# Mathematical Modelling

• Kalyan Kumar Roy
Chapter
Part of the Springer Geophysics book series (SPRINGERGEOPHYS)

## Abstract

In this chapter, a few topics on mathematical modelling used as a forward model for inversion of geoelectrical data are presented. Brief coverage is restricted mostly to 2D and 3D problems. The topics covered are (i) the finite element method, (ii) the finite difference method, (iii) the integral equation method, (iv) thin sheet modelling and (v) hybrids. In the finite element method, the mathematical formulations are presented for (i) the energy minimization method using the concept of virtual work and variational calculus and (ii) Galerkin’s method, as well as brief mention of Galerkin’s weights using isoparametric elements and natural coordinates. In the finite difference method, Fomenko and Mogi’s 3D problem in staggered grid, as well as for plane-wave electromagnetics (magnetotellurics) is discussed. In the integral equation method, the mathematical formulations using scalar and tensor Green’s functions are discussed briefly. Ting and Hohmann’s 3D problem is presented as an example. Thin sheet modelling generally deals with modelling a very large portion of the Earth. In thin sheet modelling, Ranganayaki and Madden’s Model is presented as an example. Regarding hybrids, the Lee, Pridmore and Morrison’s model is presented.

## Keywords

Mathematical modelling Geophysical data interpretation

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