Parallel three-dimensional magnetotelluric inversion using adaptive finite-element method. Part I: theory and synthetic study

This paper presents a distributed magnetotelluric inversion scheme based on adaptive finite-element method (FEM). The key novel aspect of the introduced algorithm is the use of automatic mesh refinement techniques for both forward and inverse modelling. These techniques alleviate tedious and subjective procedure of choosing a suitable model parametrization. To avoid overparametrization, meshes for forward and inverse problems were decoupled. For calculation of accurate electromagnetic (EM) responses, automatic mesh refinement algorithm based on a goal-oriented error estimator has been adopted. For further efficiency gain, EM fields for each frequency were calculated using independent meshes in order to account for substantially different spatial behaviour of the fields over a wide range of frequencies. An automatic approach for efficient initial mesh design in inverse problems based on linearized model resolution matrix was developed. To make this algorithm suitable for large-scale problems, it was proposed to use a low-rank approximation of the linearized model resolution matrix. In order to fill a gap between initial and true model complexities and resolve emerging 3-D structures better, an algorithm for adaptive inverse mesh refinement was derived. Within this algorithm, spatial variations of the imaged parameter are calculated and mesh is refined in the neighborhoods of points with the largest variations. A series of numerical tests were performed to demonstrate the utility of the presented algorithms. Adaptive mesh refinement based on the model resolution estimates provides an efficient tool to derive initial meshes which account for arbitrary survey layouts, data types, frequency content and measurement uncertainties. Furthermore, the algorithm is capable to deliver meshes suitable to resolve features on multiple scales while keeping number of unknowns low. However, such meshes exhibit dependency on an initial model guess. Additionally, it is demonstrated that the adaptive mesh refinement can be particularly efficient in resolving complex shapes. The implemented inversion scheme was able to resolve a hemisphere object with sufficient resolution starting from a coarse discretization and refining mesh adaptively in a fully automatic process. The code is able to harness the computational power of modern distributed platforms and is shown to work with models consisting of millions of degrees of freedom. Significant computational savings were achieved by using locally refined decoupled meshe

Integrated low power digital gyro control electronics

Embodiments of the invention generally encompass a digital, application specific integrated circuit (ASIC) has been designed to perform excitation of a selected mode within a vibratory rate gyroscope, damping, or force-rebalance, of other modes within the sensor, and signal demodulation of the in-phase and quadrature components of the signal containing the angular rate information. The ASIC filters dedicated to each channel may be individually programmed to accommodate different rate sensor designs/technology or variations within the same class of sensors. The ASIC architecture employs a low-power design, making the ASIC, particularly suitable for use in power-sensitive applications

Joint inversion of satellite-detected tidal and magnetospheric signals constrains electrical conductivity and water content of the upper mantle and transition zone

We present a new global electrical conductivity model of Earths mantle. The model was derived by using a novel methodology, which is based on inverting satellite magnetic field measurements from different sources simultaneously. Specifically, we estimated responses of magnetospheric origin and ocean tidal magnetic signals from the most recent Swarm and CHAMP data. The challenging task of properly accounting for the ocean effect in the data was addressed through full three-dimensional solution of Maxwell's equations. We show that simultaneous inversion of magnetospheric and tidal magnetic signals results in a model with much improved resolution. Comparison with laboratory-based conductivity profiles shows that obtained models are compatible with a pyrolytic composition and a water content of 0.01 wt and 0.1 wt in the upper mantle and transition zone, respectively

Robust and scalable 3-D geo-electromagnetic modelling approach using the finite element method

