Numerical behaviour of the downward continuation of gravity anomalies

Abstract

The numerical results of downward continuation (DWC) of point and mean gravity anomalies by the Poisson integral using point, single mean, and doubly averaged kernel are examined. Correct evaluation of the integral in its innermost zone is a challenging task. To avoid instabilities, an analytical planar approximation is used in the innermost integration zone. In addition it is shown that the single mean mode has the minimum discretization error. Downward continuation of point and mean anomalies by singly and doubly averaged kernel are the same mean anomalies on the geoid.

Planar, spherical and ellipsoidal approximations of Poisson's integral in near zone

“…Therefore the Poisson kernel, at epicenter with almost zero height, will have an extremely large value. The use of the mean Poisson kernel, K , is one practical way of solving this problem as it will be more stable than the Poisson kernel K (Sun and Vanícek, 1998;Sun, 2003, Goli, et al, 2010. It can be evaluated by breaking the cell of epicenter into very small cells.…”

“…Different discretization models, point-point, mean-mean, and point-mean have been proposed by researchers: Vanícek et al, 1996, Martinec, 1996, Sun and Vanícek, 1998, Huang, 2002, Sun, 2003, Goli, et al, 2010. In the point-point model, point surface anomalies are downward continued to the point anomalies on the geoid.…”

On estimation of stopping criteria for iterative solutions of gravity downward continuation

“…As scattered surface gravity observations are not regularly distributed, they are usually averaged and/or interpolated to a regular coordinate grid for the numerical convenience and noise reduction. For details on various discretization schemes for continuation of gravity anomalies, see, e.g., (Vaníček et al, 1996;Huang, 2002;Huang et al, 2003;Goli et al, 2011).…”