A generalized method for various data processing techniques in gravity interpretation

Summary

The various data processing techniques (downward continuation, first and second derivatives and their downward continuation) used in gravity interpretation, are analogous to different types of linear filtering operations whose theoretical filter (amplitude) responses can be derived from$(u^2 + v^2 )^{N/2} \exp (d\sqrt {u^2 + v^2 } )$ by suitably choosingN andd, whereu andv are angular frequencies in two perpendicular directions,d the height or depth of continuation in unit of grid interval; andN denotes the order of the vertical derivative. By incorporating a mathematical smoothing function,$e^{ - \lambda (u^2 + v^2 )}$ (λ being the smoothing parameter) in the theoretical filter response function, it has been possible, by selecting a suitable value of smoothing parameter, to establish an approximate equivalence of the effect of the mathematical smoothing with the inherent smoothing introduced, because of the numerical approximation (approximation error) for practically all data-processing techniques. This approximate equivalence leads to a generalized method of computing sets of weight coefficients for various data-processing techniques from filter response matching method. Several sets of weight coefficients thus have been computed with different smoothing parameter. The amplitude response curves of the various existing sets of weight coefficients have also been calculated for assessing the quality of the approximation in achieving the desired filtering operation.