Solution of the altimetry-gravimetry problem

Unique solvability of the altimetry-gravimetry problem is proved for general ocean configurations and for models which are close to the classical Stokes model provided that a zero-degree component is removed from both gravity anomaly and disturbed potential. Data and solutions are to belong to suitable Sobolev spaces. The theory of pseudodifferential operators plays an important part in the proof. Finite element methods for numerical computations are suggested and convergence rates are estimated. Holota (1980, 1981a, b, 1982) has proved wellposedness of the problem without constraints for small continents by variational methods. The present paper yields wellposedness without any constraints when the diameter of the continental area is smaller than 62°.6. There are strong indications, very disturbing considering the amount of work spent on the method for the last two decades, that the direct least squares approach is unstable for mixed sets of data.