ALBERT

Description: 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, audiomagnetotelluric (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 m 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 m 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 m resistivity, 10–33 per cent interconnected porosity and 〈15 per cent clay content is underlain by the basement with 3200–4000 m 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.

Description: The effects of neglecting ground surface topography variations in elastic full waveform inversion are investigated using two classes of synthetic example. The models include various high-contrast velocity and density anomalies, as they are often observed in near-surface applications. The first type of example shows that failing to account for even small amplitude fluctuations in topography introduces velocity artefacts in the near-surface part of the tomogram as well as degrades significantly the spatial resolution of features at greater depths. The disturbances are particularly severe when the topographic fluctuations have wavelengths comparable to the minimum seismic wavelength. The second type of synthetic example considers long wavelength topography variations of various amplitudes. It is found that neglecting topography with an amplitude fluctuation greater than half the minimum seismic wavelength leads to appreciable inversion image artefacts. Therefore, the incorporation of surface topography, even if it appears minor, is essential for successful elastic full waveform inversion of land seismic data.

Description: 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, audiomagnetotelluric (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 m 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 m 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 m resistivity, 10–33 per cent interconnected porosity and 〈15 per cent clay content is underlain by the basement with 3200–4000 m 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.

Description: We have developed a novel goal-oriented adaptive mesh refinement approach for finite-element methods to model plane wave electromagnetic (EM) fields in 3-D earth models based on the electric field differential equation. To handle complicated models of arbitrary conductivity, magnetic permeability and dielectric permittivity involving curved boundaries and surface topography, we employ an unstructured grid approach. The electric field is approximated by linear curl-conforming shape functions which guarantee the divergence-free condition of the electric field within each tetrahedron and continuity of the tangential component of the electric field across the interior boundaries. Based on the non-zero residuals of the approximated electric field and the yet to be satisfied boundary conditions of continuity of both the normal component of the total current density and the tangential component of the magnetic field strength across the interior interfaces, three a-posterior error estimators are proposed as a means to drive the goal-oriented adaptive refinement procedure. The first a-posterior error estimator relies on a combination of the residual of the electric field, the discontinuity of the normal component of the total current density and the discontinuity of the tangential component of the magnetic field strength across the interior faces shared by tetrahedra. The second a-posterior error estimator is expressed in terms of the discontinuity of the normal component of the total current density (conduction plus displacement current). The discontinuity of the tangential component of the magnetic field forms the third a-posterior error estimator. Analytical solutions for magnetotelluric (MT) and radiomagnetotelluric (RMT) fields impinging on a homogeneous half-space model are used to test the performances of the newly developed goal-oriented algorithms using the above three a-posterior error estimators. A trapezoidal topographical model, using normally incident EM waves at both MT and RMT frequencies, is adopted to further test the convergence of the newly developed algorithms against a surface integral approach. Next, the 3D-1 benchmark model from the COMMEMI project is used to show the efficiency of the goal-oriented adaptive algorithm and to compare our solutions against volume integral solutions and other finite-element solutions. For all three test cases, we found that the error estimator using face jumps of normal components of current density embedded in the goal-oriented adaptive refinement procedure shows the most robust performance.

Description: We have developed a generalized and stable surface integral formula for 3-D uniform inducing field and plane wave electromagnetic induction problems, which works reliably over a wide frequency range. Vector surface electric currents and magnetic currents, scalar surface electric charges and magnetic charges are treated as the variables. This surface integral formula is successfully applied to compute the electromagnetic responses of 3-D topography to low frequency magnetotelluric and high frequency radio-magnetotelluric fields. The standard boundary element method which is used to solve this surface integral formula quickly exceeds the memory capacity of modern computers for problems involving hundreds of thousands of unknowns. To make the surface integral formulation applicable and capable of dealing with large-scale 3-D geo-electromagnetic problems, we have developed a matrix-free adaptive multilevel fast multipole boundary element solver. By means of the fast multipole approach, the time-complexity of solving the final system of linear equations is reduced to O ( m log m ) and the memory cost is reduced to O ( m ), where m is the number of unknowns. The analytical solutions for a half-space model were used to verify our numerical solutions over the frequency range 0.001–300 kHz. In addition, our numerical solution shows excellent agreement with a published numerical solution for an edge-based finite-element method on a trapezoidal hill model at a frequency of 2 Hz. Then, a high frequency simulation for a similar trapezoidal hill model was used to study the effects of displacement currents in the radio-magnetotelluric frequency range. Finally, the newly developed algorithm was applied to study the effect of moderate topography and to evaluate the applicability of a 2-D RMT inversion code that assumes a flat air–Earth interface, on RMT field data collected at Smørgrav, southern Norway. This paper constitutes the first part of a hybrid boundary element-finite element approach to compute the electromagnetic field inside structures involving complex 3-D conductivity and permittivity distributions.

Description: SUMMARY Statistical experimental design (SED) is the field of statistics concerned with designing experiments to obtain as much information as possible about a target of interest. SED algorithms can be divided into two categories: those that assume a linear or linearized relationship between measured data and parameters, and those that account for a fully nonlinear relationship. We compare the most commonly used linear method, Bayesian D-optimization, to two nonlinear methods, maximum entropy design and DN-optimization, in a synthetic seismological source location problem where we define a region of the subsurface in which earthquake sources are likely to occur. Example random sources in this region are sampled with a uniform distribution and their arrival time data across the ground surface are forward modelled; the goal of SED is to define a surface monitoring network that optimally constrains this set of source locations given the data that would be observed. Receiver networks so designed are evaluated on performance—the percentage of earthquake pairs whose arrival time differences are above a threshold of measurement uncertainty at each receiver, the number of prior samples (earthquakes) required to evaluate the statistical performance of each design and the SED compute time for different subsurface velocity models. We find that DN-optimization provides the best results both in terms of performance and compute time. Linear design is more computationally expensive and designs poorer performing networks. Maximum entropy design is shown to be effectively impractical due to the large number of samples and long compute times required.

Description: Structural joint inversion of several data sets on an irregular mesh requires appropriate coupling operators. To date, joint inversion algorithms are primarily designed for the use on regular rectilinear grids and impose structural similarity in the direct neighbourhood of a cell only. We introduce a novel scheme for calculating cross-gradient operators based on a correlation model that allows to define the operator size by imposing physical length scales. We demonstrate that the proposed cross-gradient operators are largely decoupled from the discretization of the modelling domain, which is particularly important for irregular meshes where cell sizes vary. Our structural joint inversion algorithm is applied to a synthetic electrical resistivity tomography and ground penetrating radar 3-D cross-well experiment aiming at imaging two anomalous bodies and extracting the parameter distribution of the geostatistical background models. For both tasks, joint inversion produced superior results compared with individual inversions of the two data sets. Finally, we applied structural joint inversion to two field data sets recorded over a karstified limestone area. By including geological a priori information via the correlation-based operators into the joint inversion, we find P-wave velocity and electrical resistivity tomograms that are in accordance with the expected subsurface geology.