Spatiotemporal filtering using principal component analysis and Karhunen-Loeve expansion approaches for regional GPS network analysis
[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.
Strain and rotation rate from GPS in Tibet, Anatolia, and the Altiplano
[1] Deformation measured by regional GPS networks in continental plateaus reflects the geologic and tectonic variability of the plateaus. For two collisional plateaus (Tibet and Anatolia) and one noncollisional (the Altiplano), we analyze the regional strain and rotation rate by inverting GPS velocities to calculate the full two-dimensional velocity gradient tensor. To test the method, we use gridded velocities determined from an elastic block model for the eastern Mediterranean/Middle East region and show that to a first order, the deformation calculated directly from the GPS vectors provides an accurate description of regional deformation patterns. Principal shortening and extension rate axes, vertical axis rotation, and two-dimensional (2-D) volume strain (dilatation) are very consistent with long-term geological features over large areas, indicating that the GPS velocity fields reflect processes responsible for the recent geologic evolution of the plateaus. Differences between geological and GPS descriptions of deformation can be attributed either to GPS networks that are too sparse to capture local interseismic deformation, or to permanent deformation that accrues during strong earthquakes. The Altiplano has higher internal shortening magnitudes than the other two plateaus and negative 2-D dilatation everywhere. Vertical axis rotation changes sign across the topographic symmetry axis and is due to distributed deformation throughout the plateau. In contrast, the collisional plateaus have large regions of quasi-rigid body rotation bounded by strike-slip faults with the opposite rotation sense from the rotating blocks. Tibet and Anatolia are the mirror images of each other; both have regions of positive dilatation on the outboard sides of the rotating blocks. Positive dilatation in the Aegean correlates with a region of crustal thinning, whereas that in eastern Tibet and Yunnan province in China is associated with an area of vertical uplift. Rollback of the Hellenic trench clearly facilitates the rotation of Anatolia; rollback of the Sumatra–Burma trench probably also enables rotation about the eastern syntaxis of Tibet.
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