On the synthesis of a large geomagnetic array from small overlapping arrays

We describe a general method for combining multiple station transfer function results (i.e., uniform source response space estimates) from a large number of overlapping small geomagnetic arrays, to produce an estimate of the uniform source response for a large synthetic array. The resulting synthesized response can be used to plot anomalous magnetic fields in a region covered by the non-simultaneous arrays. We show that this general array synthesis problem can be approximately reduced to a fairly simple non-linear least-squares problem. Because the number of parameters is very large, we develop a specialized and efficient estimation scheme which exploits the special structure of the problem. We also discuss the computation of a large sample approximation to the covariance matrix of the earth response parameters. While the method has been developed for combining non-simultaneous arrays, it can also be used to ‘patch up’ large simultaneous arrays with some missing data. Both aspects of the method are illustrated on an overlapping set of 19 three-five-station three-component magnetovariational arrays from southwestern Washington. Results from the synthetic 49 station three-component array are discussed briefly.