Downward continuation of the gravitational gradient components to gravitational field quantities by spheroidal spectral combination technique

The spectral combination method or technique encompasses all procedures to combine heterogeneous datasets by spectral weights, which depend on spherical harmonic degree n. This method was developed primarily to combine a global geopotential model (GGM) with terrestrial gravity data that is transformed into the gravity potential by integral formulas. Later, this method was extended to combine solutions to boundary-value problems (BVPs). The spectral combination method is based on the stochastic characteristics of measured gravity data, i.e., their signal and error degree-order variances. This technique represents the integral transform, in which the integral kernel is modified by spectral weights determined by the least-squares method.

So far, the spectral combination method has been applied only to solutions to spherical BVPs. In this contribution, we extend this method to solutions of vertical and horizontal spheroidal BVPs. Solutions of vertical and horizontal spheroidal BVPs for the gravitational potential have been presented by (Šprlák and Tangdamrongsub, 2018). Here, we derive corresponding solutions of vertical and horizontal spheroidal BVPs for first-, second- and third-order directional derivatives. Secondly, we derive the spectral weights for the corresponding solutions of vertical and horizontal spheroidal BVPs. Finally, we check the numerical correctness of the derived solutions of vertical and horizontal spheroidal BVPs and spectral weights in a closed-loop test with data from GGM.