A least-squares standard deviation method to interpret magnetic anomalies due to thin dikes

We have developed a least-squares method to determine simultaneously the depth and the horizontal position (origin) of a buried thin dike that extends in both strike direction and down dip (2D) and in which the depth is much greater than the thickness from horizontal gradients obtained numerically from magnetic data using filters of successive window lengths. The method involves using a relationship between the depth and the horizontal position of the source and a combination of windowed observations. The method is based on computing the standard deviation of the depths determined from all horizontal gradient anomalies for each horizontal position. The standard deviation may generally be considered as a criterion for determining the correct depth and the horizontal position of the buried dike. When the correct horizontal position value is used, the standard deviation of the depths is less than the standard deviation using incorrect horizontal position values. This method can be applied to residuals as well as to the observed magnetic data. The method is applied to synthetic examples with and without random errors. The present method was able to provide both the depth and horizontal position of the source accurately. The practical utility of the method is tested on an outcropping dike in Canada.