A least-squares standard deviation method to interpret gravity data due to finite vertical cylinders and sheets

We have developed a least-squares approach to determine simultaneously the depth to both the top and base of a buried finite vertical cylinder (vertical line element approximation) and a 2-D vertical thin sheet from moving average residual anomaly profiles obtained from gravity data using filters of successive window lengths. The method involves using a relationship between the depth to the top, and base of the source and a combination of windowed observations. The method is based on computing the standard deviation of the depths to the top, determined from all moving average residual anomalies for each value of the depth to the base. The standard deviation may generally be considered a criterion for determining the correct depth to the top and base of the buried structure. When the correct depth to the base value is used, the standard deviation of the depths to the top is less than the standard deviation using incorrect values of the depth to the base. This method can be applied to residuals as well as to the observed gravity data. The method is applied to synthetic examples with and without random errors and tested on two field examples from the USA and Canada.