Grid Of Prisms Research Articles

In-depth 3D magnetic inversion of basement relief

We have developed an iterative, efficient, and stable 3D magnetic inversion method to estimate the depth to the basement of a sedimentary basin, the volume of which is approximated by a grid of rectangular prisms with tops at an arbitrary surface and thicknesses estimated iteratively. To compute the thicknesses corrections at the kth iteration, we first compute an approximate sparse sensitivity matrix in which the nonnull elements of a given line are obtained by differentiating the fitting function at the observation position (which occupies the center of a small moving data window) relative to the thicknesses of the prisms situated inside the window. By moving the data window around, all nonnull elements of all lines are computed. This sparse matrix is used to calculate an approximate Gauss-Newton gradient and an approximate diagonal Gauss-Newton Hessian matrix. Finally, by dividing each element of the gradient vector by the corresponding diagonal element of the approximate Hessian matrix, we obtain the corrections of all parameters at a given iteration. The solution is stable because of (1) the small parameter corrections inherent to the method, combined with the initial estimate at the surface and (2) the application of a moving average operator to the solution. Any magnetization orientation, except horizontal (and parallel to any vertical side of the prisms), yields good results. In the case of magnetization inclinations of approximately 45°, the rectangular prisms may induce spurious ripples on the surface of the estimated relief, which can be eliminated by simultaneously reducing the horizontal dimensions of the prisms and applying an appropriate moving average to the solution. Application of our method to real data in a rift area discloses a confined basin with steep and asymmetric borders, confirming the practical utility of the method.

Geomagnetic inverse modeling to estimate the volume of magnetization in areas with topographic variations

A three-dimensional geomagnetic modeling is proposed to obtain information about a magnetization over topographic area from magnetic total force from land data survey. The model is divided into three-dimensional mesh grid of rectangular prisms that cover a finite depth below topographic elevation. The model parameter is assigned to each prism describing magnetization. A set of linear equations was formulated in terms of volume magnetization for each prism. The inverse calculation is obtained using the solution of over-determined problems. In this inverse calculation over three-dimensional mesh grid, the weighted matrix will be used to determine distribution of volume magnetization in the subsurface and keep the zero value of volume magnetization above the surface. A computer program has been tested with artificial topographic data and applied to digital elevation model of Bandung. The result of the inversion shows the comparison between synthetic model and inverse model to provide several analysis of algorithm performance. The high magnetization value can be characterize using inverse model up to 77% of volume area with average success recovery of model parameter value up to 56%.

Finite-difference time-domain method for three-dimensional grid of hexagonal prisms

The finite-difference time-domain (FDTD) method was applied in a grid of hexagonal prisms, having as objective to yield less numerical anisotropy of phase velocity than the Yee FDTD method (with hexahedral cells). Comparisons of wave propagation are made between the FDTD method with grid of hexagonal prisms and the Yee FDTD method. The theoretical analyses of the numerical anisotropy, dispersion and stability condition are obtained using the Fourier analysis in the FDTD method with grid of hexagonal prisms. Measurements of numerical anisotropy are also accomplished in this FDTD method, and then ones are compared with the results of the Fourier analysis. As a result, the grid of hexagonal prisms yielded somewhat less numerical anisotropy and dispersion than the Yee grid. Additionally, a simplification in compensation of numerical dispersion in the grid of hexagonal prisms may improve on the accuracy and density of mesh for indoor buildings that are large, mainly in the xy-plane.

Robust 3D gravity gradient inversion by planting anomalous densities

We have developed a new gravity gradient inversion method for estimating a 3D density-contrast distribution defined on a grid of rectangular prisms. Our method consists of an iterative algorithm that does not require the solution of an equation system. Instead, the solution grows systematically around user-specified prismatic elements, called “seeds,” with given density contrasts. Each seed can be assigned a different density-contrast value, allowing the interpretation of multiple sources with different density contrasts and that produce interfering signals. In real world scenarios, some sources might not be targeted for the interpretation. Thus, we developed a robust procedure that neither requires the isolation of the signal of the targeted sources prior to the inversion nor requires substantial prior information about the nontargeted sources. In our iterative algorithm, the estimated sources grow by the accretion of prisms in the periphery of the current estimate. In addition, only the columns of the sensitivity matrix corresponding to the prisms in the periphery of the current estimate are needed for the computations. Therefore, the individual columns of the sensitivity matrix can be calculated on demand and deleted after an accretion takes place, greatly reducing the demand for computer memory and processing time. Tests on synthetic data show the ability of our method to correctly recover the geometry of the targeted sources, even when interfering signals produced by nontargeted sources are present. Inverting the data from an airborne gravity gradiometry survey flown over the iron ore province of Quadrilátero Ferrífero, southeastern Brazil, we estimated a compact iron ore body that is in agreement with geologic information and previous interpretations.

A User-editable C1-Continuous 2.5D Space Deformation Method For 3D Models

Shape deformation methods are important in such fields as geometric modeling and computer animation. In biology, modeling of shape, growth, movement and pathologies of living microscopic organisms or cells require smooth deformations, which are essentially 2D with little change in depth. In this paper, we present a 2.5D space deformation method. The 3D model is modified by deforming an enclosing control grid of prisms. Spline interpolation is used to satisfy the smoothness requirement. We implemented this method in an editor which makes it possible to define and modify the deformation with the mouse in a user-friendly way. The experimental results show that the method is simple and effective.