![]() ![]() A comparison with the proper eigenvalue analysis shows that these criteria provide a fairly reliable view into the conditionality of the problem. We derive two simplified criteria for analysing the conditionality of the discrete downward continuation problem. The eigenvalue analysis of this matrix for a particularly rugged region of the Canadian Rocky Mountains shows that the discrete downward continuation problem is stable once the topographical heights are discretized with a grid step of size 5 arcmin or larger. The posedness of the downward continuation problem is then expressed by means of the conditionality of the matrix of a system of linear equations. The discrete form of Poisson's integral is used to set up the system of linear algebraic equations describing the problem. We investigate the stability of a discrete downward continuation problem for geoid determination when the surface gravity observations are harmonically continued from the Earth's surface to the geoid.
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