Three-dimensional modelling in magnetotelluric and magnetic variational sounding

Three-Dimensional Electromagnetic Modelling and Inversion from Theory to Application

“…This apparent attraction is counterbalanced by a nontrivial and usually time-consuming construction of the finite elements themselves. The FE approach has been implemented by many developers (Reddy et al, 1977;Pridmore et al, 1981;Paulsen et al, 1988;Boyce et al, 1992;Livelybrooks, 1993;Lager and Mur, 1998;Sugeng et al, 1999;Zunoubi et al, 1999;Ratz, 1999;Ellis, 1999;Haber, 1999;Zyserman and Santos, 2000;Badea et al, 2001;Mitsuhata and Uchida, 2004, among others).…”

Three-dimensional finite-element modelling of magnetotelluric data with a divergence correction

“…They are attractive because they are better suited to unstructured meshes than finite-difference methods, and such meshes enable more faithful representation of topography and realistic subsurface interfaces than rectilinear grids. The first applications of the finite-element method to computing electromagnetic fields in a 3-D subsurface conductivity model used nodal elements: Livelybrooks (1993), Pridmore et al (1981), Reddy et al (1977) and Mogi (1996). These applications all used a rectilinear mesh.…”

“…This is contrary to the true electric field which, because the conductivity is uniform within each cell, is divergence-free within each cell (not containing a source of current or charge). Reddy et al (1977) and Pridmore et al (1981) were aware that the continuity of normal current density between cells of different conductivities was violated in the nodal-element formulation and attempted to asses to what extent it impaired their results. Livelybrooks (1993) enforced continuity of the normal current density between cells of different conductivities by introducing two sets of coincident but distinct nodes on the interface between the cells, and using the continuity of normal current density to relate the normal component of the approximate electric field on one set of nodes to its normal component on the other set of coincident nodes.…”

Numerical Modelling in Geo-Electromagnetics: Advances and Challenges

“…The material properties are assumed to have constant values within each cell. To obtain a sufficiently accurate numerical solution, the grid spacing has to be very dense near a source, which in our case is located at the center of the cube Since then, a number of authors have successfully used the FE method for electromagnetic modelling (Reddy et al 1977;Pridmore et al 1981;Livelybrooks 1993;Zyserman and Santos 2000;Badea et al 2001;Pain et al 2002;Ruecker et al 2006). One of the difficulties in the numerical modelling of electromagnetic field problems using FE is a possible jump of normal components across discontinuities of material properties.…”