Understanding the constraints to the correct application of tilt derivative operation to a vertical prism in gravity data processing

Analytical simulation of a buried 3D vertical square prism with known density contrast, depth to the top of the buried body, thickness and cross-section area has been done, and tilt angle derivative enhancement operation has been applied to the data in order to establish the constraints that could impede the correct application of tilt derivative operation on gravity data. From the tilt derivative map generated for the data, the distances between contours “-45° to + 45°” and “-30° to + 30°” were used to estimate the depth to the bottom and top of the prism respectively. Where the depth estimates differ significantly from the depth values used for the simulation, the grid size was varied until estimated depth values that were in good agreement with the simulated depths were gotten. By revealing that estimated depth values from the tilt derivative operation will not be accurate when the simulated depth to the top or bottom of the buried body is too small or large compared with the grid size, the results enshrined the importance of optimum grid size on the accuracy of the result. The optimum grid size for the research was found to be between 6.6 and 10 times the depth of burial. Based on the analytical simulation, the research concluded that depth estimate results obtained from the tilt derivative analysis of gravity data is only accurate when the grid size of data sample is between 6.6 and 10 times the depth of burial of the target. The best result was obtained when the grid size of data sample is about 7.5 times the depth of burial. Typical tilt-angle derivative map for cases where grid size was adequate and aliasing was avoided. • The depth to the top of a buried square prism can be evaluated as half the distance between −30° and + 30° contour lines (expressed in terms of the scale of the map). • The depth to the bottom of a buried body can be evaluated as half the distance between −45° and + 45° contour lines (expressed in terms of the scale of the map). • Depth results obtained from the tilt derivative analysis of gravity data is only valid when the grid size of data sample is between 6.6 and 10 times the depth of burial of the target.