Potential Coefficient and Anomaly Degree Variance Modelling Revisited

摘要

The decay of the power spectrum of the earth's gravitational potential is modeled using the GEM 10B solution of NASA and a solution complete to degree 180 at OSU. The modelling was first done using the form of A/lb where A and B were parameters determined by various adjustment techniques. For degrees 3 through 36, the best estimate of A is .0000106 and B = 2.17 based on the GEM 10B data. Earlier models by Kaula and Tscherning/Rapp contain too much power as compared to the actual field beyond degree 8. If B were fixed at either 2 or 2.5, the best fit for the range 3 to 36 is obtained with B = 2. Anomaly degree variance models were also computed from the anomaly degree variances of the 180 solution and other data such as a point anomaly variance, and a horizontal gradient variance. With this data, we found that the parameters of the earlier Tscherning/Rapp model are still valid provided one is willing to accept a high gradient variance. Excellent fit to all data types is obtained with the two component model suggested by Moritz and described in detail by Jekeli. All models used in the study, and models by Wagner/Colombo and Heller/Jordan are compared in terms of common parameters such as point anomaly variance, gradient variance, undulation variance and fits to observed potential coefficient variations. (Author)