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 Today, transient electromagnetic (TEM) data are often collected in very large surveys. Despite several 3D schemes being available, the large data amounts favour the robust and fast 1D schemes over 3D inversions, which are very time and memory consuming. However, some geological structures cannot be assumed one-dimensional, which means that 3D effects will be introduced into the 1D-model results. In such cases, 2D or 3D codes are required to produce reliable results. Here, we present a 2.5 inversion approach combining a 2D model grid with a halved 3D forward modelling mesh, which speeds up the computation time with a factor 2.5 compared to a full solution. The approach exploits the symmetry of the forward problem, which lets us halve the 3D mesh along the data collection line, when the right boundary conditions are employed. We demonstrate the approach on a synthetic example and on field data, and we show that compared to a 1D inversion, the 2.5D approach resolves resistivity contrasts and structures more accurately.
Over several decades, much research has been done to develop 3D electromagnetic inversion algorithms. Due to the computational complexity and the memory requirements for 3D time-domain electromagnetic (TEM) inversion algorithms, many real-world surveys are inverted within one dimension. To speed up calculations and manage memory for 3D inversions of TEM data, we have developed an approach using three uncoupled meshes: an inversion mesh, a forward-model mesh, and a mesh for Jacobian calculations. The inversion mesh is a coarse regular and structured mesh, such that constraints are easily enforced between the model parameters. Forward responses are calculated on a dense unstructured mesh to obtain accurate electromagnetic fields, whereas the Jacobian is calculated on a coarse unstructured mesh. We found that using a coarse mesh for the Jacobian is sufficient for the inversion to converge and, equally important, that it provides a significant speed boost in the overall inversion process, compared to calculating it on the forward-modeling mesh. The unstructured meshes are made of tetrahedral elements, and the electromagnetic fields are calculated using the finite-element method. The inversion optimization uses a standard Gauss-Newton formulation. For further speed up and memory optimizing of the inversion, we use domain decomposition for calculating the responses for each transmitter separately and parallelize the problem over domains using OpenMP. Compared to a 1D solution, the accuracy for the Jacobian is 1%–5% for the dense mesh and 2%–7% for the coarse mesh, but the calculation time is approximately five times faster for the coarse mesh. We also examined the algorithm on a small ground-based TEM data set acquired in an area where a 3D earth distorts the electromagnetic fields to such a degree that a 1D inversion is not feasible.
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