Noise in tectonomagnetic experiments caused by geomagnetic variations due to nonlocal sources can be reduced by applying multivariate linear regression to data from a network of magnetometer sites. Residuals obtained by subtracting from the observed values at a particular site the values calculated from a regression expression using the simultaneous values at a number of other sites tend to have nonlocal variations suppressed and hence to emphasize effects local to that particular site. For total field data from central California, at periods greater than a day, this method provided a moderate reduction of the noise below the level obtained by two-site differencing. The effectiveness varied considerably from site to site, with an average improvement in the standard deviation of the corrected time series of roughly a factor of two, compared with two-site differences. It was possible to find regression expressions that remove most of the long-period (T > ~100 days) variations from the available data, although they may not be statistically reliable.