectric effect is a crucial improvement over existing quasi-static 2-D inverse schemes. Synthetic data from a 2-D model with constant dielectric permittivity and a conductive block buried in a highly resistive layer which in turn is underlain by a conductive layer are inverted. In the quasi-static inverse model, the depth to the conductive structures is overestimated, artefactual resistors appear on both sides of the conductive block, and a spurious conductive layer is imaged at the surface.High-frequency RMT field data from Ävrö, Sweden, are re-interpreted using the newly developed 2-D inversion scheme which includes displacement currents. In contrast to previous quasi-static modelling, the new inverse models have electrical resistivity values comparable to a normal-resistivity borehole log and boundaries between resistive and conductive structures which correlate with the positions of seismic reflectors.
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| 7. |
- Rosas-Carbajal, M., et al.
(author)
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Probabilistic 3-D time-lapse inversion of magnetotelluric data: application to an enhanced geothermal system
- 2015
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In: Geophysical Journal International. - : Oxford University Press (OUP). - 0956-540X .- 1365-246X. ; 203:3, s. 1946-1960
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Journal article (peer-reviewed)abstract
- Surface-based monitoring of mass transfer caused by injections and extractions in deep boreholes is crucial to maximize oil, gas and geothermal production. Inductive electromagnetic methods, such as magnetotellurics, are appealing for these applications due to their large penetration depths and sensitivity to changes in fluid conductivity and fracture connectivity. In this work, we propose a 3-D Markov chain Monte Carlo inversion of time-lapse magnetotelluric data to image mass transfer following a saline fluid injection. The inversion estimates the posterior probability density function of the resulting plume, and thereby quantifies model uncertainty. To decrease computation times, we base the parametrization on a reduced Legendre moment decomposition of the plume. A synthetic test shows that our methodology is effective when the electrical resistivity structure prior to the injection is well known. The centre of mass and spread of the plume are well retrieved. We then apply our inversion strategy to an injection experiment in an enhanced geothermal system at Paralana, South Australia, and compare it to a 3-D deterministic time-lapse inversion. The latter retrieves resistivity changes that are more shallow than the actual injection interval, whereas the probabilistic inversion retrieves plumes that are located at the correct depths and oriented in a preferential north–south direction. To explain the time-lapse data, the inversion requires unrealistically large resistivity changes with respect to the base model. We suggest that this is partly explained by unaccounted subsurface heterogeneities in the base model from which time-lapse changes are inferred.
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| 8. |
- Rosas-Carbajal, Marina, et al.
(author)
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Two-dimensional probabilistic inversion of plane-wave electromagnetic data : methodology, model constraints and joint inversion with electrical resistivity data
- 2014
-
In: Geophysical Journal International. - : Oxford University Press (OUP). - 1365-246X .- 0956-540X. ; 196:3, s. 1508-1524
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Journal article (peer-reviewed)abstract
- Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space is high dimensional. Here, we present a 2-D pixel-based MCMC inversion of plane-wave electromagnetic (EM) data. Using synthetic data, we investigate how model parameter uncertainty depends on model structure constraints using different norms of the likelihood function and the model constraints, and study the added benefits of joint inversion of EM and electrical resistivity tomography (ERT) data. Our results demonstrate that model structure constraints are necessary to stabilize the MCMC inversion results of a highly discretized model. These constraints decrease model parameter uncertainty and facilitate model interpretation. A drawback is that these constraints may lead to posterior distributions that do not fully include the true underlying model, because some of its features exhibit a low sensitivity to the EM data, and hence are difficult to resolve. This problem can be partly mitigated if the plane-wave EM data is augmented with ERT observations. The hierarchical Bayesian inverse formulation introduced and used herein is able to successfully recover the probabilistic properties of the measurement data errors and a model regularization weight. Application of the proposed inversion methodology to field data from an aquifer demonstrates that the posterior mean model realization is very similar to that derived from a deterministic inversion with similar model constraints.
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| 9. |
- Rulff, Paula, et al.
