## 1. Introduction

[2] As with many other geophysical phenomena, noise in GPS position time series can be described as a power law process [*Mandelbrot*, 1983; *Agnew*, 1992], or one with time domain behavior that has power spectrum of the form

where *f* is the temporal frequency, *P*_{0} and *f*_{0} are normalizing constants, and κ is the spectral index [*Mandelbrot and Van Ness*, 1968]. Naturally occurring processes often have more power at low frequencies compared to higher frequencies and have negative indices ranging from −3 < κ < −1. Such nonstationary processes, including classical Brownian motion (or “random walk”) with κ = −2 (or *P*_{x} ∝ 1/*f*^{2}) are called “fractional Brownian motions.” Stationary processes with −1< κ < 1, including the special case of uncorrelated white noise (κ = 0, *P* is flat), are called “fractional Gaussian” processes. The special case of κ = −1 (or *P*_{x} ∝ 1/*f*) called “flicker” noise is commonly observed in a wide variety of dynamical processes, including sunspot variability, the wobble of the Earth about its axis, undersea currents, and uncertainties in time measured by atomic clocks [*Gardner*, 1978; *Mandelbrot*, 1983].

[3] It is important to understand the noise content of GPS position data so that realistic uncertainties can be assigned to parameters estimated from them. The assumption that the noise is purely white leads, for example, to grossly underestimated site rate uncertainties. *Zhang et al.* [1997] concluded that rate uncertainties were 3–6 times greater when the preferred white plus flicker noise model was used instead of the white noise only model. Likewise, *Mao et al.* [1999] concluded that their rate uncertainties were underestimated by as much as an order or magnitude if they neglected the correlated noise. The estimate of the standard error in rate is dependent upon several parameters of power law noise including the amplitude, spectral index, and sampling interval [*Williams*, 2003a]. It is clear that the assumed noise type greatly affects the resulting rate uncertainty, and so an important part of deriving crustal motion models from GPS data is to classify and quantify the noise components.

[4] While analyzing the noise in GPS time series is important for providing realistic parameter uncertainties, it does not provide a means for reducing that noise. However, classification of the noise components can provide clues as to the source of the noise and point to the right fields of research to help increase the accuracy and precision. For example, geodetic monument instability due to varying conditions of the anchoring media (e.g., soil, bedrock, buildings) is considered an important source of noise, thought to follow a random walk process [*Johnson and Agnew*, 1995]. Therefore some continuous GPS arrays have adopted very expensive deep drill braced monuments [*Wyatt et al.*, 1989] as the preferred approach to minimize this error source [e.g., *Bock et al.*, 1997; *Wernicke et al.*, 2000]. The new western North America Plate Boundary Observatory (PBO) [*Silver et al.*, 1999] is planning to install about 850 new continuous GPS monuments using the deep drill braced monument designed by F. Wyatt for SCIGN and adopted by other continuous GPS (CGPS) networks in this region. An error analysis of existing CGPS time series, some with histories of over a decade, can help to distinguish if these monuments are necessary, or whether other much less expensive solutions are sufficient.

[5] The presence of a spatially correlated, common mode, positioning error in GPS time series [*Wdowinski et al.*, 1997] has, to a certain extent, divided GPS time series analysis into two types, global and regional, which mirrors the global and regional nature of GPS networks. Where there is a network of sites with sufficiently small baseline distances, the common mode signal can be reduced either by the use of a filtering algorithm (also known as stacking) [*Wdowinski et al.*, 1997] or by the use of a regional reference frame and daily Helmert transformations [e.g., *Hurst et al.*, 2000]. In the case of a globally distributed set of sites the baseline distances are generally so large that the sites are considered to be uncorrelated from each other. The common mode noise cannot therefore be reduced, and the noise in the series is typically higher than for regional networks [*Mao et al.*, 1999].

[6] The work presented here follows from previous studies in this field. The time between this study and those previous studies has allowed us to collect longer time series, a recognized shortcoming in the previous work. In addition, we have attempted to analyze a greater number of sites, both global and regional, from several different GPS solutions to hopefully gain a bigger insight into the nature of the noise components.