Spectral Combination in Vector Gravimetric Boundary Value Problems

f there are more than a unique type of boundary value problem, so there may not be just one solution for problem. The vector gravimetric boundary value problem is one of the types of such problems which include two integral solutions. In this paper, this problem is solved in spectral domain, and then the solutions will be converted to integrals in spatial domain. The kernels of these integrals are divergent but by using spectral combination they become convergent and even they will have the downward continuation property. To do so, different stochastic estimators for recovering the disturbing potential at sea level are presented, and for each one of them the spectral coefficients are derived. Numerical computations show that the convergent kernels have the property of modifying the integral formulas in addition to the downward continuation and Wiener filtering, so that the kernels are well-behaved and reduce the contributions of far-zone data easily. The method presented in this paper can be applied for combination of satellite or air-borne vector gravimetric data.