Thus, the image recovery is highly ill-posed and the problem is further complicated by the presence of breathing and cardiac motion. 2019 Oct;38(10):2303-2313. doi: 10.1109/TMI.2019.2908140. We are now able to use equivalent regularization approaches on both rectilinear and unstructured meshes, thus ensuring that no functionality is lost when moving to work on unstructured meshes.

Several meshes have been used: (a) and (b) use the regular rectilinear mesh of Lelièvre & Oldenburg (2009); (c) and (d) use a finer regular rectilinear mesh; (e) and (f) use a triangular mesh with an underlying regular rectilinear mesh; (g) and (h) use a fully unstructured triangular mesh. (6) with j = 1.

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We propose a novel navigator-based acquisition scheme which aids the detection of the neighbours of each frame on the manifold. We thank Brandon Reid and Cassandra Tycholiz for developing the Voisey's Bay examples, Robert Eso for his help investigating sensitivity matrix compression strategies for unstructured meshes, Lapo Boschi and anonymous reviewers for their careful and helpful reviews and J. R. Shewchuk and H. Si for making the Triangle and TetGen programs openly available to the scientific community. For 3-D tetrahedral meshes, our approach follows that above for 2-D triangular meshes.

A large amount of drilling has provided a detailed geological model of the subsurface; we have modified some details for illustrative purposes and we use the resulting model, shown in Fig. 5 shows the results of inversions on the two rectilinear and two triangular meshes. Filled circles denote mesh nodes. The BH dataset…, NLM Smoothness is controlled by the choice of the regularization operator and the scaling parameter .. Computationally efficient algorithms that rely on structured cell ordering are then difficult or impossible to implement or apply on unstructured meshes. \Phi _m(\mathbf {m}) &=& \left\Vert \mathbf {W}_s \bigl ( \mathbf {m}- \mathbf {m}_{{\rm ref}} \bigr ) \right\Vert ^2 \nonumber\\
For our second inversion, we assume that a 3-D wireframe model of the troctolite unit has been created from surface and downhole observations.

eCollection 2020. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. equivalent to applying an implicit Euler finite-difference scheme to Result: Our reconstructions on an in-vivo free-breathing ungated cardiac dataset are of comparable quality to a breath-held gated reconstruction. Filled circles denote mesh nodes.

We test our inversion methods on illustrative 2-D examples used in Lelièvre & Oldenburg (2009). 0000012554 00000 n

The magnetics TMI (total magnetic intensity) data are plotted as coloured points corresponding to the colour scale bar to the right.

Is there a Linear Programming Library that natively supports fractions instead of floating point arithmetic? This means that the bound must apply to the smoothness of the worst point of the function, which is not necessarily the average such as L2. 0000051695 00000 n
(2008), Williams (2008) and others have demonstrated the use of such functionality.

The colour bar for all models is at the top: the scale has been set to [−0.01, 0.10] g cc−1 for all models.

The exploration question here is how far the body may extend to depth. 0000024934 00000 n

For this purpose, we do not use the surface from the true model but, instead, generate a rough approximation independently from sparse information.

We used wavelet compression with the Daubechies-2 wavelet with a relative threshold value of 0.05, which achieved a compression ratio of 3.3 (the number of elements in the full matrix divided by the number of wavelet coefficients kept in the compression). The subsurface contains a sulphide unit hosted within a troctolite unit.

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Our model is essentially like that from Lelièvre & Oldenburg (2009) but with part of their lower layer removed on the right.

A second patchwork pattern on a 2-D triangular mesh.

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To aid in comparison, we show scaled magnetic susceptibly values equal to 100 times the recovered susceptibility values, such that the scaled value for the magnetic layers in the true model is 1.0. The outlines of the true bodies are superimposed in black on top of the recovered models.

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© The Authors 2013.

\mathbf {q}&=& ( \mathbf {A}^{\rm {T}}\mathbf {A})^{-1} \mathbf {A}^{\rm {T}}{\omega }\nonumber\\

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Illustration of the weight matrix and the ability of the scheme to enable implicit motion resolved recovery.

\end{equation}, Transdimensional tomography with unknown data noise, Joint inversion of gravity and magnetic data under lithologic constraints, High- and low-resolution images of the earth's mantle: implications of different approaches to tomographic modeling, Renumbering unstructured grids to improve the performance of codes on hierarhical memory machines, Fast solution of geophysical inversion using adaptive mesh, space-filling curves and wavelet compression, Constraining 3-D electrical resistance tomography with GPR reflection data for improved aquifer characterization, Constructing piecewise-constant models in multidimensional minimum-structure inversions, Non-linear inversions using general measures of data misfit and model structure, Geologically constrained gravity inversion for the Voisey's Bay ovoid deposit, Cross-gradients joint 3D inversion with applications to gravity and magnetic data, Joint two-dimensional DC resistivity and seismic travel time inversion with cross-gradients constraints, Hierarchical tree-based finite element mesh generation, Three-dimensional modelling and inversion of DC resistivity data incorporating topography—II.

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