Construction of regional geoid using a virtual spherical harmonics model

Abstract

Abstract The spherical cap harmonics (SCH) method can be used in regional geoid modeling. The core of this approach is the computation of its associated Legendre functions (ALF) with non-integer degree. However, it is unlikely to obtain a large number of zero-root values for the non-integer ALF. To overcome this problem, a new approach called virtual spherical harmonics (VSH) is proposed in this paper to transform the cap range into the whole sphere so that unlimited numbers of zero-root values can be obtained. The new approach was tested using four cap ranges with the radii of {30^{\circ }}, {15^{\circ }}, {10^{\circ }} and {5^{\circ }}, and geoid undulations for each of the regions are calculated from EGM2008. For each of the regions, the geoid undulations were used to construct three models with three different degrees of 20, 30 and 40. Numerical results showed that with the increase in the degree of the VSH model, the value of the maximum error decreases; and the maximum error of the model was less than 1 mm while the maximum degree is 40.