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- Abtahi, Sayyed Mohammad, et al.
(författare)
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A new reference model for 3D inversion of airborne magnetic data in hilly terrain : A case study from northern Sweden
- 2018
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Ingår i: Geophysics. - : SOC EXPLORATION GEOPHYSICISTS. - 0016-8033 .- 1942-2156. ; 83:1, s. B1-B12
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Tidskriftsartikel (refereegranskat)abstract
- The inherent nonuniqueness in modeling magnetic data can be partly reduced by adding prior information, either as mathematical constructs or simply as bounds on magnetization obtained from laboratory measurements. If a good prior model can be used as a reference model, then the quality of estimated models through an inverse approach can be greatly improved. But even though data on magnetic properties of rocks might exist, their distribution may often be quite irregular on local and regional scales, so that it is difficult to define representative classes of rock types suitable for constraining geophysical models of magnetization. We have developed a new way of constructing a reference model that varies only laterally and is confined to the part of the terrain that lies above the lowest topography in the area. To obtain this model, several estimated 2D magnetization distributions were constructed by data inversion as a function of the iteration number. Then, a suitable 2D model of the magnetization in the topography was chosen as a starting point for constructing a 3D reference model by modifying it with a vertical decay such that its average source depth was the same for all horizontal positions. The average source depth of the reference model was chosen to satisfy the average source depth obtained from analyzing the radial power spectrum of the area studied. Finally, the measured magnetic data were inverted in three dimensions using the given reference model. For a selected reference model, shallow structures indicated a better overall correlation with large remanent magnetizations measured on rock samples from the area. Throughout the entire model, the direction of magnetization was allowed to vary freely. We found that the Euclidean norm of the estimated model was reduced compared with the case where the magnetization direction was fixed.
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| 3. |
- Buntin, Laura M.
(författare)
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Efficient Electromagnetic Induction Modelling : Adaptive mesh optimisation, advanced boundary methods and iterative solution techniques
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Forward modelling of electromagnetic induction data simulates the electric and magnetic fields within a computational domain for a given distribution of electromagnetic material properties and a given source of the electromagnetic field. The quantities of interest are the fields at receiver locations at the Earth's surface. Reliable results require high accuracy solutions at the receivers. First and foremost, numerical computations need to be accurate, but ideally they are also resource efficient, i.e., as fast and cheap as possible. Run time and memory demand mainly depend on the size of the numerical problem to be solved. This thesis addresses specific steps within the forward modelling procedure of electromagnetic induction data in order to improve the solution accuracy of forward modelling as well as to reduce computational resources. The solution accuracy is strongly influenced by the spatial discretisation of the computational domain, which directly correlates with the numerical problem size. To optimise the solution accuracy while keeping the numerical problem size as small as possible, a goal-oriented adaptive mesh refinement scheme for three-dimensional controlled-source electromagnetic models is developed. In addition, this thesis investigates the influence of different types of boundary methods on the solution accuracy at the receivers. To replace inhomogeneous boundary conditions in magnetotelluric total-field modelling by perfectly-matched layers (PML), a domain decomposition approach (the total and scattered field decomposition) is adapted for Earth models. By reducing boundary effects, the approach yields superior solution accuracy for specific types of models. The fastest and most memory-efficient way to solve large numerical problems are iterative solution methods. Iterative solvers, however, work poorly for numerical systems arising from domains bounded by PML. In this thesis a preconditioned iterative solution framework that efficiently solves PML-bounded magnetotelluric models is proposed.
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| 4. |
- Buntin, Laura M., et al.
(författare)
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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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Ingår i: Geophysical Journal International. - : Oxford University Press (OUP). - 0956-540X .- 1365-246X. ; 235:2, s. 1201-1217
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Tidskriftsartikel (refereegranskat)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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| 6. |
- Chen, Chaojian, et al.
(författare)
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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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Ingår i: Geophysical Journal International. - : Oxford University Press. - 0956-540X .- 1365-246X. ; 214:3, s. 2115-2132
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Tidskriftsartikel (refereegranskat)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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| 9. |
- Kalscheuer, Thomas, 1975-
(författare)
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Improvement and Assessment of Two-Dimensional Resistivity Models Derived from Radiomagnetotelluric and Direct-Current Resistivity Data
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Two-dimensional (2-D) models of electrical resistivity are improved by jointly inverting radiomagnetotelluric (RMT) and direct-current resistivity (DCR) data or by allowing for displacement currents in the inversion of RMT data collected on highly resistive bedrock. Uniqueness and stability of the 2-D models are assessed with a model variance and resolution analysis that allows for the non-linearity of the inverse problem.Model variance and resolution are estimated with a truncated singular value decomposition (TSVD) of the sensitivity matrix. In the computation of model errors, inverse singular values are replaced by non-linear semi-axes and the number of included eigenvectors is increased until a given error threshold is reached. Non-linear error estimates are verified with most-squares inversions. For the obtained truncation levels, model resolution matrices are computed. For RMT data, non-linear error appraisals are smaller than linearized ones. Hence, the consideration of the non-linearity in RMT data leads to reduced model errors or enhanced model resolution.The dielectric effect on RMT data is investigated with a new 2-D forward and inverse code that allows for displacement currents. As compared to the quasi-static approximation, apparent resistivities and phases of the impedance tensor elements are found to be significantly smaller and the vertical magnetic transfer function exhibits more distinct sign reversals. More reliable models of electrical resistivity are obtained from areas with highly resistive bedrock, if displacement currents are allowed for. In contrast, inversions with a quasi-static scheme introduce artefactual structures with extremely low or high resistivities.A smoothness-constrained 2-D joint inversion of RMT and DCR data is presented. The non-linear model variance and resolution analysis is applied to single and joint inverse models. For DCR data, the errors estimated by most-squares inversions are consistently larger than those estimated by the non-linear semi-axes, indicating that DCR models are poorly resolved. Certain areas of the joint inverse models are better resolved than in the single inverse models.
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