We present a robust and scalable solver for time-harmonic Maxwell's equations for problems with large conductivity contrasts, wide range of frequencies, stretched grids and locally refined meshes. The solver is part of the fully distributed adaptive 3-D electromagnetic modelling scheme which employs the finite element method and unstructured non-conforming hexahedral meshes for spatial discretization using the open-source software deal.II. We use the complex-valued electric field formulation and split it into two real-valued equations for which we utilize an optimal block-diagonal pre-conditioner. Application of this pre-conditioner requires the solution of two smaller real-valued symmetric problems. We solve them by using either a direct solver or the conjugate gradient method pre-conditioned with the recently introduced auxiliary space technique. The auxiliary space pre-conditioner reformulates the original problem in form of several simpler ones, which are then solved using highly efficient algebraic multigrid methods. In this paper, we consider the magnetotelluric case and verify our numerical scheme by using COMMEMI 3-D models. Afterwards, we run a series of numerical experiments and demonstrate that the solver converges in a small number of iterations for a wide frequency range and variable problem sizes. The number of iterations is independent of the problem size, but exhibits a mild dependency on frequency. To test the stability of the method on locally refined meshes, we have implemented a residual-based a posteriori error estimator and compared it with uniform mesh refinement for problems up to 200 million unknowns. We test the scalability of the most time consuming parts of our code and show that they fulfill the strong scaling assumption as long as each MPI process possesses enough degrees of freedom to alleviate communication overburden. Finally, we refer back to a direct solver-based pre-conditioner and analyse its complexity in time. The results show that for multiple right-hand sides the direct solver-based pre-conditioner can still be faster for problems of medium size. On the other hand, it also shows non-linear growth in memory, whereas the auxiliary space method increases only linearly.ISSN:0956-540XISSN:1365-246

Swarm Satellites in EM Induction Studies

There exists no single EM induction source that is sensitive to the whole mantle.We need to integrate several natural sources in order to bridge across the scales.On the global scale, the most promising methodology is to combine magnetospheric and ocean tidal signals to image mantle under both continents and oceans

Satellite tidal magnetic signals constrain oceanic lithosphere-asthenosphere boundary

The tidal flow of electrically conductive oceans through the geomagnetic field results in the generation of secondary magnetic signals, which provide information on the subsurface structure. Data from the new generation of satellites were shown to contain magnetic signals due to tidal flow; however, there are no reports that these signals have been used to infer subsurface structure. We use satellite-detected tidal magnetic fields to image the global electrical structure of the oceanic lithosphere and upper mantle down to a depth of about 250 km. The model derived from more than 12 years of satellite data reveals a ≈72-km-thick upper resistive layer followed by a sharp increase in electrical conductivity likely associated with the lithosphere-asthenosphere boundary, which separates colder rigid oceanic plates from the ductile and hotter asthenosphere.ISSN:2375-254

Satellite Tidal Magnetic Signals Constrain Oceanic Lithosphere-Asthenosphere Boundary Earth Tomography with Tidal Magnetic Signals

The tidal flow of electrically conductive oceans through the geomagnetic field results in the generation of secondary magnetic signals, which provide information on the subsurface structure. Data from the new generation of satellites were shown to contain magnetic signals due to tidal flow; however, there are no reports that these signals have been used to infer subsurface structure. Here we use satellite-detected tidal magnetic fields to image the global electrical structure of the oceanic lithosphere and upper mantle down to a depth of about 250 km. The model derived from more than 12 years of satellite data reveals an Approximately 72 km thick upper resistive layer followed by a sharp increase in electrical conductivity likely associated with the lithosphere-asthenosphere boundary, which separates colder rigid oceanic plates from the ductile and hotter asthenosphere

Resolving the sign conflict problem for hp–hexahedral Nédélec elements with application to eddy current problems

The eddy current approximation of Maxwell’s equations is relevant for Magnetic Induction Tomography (MIT), which is a practical system for the detection of conducting inclusions from measurements of mutual inductance with both industrial and clinical applications. An MIT system produces a conductivity image from the measured fields by solving an inverse problem computationally. This is typically an iterative process, which requires the forward solution of a Maxwell’s equations for the electromagnetic fields in and around conducting bodies at each iteration. As the (conductivity) images are typically described by voxels, a hexahedral finite element grid is preferable for the forward solver. Low order Nédélec (edge element) discretisations are generally applied, but these require dense meshes to ensure that skin effects are properly captured. On the other hand, hp–Nédélec finite elements can ensure the skin effects in conducting components are accurately captured, without the need for dense meshes and, therefore, offer possible advantages for MIT. Unfortunately, the hierarchic nature of hp–Nédélec basis functions introduces edge and face parameterisations leading to sign conflict issues when enforcing tangential continuity between elements. This work describes a procedure for addressing this issue on general conforming hexahedral meshes and an implementation of a hierarchic hp–Nédélec finite element basis within the deal.II finite element library. The resulting software is used to simulate Maxwell forward problems, including those set on multiply connected domains, to demonstrate its potential as an MIT forward solver