Robust nonlinear inversion of wave-tilt data

A robust method for characterizing homogeneous or layered geophysical media is proposed. It determines the electrical constitutive parameters and the thicknesses of the layers that make up the probed medium by inverting magnetic wave-tilt data collected on or above the ground surface. An algorithm is presented for establishing whether the medium should be considered homogeneous or stratified. An exact analytical solution to the inverse problem of homogeneous media is deduced. The inverse problem of stratified media is solved by a three-layer feedforward neural network. An algorithm is proposed for speeding up the training of the neural network. Compared to the standard back-propagation algorithm, the new algorithm is faster, more robust, and easier to implement both in hardware form and in software form. Also, the new algorithm requires less memory space. Such an algorithm stems from applying a new gradient-based method to the problem of adjusting the free parameters of a feedforward neural network. A versatile network-pruning technique is proposed. It explores the fact that the free parameters of a trained neural network tend to take on values close to their mean. The characteristics of magnetic wave-tilt data are analysed in detail. The insight provided by this analysis helps to properly interpret the results of the inversions.