STATISTICAL EVALUATION OF ELECTRICAL SOUNDlNG METHODS. PART I: EXPERIMENT DESIGN

Abstract

Traditional experiment design techniques, widely applied to both linear and nonlinear problems in many scientific fields, is applicable to the design of exploration geophysical surveys. The design technique is formulated using the mathematics of the generalized inverse and its construction via eigenvalue decomposition. The design technique is demonstrated by the designing of electromagnetic sounding surveys for a horizontal loop source. The experiment is designed whereby it is determined (1) which one of the electromagnetic field quantities, vertical and horizontal magnetic field amplitudes or phases, and polarization ellipse quantities, tilt angle, and ellipticity, and (2) which set of transmitter and receiver separations and transmitter frequencies, best resolve the conductivities and thicknesses of a given layered earth model. Model resolution is sensitive to the data error. As an example, for different assumed data errors, a model is best resolved in one instance by the phase of the two components of the magnetic field, while in another instance it is best resolved by tilt angle and ellipticity measurements. The best designs are obtained using field measurements made at several transmitter frequencies and at two or more transmitter and receiver separations. The functional relationship between the earth model parameters and the magnetic field quantities is nonlinear. The effect of this nonlinearity on the statistics applied in the method of experiment design has been reported in the literature and is reexamined here. Based on Beale's measure of nonlinearity, the models studied here exhibit adequate linearity to permit use of the linear statistics for experiment design. A study of the eigenvectors and information density matrix provide insight to model parameter correlations and measurement correlations which can be exploited for improving the design of an experiment.