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

This article discusses methods for selecting criteria used for stopping iterative regularization methods applied to solving continuation of gravity observed at or outside the Earth's surface down to the geoid. This computational step is required for determination of the gravimetric geoid by the Stokes approach. For surface gravity data measured with spatial resolutions at the kilometer level and higher, their downward continuation becomes ill posed and its solution numerically unstable. Two iterative methods often used for solving this problem, namely the Landweber and conjugate gradient least-squares (CGLS) methods, are investigated using a sample of surface gravity data synthesized from a global gravitational model over a mountainous test area in Colorado, USA. Five different commonly used stopping criteria are applied to both iterative methods and neither of them, except L-curve, succeed to stop the iterative process at the reasonable solution. A simple approach is proposed to stop the iterative methods exploiting stochastic properties of surface gravity data. Results of numerical tests suggest that a rather simple stopping criterion based on stochastics parameters of surface gravity data estimated using a leave-one-out cross-validation procedure yields results superior to those based on the L-curve approach which is best performing among the five standard methods for selecting the stopping criterion. Results based on the Landweber method outperform those based on the CGLS method. Iterative methods based on optimum numbers of iterations represent an alternative to commonly used regularization techniques for solving ill-posed inverse problems, such as Tikhonov, that require optimal estimates of regularization parameters. [ABSTRACT FROM AUTHOR]