Spatiotemporal filtering using principal component analysis and Karhunen‐Loeve expansion approaches for regional GPS network analysis

Abstract

[1] Spatial filtering is an effective way to improve the precision of coordinate time series for regional GPS networks by reducing so-called common mode errors, thereby providing better resolution for detecting weak or transient deformation signals. The commonly used approach to regional filtering assumes that the common mode error is spatially uniform, which is a good approximation for networks of hundreds of kilometers extent, but breaks down as the spatial extent increases. A more rigorous approach should remove the assumption of spatially uniform distribution and let the data themselves reveal the spatial distribution of the common mode error. The principal component analysis (PCA) and the Karhunen-Loeve expansion (KLE) both decompose network time series into a set of temporally varying modes and their spatial responses. Therefore they provide a mathematical framework to perform spatiotemporal filtering. We apply the combination of PCA and KLE to daily station coordinate time series of the Southern California Integrated GPS Network (SCIGN) for the period 2000 to 2004. We demonstrate that spatially and temporally correlated common mode errors are the dominant error source in daily GPS solutions. The spatial characteristics of the common mode errors are close to uniform for all east, north, and vertical components, which implies a very long wavelength source for the common mode errors, compared to the spatial extent of the GPS network in southern California. Furthermore, the common mode errors exhibit temporally nonrandom patterns.

Coseismic and early postseismic slips associated with the 2011 off the Pacific coast of Tohoku Earthquake sequence: EOF analysis of GPS kinematic time series

“…The GPS time series thus calculated contain significant CMEs, which are considered to be caused by unmodeled, or mismodeled, motions of satellite orbits, reference frame, or earth orientation parameters (Dong et al, 2006). The CMEs were removed prior to the EOF analysis to avoid any leakage of coseismic/postseismic signals into the modes representing CMEs.…”

“…They subsequently used it to extract the interseismic vertical deformation field of the Japanese islands. Dong et al (2006) used EOF analysis to identify/remove the modes corresponding to common mode errors (CMEs) that are often associated with the GPS time series. In the case of the 2011 Tohoku-oki earthquake, Chang and Chao (2011) applied EOF analysis to the GPS kinematic time series obtained from GEONET and identified several modes corresponding to the coseismic, and postseismic, deformations.…”

Improved Constraints on Models of Glacial Isostatic Adjustment: A Review of the Contribution of Ground-Based Geodetic Observations

“…This empirical method, equivalent to a three-parameter Helmert transformation (Dong et al 2006), was shown (see Table 3) to significantly reduce the amplitudes of the flicker and white noise in the time series (Williams et al 2004). A more rigorous approach to the problem using principal component analysis and Karhunen-Loeve expansion was performed by Dong et al (2006) who found that the results were similar to the stacking method because the sites were spatially correlated over large wavelengths. Other groups have also applied empirical orthogonal functions to the problem with similar results (Johansson et al 2002).…”

Observation of Core Phase ScS from the Mw 9.0 Tohoku-Oki Earthquake with High-Rate GPS

“…However, signals retrieved with the PPP approach could be contaminated by common mode error (CME), which may be present for multiple reasons (Dong et al, 2006). CME for time scale of days has been explored, but CME from high-rate GPS for a time scale of one hundred to one thousand seconds are little studied.…”