Three-dimensional magnetotelluric inversion using non-linear conjugate gradients

We have formulated a 3-D inverse solution for the magnetotelluric (MT) problem using the non-linear conjugate gradient method. Finite difference methods are used to compute predicted data efficiently and objective functional gradients. Only six forward modelling applications per frequency are typically required to produce the model update at each iteration. This efficiency is achieved by incorporating a simple line search procedure that calls for a sufficient reduction in the objective functional, instead of an exact determination of its minimum along a given descent direction. Additional efficiencies in the scheme are sought by incorporating preconditioning to accelerate solution convergence. Even with these efficiencies, the solution's realism and complexity are still limited by the speed and memory of serial processors. To overcome this barrier, the scheme has been implemented on a parallel computing platform where tens to thousands of processors operate on the problem simultaneously. The inversion scheme is tested by inverting data produced with a forward modelling code algorithmically different from that employed in the inversion algorithm. This check provides independent verification of the scheme since the two forward modelling algorithms are prone to different types of numerical error.     

Finite-difference modelling of magnetotelluric fields in two-dimensional anisotropic media

An algorithm for the numerical modelling of magnetotelluric fields in 2-D generally anisotropic block structures is presented. Electrical properties of the individual homogeneous blocks are described by an arbitrary symmetric and positive-definite conductivity tensor. The problem leads to a coupled system of partial differential equations for the strike-parallel components of the electromagnetic field. E _x, and H _x These equations are numerically approximated by the finite-difference (FD) method, making use of the integro-interpolation approach. As the magnetic component H _x, is constant in the non-conductive air, only equations for the electric mode are approximated within the air layer. The system of linear difference equations, resulting from the FD approximation, can be arranged in such a way that its matrix is symmetric and band-limited, and can be solved, for not too large models, by Gaussian elimination. The algorithm is applied to model situations which demonstrate some non-trivial phenomena caused by electrical anisotropy. In particular, the effect of 2-D anisotropy on the relation between magnetotelluric impedances and induction arrows is studied in detail.     

Magnetotelluric response of anisotropic 2-D structures

b
The effect of anisotropy on the distribution of Earth's conductivity is evaluated by calculating the electromagnetic response of multilayered 2-D structures. The electric and magnetic fields are expanded in terms of Fourier series, the coefficients being obtained by applying the corresponding boundary conditions on each interface, given by arbitrary analytical functions. Then the results are used to analyse some particular structures.     

A model study of telluric fields in two-dimensional structures

Summary. In recent years telluric sounding has been replaced by MT (magnetotellurics). However, several new purely telluric parameters, besides the traditional Jacobian, have been shown to be efficient geophysical indicators of lateral conductivity variations. A set of typical two-dimensional structures is analysed to demonstrate the resolving power of the new indicators. For such telluric studies, a wide frequency band is a great asset, especially because the indicators are best displayed as pseudo-sections in the frequency domain. However, a wide frequency range is easily achieved when only the telluric field needs to be measured. In MT the magnetic sensing coils often severely reduce the available bandwidth.