(author)
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Efficient goal-oriented mesh refinement in 3-D finite-element modelling adapted for controlled source electromagnetic surveys
- 2021
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In: Geophysical Journal International. - : Oxford University Press. - 0956-540X .- 1365-246X. ; 227:3, s. 1624-1645
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Journal article (peer-reviewed)abstract
- We developed a 3-D forward modelling code, which simulates controlled source electromagnetic problems in frequency domain using edge-based finite elements and a total electric field approach. To evaluate electromagnetic data acquired across complex subsurface structures, software performing accurate 3-D modelling is required, especially for incorporation in inversion approaches. Our modelling code aims at finding a good compromise between the necessary solution accuracy at the points of interest and the general problem size by using a goal-oriented mesh refinement strategy designed for models of variable electric conductivity and magnetic permeability. To formulate an improved error estimator suitable for controlled source electromagnetic problems, we developed literature approaches of mesh refinement further targeting three aspects. First, to generate a roughly homogeneously fine mesh discretization around all receiver sites, our new error estimator weights the adjoint source term by the approximate decay of the electric field with increasing distance from the primal source using the expression for a homogeneous half-space. This causes almost no additional computational cost. Second, the error estimator employed in the refinement approach can be optimized for models with pronounced conductivity and magnetic permeability contrasts as often encountered in, for example, mineral prospecting scenarios by optionally including terms that measure the continuity of the normal component of current flow and the tangential component of the magnetic field across interfaces of abutting elements. Third, to avoid amplitude-dependent over-refining of the mesh, we formulate our element-wise error estimators relative to the local amplitude of the electromagnetic field. In this work, we evaluate the implemented adaptive mesh refinement approach and its solution accuracy comparing our solutions for simple 1-D models and a model with 3-D anomalies to semi-analytic 1-D solutions and a second-order finite-element code, respectively. Furthermore, a feasibility study for controlled-source electromagnetic measurements across ferrous mineral deposits is conducted. The numerical experiments demonstrate that our new refinement procedure generates problem-specific finite-element meshes and yields accurate solutions for both simple synthetic models and realistic survey scenarios. Especially for the latter, characteristics of our code, such as the possibility of modelling extended sources as well as including arbitrary receiver distributions and detailed subsurface anomalies, are beneficial.
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| 10. |
- Wang, Shunguo, et al.
(author)
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Boat-towed radio-magnetotelluric and controlled source audio-magnetotelluric study to resolve fracture zones at Äspö Hard Rock Laboratory site, Sweden
- 2019
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In: Geophysical Journal International. - : OXFORD UNIV PRESS. - 0956-540X .- 1365-246X. ; 218:2, s. 1008-1031
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Journal article (peer-reviewed)abstract
- Boat-towed radio-magnetotelluric (RMT) measurements using signals between 14 and 250 kHz have attracted increasing attention in the near-surface applications for shallow water and archipelago areas. A few large-scale underground infrastructure projects, such as the Stockholm bypass in Sweden, are planned to pass underneath such water zones. However, in cases with high water salinity, RMT signals have a penetration depth of a few metres and do not reach the geological structures of interest in the underlying sediments and bedrock. To overcome this problem, controlled source signals at lower frequencies of 1.25 to 12.5 kHz can be utilized to improve the penetration depth and to enhance the resolution for modelling deeper underwater structures. Joint utilization of boat-towed RMT and controlled source audio-magnetotellurics (CSAMT) was tested for the first time at the Aspo Hard Rock Laboratory (HRL) site in south-eastern Sweden to demonstrate acquisition efficiency and improved resolution to model fracture zones along a 600-m long profile. Pronounced galvanic distortion effects observed in 1-D inversion models of the CSAMT data as well as the predominantly 2-D geological structures at this site motivated usage of 2-D inversion. Two standard academic inversion codes, EMILIA and MARE2DEM, were used to invert the RMT and CSAMT data. EMILIA, an object-oriented Gauss-Newton inversion code with modules for 2-D finite difference and 1-D semi-analytical solutions, was used to invert the RMT and CSAMT data separately and jointly under the plane-wave approximation for 2-D models. MARE2DEM, a Gauss-Newton inversion code for controlled source electromagnetic 2.5-D finite element solution, was modified to allow for inversions of RMT and CSAMT data accounting for source effects. Results of EMILIA and MARE2DEM reveal the previously known fracture zones in the models. The 2-D joint inversions of RMT and CSAMT data carried out with EMILIA and MARE2DEM show clear improvement compared with 2-D single inversions, especially in imaging uncertain fracture zones analysed in a previous study. Our results show that boat-towed RMT and CSAMT data acquisition systems can be utilized for detailed 2-D or 3-D surveys to characterize near-surface structures underneath shallow water areas. Potential future applications may include geo-engineering, geohazard investigations and mineral exploration.
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