On the existence of solutions for the method of Bjerhammar in the continuous case

The method of Bjerhammar is studied in the continuous case for a sphere. By varying the kernel function, different types of unknowns (u^*) are obtained at the internal sphere (the Bjerhammar sphere). It is shown that a necessary condition for the existence of u^* is that the degree variances (σ _n ² ) of the observations are of an order less than n⁻². According to Kaula’s rule this condition is not satisfied for the earth’s gravity anomaly field (σ _n ² =n⁻¹) but well for the geopotential (σ _n ² =n⁻³).