Hormoz Jahandari

Forward Modelling of Geophysical Electromagnetic Data on Unstructured Grids Using a Finite-volume Approach

The application of unstructured grids can improve the solution of total field electromagnetic problems as these grids allow efficient local refinement of the mesh at the locations of high field gradients. Unstructured grids also provide the flexibility required for representing arbitrary topography and sub-surface interfaces. This study investigates the generalization of the standard Yees staggered scheme to unstructured tetrahedral-Voronoi grids using a finite-volume approach. We discretize the Helmholtz equation for the electric field in the frequency domain and solve the problem to find the projection of the total electric field along the edges of the tetrahedral elements. To compute the electric and magnetic fields at the observation points an interpolation technique is employed which uses the edge vector interpolation functions of the tetrahedral elements. An example is included which shows the computation of the total and secondary fields due to an electric source in a halfspace that contains an anomalous body. The results show good agreement with those from the literature.

Towards Real Earth Models - Computational Geophysics on Unstructured Tetrahedral Meshes?

Using unstructured tetrahedral meshes to specify 3D geophysical Earth models has a numer of advantages. Such meshes can conform exactly to the triangularly tessellated wireframe surfaces in the 3D Earth models used by geologists. This offers up the possibility of both geophysicists and geologists working with a single unified Earth model. Unstructured tetrahedral meshes are extremely flexible, and so can accurately mimic arbitrarily complicated subsurface structures and topography. Also, in the context of electromagnetic methods, unstructured tetrahedral meshes can be very finely discretized around sources and yet can transition to a coarse discretization in the extremities of the solution domain without, in principle, affecting the quality of the mesh. However, using unstructured tetrahedral meshes for geophysical Earth models has its challenges. The tessellated surfaces in wireframe geological models are often not immediately suitable for computational techniques as they can contain intersecting facets and facets with extreme aspect ratios. Generating tetrahedral meshes that are of sufficient quality from real wireframe geological models can therefore be difficult. This presentation will aim to discuss the pros and cons of using unstructured tetrahedral meshes for geophysical Earth models, keeping in mind the complexities of the real subsurface that we are ultimately trying to represent.

Forward modelling of gravity data for unstructured grids using the finite-volume method

Forward modelling of gravity data in three dimensions by both closed-form formulae and numerical methods is reflected in the recent literature. While the former methods give the exact response and are efficient for a small number of observation points, numerical methods are well-suited for large numbers of points in terms of computation time and are preferred for certain inversion methods due to the sparsity of their resultant matrices. Using unstructured grids to discretize the space increases the capability for modelling underground structures. Methods like finite-volume and finite-element result in robust schemes for such domains. In this study, the Poisson’s equation for gravitational potential is discretized by a finite-volume scheme for tetrahedral grids and their dual Voronoi meshes and a system of equations solved for computing the potential at discrete points inside the grid. Gravity is then computed from the potential by a finite-difference approximation. The accuracies of these schemes are analyzed and their time-efficiency compared with a closed-form formulae method.