Assessment of Aliasing Errors in Low-Degree Coefficients Inferred from GPS Data

With sparse and uneven site distribution, Global Positioning System (GPS) data is just barely able to infer low-degree coefficients in the surface mass field. The unresolved higher-degree coefficients turn out to introduce aliasing errors into the estimates of low-degree coefficients. To reduce the aliasing errors, the optimal truncation degree should be employed. Using surface displacements simulated from loading models, we theoretically prove that the optimal truncation degree should be degree 6-7 for a GPS inversion and degree 20 for combing GPS and Ocean Bottom Pressure (OBP) with no additional regularization. The optimal truncation degree should be decreased to degree 4-5 for real GPS data. Additionally, we prove that a Scaled Sensitivity Matrix (SSM) approach can be used to quantify the aliasing errors due to any one or any combination of unresolved higher degrees, which is beneficial to identify the major error source from among all the unresolved higher degrees. Results show that the unresolved higher degrees lower than degree 20 are the major error source for global inversion. We also theoretically prove that the SSM approach can be used to mitigate the aliasing errors in a GPS inversion, if the neglected higher degrees are well known from other sources.