Correlated errors in geodetic time series: Implications for time-dependent deformation

J. Langbein, H. Johnson
U.S. Geological Survey MS 977, 345 Middlefield RD Menlo Park, CA 94025, USA

Abstract:

Analysis of frequent trilateration observations from the two-color EDM networks in California, demonstrate that the noise power spectra are dominated by white noise at higher frequencies and power-law behavior at lower frequencies which contradict prior assumptions that only white noise is present in a geodetic time-series, After removing a linear trend from the two-color data, it becomes evident that there are primarily two recognizable types of time-correlated noise present in the residuals. The first type is a seasonal variation in displacement which is probably a result of measuring to shallow surface monuments installed in clayey soil which responds to seasonally occurring rainfall. The second type of correlated noise becomes evident only after spectral analysis of line-length changes and shows a functional relation at long periods between power and frequency of where f is frequency and . With , this type of correlated noise is termed random-walk noise and its source is mainly thought to be small random motions of geodetic monuments with respect to the Earth's crust, though other sources are possible. Because of problems associated with spectral analysis of these data, we assume that there are only two sources of noise (white noise and random-walk) and use maximum likelihood estimation to measure the size of each component. We find that the random-walk noise level averages about and that our estimates of the white noise component confirm theoretical limitations of the measurement technique. Because of the presence of random-walk noise in these time series, modeling and interpretation of the geodetic data must account for this source of error.

AGU Index Terms: 1294 Geodesy; Instruments and Techniques; 1244 Standards and absolute measurements
Keywords/Free Terms: Geodesy, Error analysis, Monument noise

JGR-Solid Earth 96JB02945
Vol. 102 , No. B1 , p. 591