A Comparison of Different Integral-Equation-Based Approaches for Local Gravity Field Modelling: Case Study for the Canadian Rocky Mountains

Abstract

We compare the accuracy of local gravity field modelling in rugged mountains using three different discretised integral equations; namely (1) the single layer approach, (2) Poisson’s integral approach, and (3) Green’s integral approach. The study area comprises a rough part of the Canadian Rocky Mountains with adjacent plains. The numerical experiment is conducted for gravity disturbances and for topographically corrected gravity disturbances. The external gravity field is parameterized by gravity disturbances (Poisson’s integral approach) and disturbing potential values (Green’s integral approach), both discretised below the data points at the same depth beneath the Bjerhammar sphere. The point masses in the single layer approach are discretised below the data points on a parallel surface located at the same depth beneath the Earth’s surface. The accuracy of the gravity field modelling is assessed in terms of the STD of the differences between predicted and observed gravity data. For the three chosen discretisation schemes, the most accurate gravity field approximation is attained using Green’s integral approach. However, the solution contains a systematic bias in mountainous regions. This systematic bias is larger if topographically corrected gravity disturbances are used as input data.