Use of High Performance Computing for the Rigorous Estimation of Very High Degree Spherical Harmonic Gravity Field Models

The estimation of the global Earth’s gravity field parameterized as a finite spherical harmonic series is computationally demanding. The computational effort depends on the one hand on the maximal resolution of the spherical harmonic expansion and on the other hand on the number of observations which might be several millions. All global high-resolution Earth’s gravity field models currently available above degree and order 360 were computed introducing approximations, significantly reducing the numerical complexity. For example, the prerequisites for the orthogonality of the spherical harmonic base functions, leading to a block diagonal system of normal equations, are often introduced artificially by working with equally distributed data along parallels assuming constant accuracy. These methods do not allow for a complex modeling of the observation errors, or the inclusion of redundant observations. Within this contribution, we demonstrate how high-performance computers can be used for very high degree gravity field determination without introducing approximations. In addition, complex modeling of the observation errors is made possible within the algorithm to derive consistent error estimates for the spherical harmonic coefficients. Based on the high performance computing library ScaLAPACK, a gravity field solver was implemented which allows for the estimation of high degree gravity fields (e.g. degree and order 720, resulting in more than 500, 000 unknown parameters) from various data sources with the direct solution method using assembly and solution of full normal equations.