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This paper presents a digital linear filter which maps composite resistivity transforms to apparent resistivities for any four-electrode array over a horizontally layered earth. A filter is provided for each of three sampling rates; the choice of filter will depend on resistivity contrasts and computational facilities.Two methods of filter design are compared. The Wiener-Hopf least-squares method is preferable for low sampling rate filters. The Fourier transform method is more successful in producing a filter with a high sampling rate which can handle resistivity contrasts of 100 000 : 1.

Absbnct -Optimization techniques based on natural evolutionary processes, known as genetic algorithms, are applied to the problem of element placement in a discrete linear lattice, which is combinatorial in nature and cannot be analytically optimized. Representation of potential array occupancy patterns as binary vectors allows iterative utilization of numerical models of differential reproduction, crossover and mutation to converge on near-optimal solutions. Results are presented for the placement of 31 elements within a h e a r lattice of 63 locations under the design constraints of center and end position occupancy and bilateral symmetry. "Fitness" of the configuration is given in terms of mainlobe width and sidelobe levels of the corresponding response pattern. When results of multiple optimization runs are compared with expectations of random search, genetic algorithms show greater efficiency, especially when increasingly rarer solutions are sought.

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