HR: 0800h
AN: T41A-04    [Abstracts]
TI: Using Taylor Series for Analyzing Non-uniform Deformation in a GPS Network
AU: * Griffiths, J H
EM: jake.griffiths@noaa.gov
AF: NOAA, National Geodetic Survey, N/NGS22, 1315 East-West Highway SSMC-3 #8104, Silver SPring, MD 20910, United States
AU: Johnson, A M
EM: gotesson@purdue.edu
AF: Purdue University, 550 Stadium Mall Drive, West Lafayette, IN 47907, United States
AB: We have found a way of using Taylor series to distinguish domains of deformation within a Global Positioning System (GPS) or other geodetic network. Taylor's theorem states that any function, f(x,y), possessing continuous derivatives in the domain defined by [xr,xb] and yr yi yb can be expanded for all points (xi, yi) within the domain. The object of Taylor's formula is to express, via Taylor series, the value of the function, f(x,y)i, at some point, (xi, yi), in terms of the values of the function, f(x,y)r, and its derivatives at the reference point, (xr, yr). Our use of Taylor series is rather non-traditional; we use it to define and describe domains of deformation within a GPS network. Our approach consists of six basic steps: 1) Write the first-order Taylor series for the displacements (or velocities) at some point in terms of the diplacements (or velocities) and their derivatives at the reference point 2) Use displacement data from three GPS sites and solve the first-order series at the centroid of the triangle. 3) Store the solution. 4) Add data from a fourth site and re-solve the Taylor series at the same reference point to obtain a new set of first order terms 5) Compare the first-order terms from the two solutions, if the two solutions are indistinguishable at the 95% confidence-level, then the domain is expanded to include the fourth site. 6) Repeat until the network has been analyzed. Compare the number of data points to the number of unknown terms in the next order of Taylor series. If there are enough data to increase the order, then re-write the Taylor series. Of course, it is unwise to let the Taylor series grow to very high order. Some guidance in choosing the maximum order is provided by mechanical equilibrium, which requires that only the fourth derivatives be continuous within a domain. The method is challenged using GPS velocities in central California, where we are able to distinguish and describe the kinematics of different domains of deformation from the Pacific Ocean to the Sierra Nevada.
DE: 6924 Interferometry (1207, 1209, 1242)
DE: 7209 Earthquake dynamics (1242)
DE: 8011 Kinematics of crustal and mantle deformation
DE: 8020 Mechanics, theory, and modeling
SC: Tectonophysics [T]
MN: 2007 Joint Assembly