A method for pattern completion based on the application of artificial neural networks and possessing many operational objectives of the ordinary kriging approach, neural kriging, is developed. A neural kringing (NK) network id described, implemented in a parallelizing algorithm, and applied to develop maps of discrete spatially distributed fields (e.g., log hydraulic conductivity). NK is, in the case of two discrete field values, similar to indicator kriging. It uses a feed-forward counterpropagation training approach because field observations are available and because fast yet reliable results are obtained. NK is data-driven and requires no estimate of a convariance function. The optimal design of the NK network is found to depend on the number of hidden units in a more complex way than expected. The quality of the estimate of each pixel of the NK maps can be presented as well, as in kriging, to help identify areas in which additional information will be most beneficial. A comparison with a reference field shows that the NK network produces unbiased errors relative to sample bias and reproduces the variogram of a quantized random field with reasonable accuracy.

Ordinary kriging (OK) followed by quantization can also perform well; however, estimation errors in the variogram selected for use in OK (in this case the range coefficient in particular) must be carefully examined and treated. The NK method can provide multiple realizations of the estimated field, all of which respect observations; hence conditional simulation is demonstrably possible. The combination of simplicity, interpolation, reasonably accurate prediction statistics, ability to provide conditional simulations, and computational speed suggest that artificial neural networks can be useful tools in geohydrology when applied to specific well-defined problems for which they are suited, such as aquifer characterization. ¿American Geophysical Union 1994