This article describes a method that aims to incorporate the systematic as well as stochastic variations of the background radiation. We introduce a weighted moving average where the weights are calculated from existing AGS data, supplied by the Geological Survey of Sweden. To test the method we chose an area with strong background gradients, especially in the thorium component. Within the area we identified two roads which pass through the high-variability locations. The proposed method is compared with an unweighted moving average. The results show that the weighting reduces the excess false positives in the positive background gradients without introducing an excess of failures to detect a source during passage in negative gradients.