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In the winter of 1811-12, three of the most powerful earthquakes in U.S. history struck the New Madrid region of the central United States. Because events similar to these have tremendous destructive power were they to occur today, much work has been done in recent years to assess recurrence intervals, strain accumulation, and fault displacements within the New Madrid seismic zone (NMSZ). Paleoseismological field evidence is consistent with significant earthquakes occurring every 500 to 800 years. Using these recurrence intervals, the predicted peak ground acceleration expected in 50 years at 2% probability for the NMSZ exceeds that of San Francisco.

To assess surface strain accumulation in the New Madrid seismic zone, investigators began Global Positioning System (GPS) geodetic studies in the region in the 1990’s. Recent results are consistent with little or no motion within error. The apparent low rates are difficult to reconcile with interpretations of high earthquake recurrence intervals from paleoseismology (Figure 1). Recently, attention has been directed to models in which far-field stresses act on either a lower crustal detachment fault or zone of weakness. Both models predict small average strain rates, ~1x10-8 per year, that are difficult to detect with geodetic techniques despite the significant probability of another large-magnitude event in the next few to several hundred years. To compound the problem, errors associated with monument instability, atmospheric variability, measurement accuracy, observation interval, and site distribution may overwhelm the tectonic signal.

Monument motion is likely significant in the NMSZ, which is dominated by unconsolidated sediments of the Lower Mississippi Valley. Detailed study of the error budget, however, has not been undertaken to date within the NMSZ. We are conducting a systematic analysis of monument stability and noise characteristics for selected sites in the NMSZ to constrain errors associated with continuous and campaign sites. The purpose is twofold: 1) to assess quantitatively noise related to monument motion in different geological substrates; and 2) to evaluate the suitability of different monument types in low strain environments. Work is done in collaboration with Bob Smalley of CERI (Center for Earthquake Research and Information) at the University of Memphis who maintains a network of continuous GPS stations within the NMSZ (Figure 2).

All geodetic data, including GPS velocity estimates, contain both colored, or time-correlated, and white, or time independent, noise. Because several years may be required to obtain accurate site velocity estimates from GPS data time series in areas of small strain, a variety of errors with different timescales may corrupt the data. In addition, the nature of the error source may change with time. Time-correlated noise includes effects associated with potential monument motion, satellite orbit uncertainties, and atmospheric and local environmental variables. Although frequent measurement and averaging can minimize white noise, these methods are less useful for time-correlated noise. Models that incorporate only white noise, however, underestimate the uncertainty. Regionally correlated noise can be reduced by implementation of a filtering algorithm that subtracts the common mode, nontectonic signals from the GPS time series. This method is most applicable to a relatively dense network of continuous sites. Monument instability is an important noise source in geodetic studies and is likely a substantial source of time-correlated noise in long-term GPS experiments, introducing spurious position shifts unrelated to tectonic signals. Assumptions of monument behavior generally are not well constrained, particularly for different types of monuments in various geologic settings.

We examined data from the International GPS Service for Geodynamics global tracking site at North Liberty, Iowa (NLIB) (Figure 3) located ~700 km NW of the NMSZ, which should reflect in a general way some of the time-correlated noise characteristics, such as those related to seasonal atmospheric variability and orbit precession, that we would expect for new and existing NMSZ CGPS sites. In order to examine the potential error sources in the NLIB time series, several methods were employed. First, the residual time series were subjected to spectral analysis using standard Fast Fourier Transform (FFT) techniques implemented as software modules in GMT. FFT techniques are optimal for finite datasets with uniformly spaced continuous samples. In the case of NLIB, nearly 93% of the possible daily solution residuals are available for spectral analysis, making it well-suited for the FFT method. Spectral power was calculated in 512 discrete frequency bins from 185.18 cycles/yr (0.0054 yr or ~2 days) to 0.36 cycles/yr (2.78 yr) for each geodetic component residual (Figure 4). The resultant power spectrum was then fit over this frequency range, assuming that it follows a simple power law relationship of the form y=ax-k. The exponent, k, is often referred to as the spectral index of the phenomenon and high values indicate relative smoothness of the process being studied. For example, it is well known that classical white (time invariant) noise has a k of 0, while flicker (time-correlated) noise has a k of 1. Values between 0 and 1 are commonly referred to as “colored noise,” as it has characteristics of both end-members. Brownian, or random walk, processes have a k of 2. As seen in Figure 4, our derived k for NLIB is ~0.5±0.2. The k’s are similar for all three components, suggesting that a common phenomenon is responsible for the noise characteristics in all three geodetic components. We note, however, that our analysis treats each component residual as independent, when, in fact, they are highly correlated.

We illustrate the impact of a range of 1.5 to 4 mm/√yr for random walk noise on the total error budget for the NLIB north component. We used white noise and flicker noise values derived from a maximum likelihood estimator (MLE) algorithm (Figure 5). The MLE code module returns the average of the 5 maximum values calculated for the entire NLIB dataset. The data are binned according to the total number of available observations; for the 5.77 yr NLIB time series, 126 estimates are generated. Using the calculated white noise of 3.3 mm/yr and flicker noiseof 4.9 mm/yr and a conservative maximum estimate of white noise of 4.0 mm/√yr, we can see that the total noise remains above 5 mm/yr even after 10 years of continuous GPS observations. The total noise of the east and vertical components will be 1.5 to 3 times worse. As shown in Figure 5, the random walk component in the overall error will become dominant after 0.72 and 5.14 years if random walk noise is 4.0 mm/√yr or 1.5 mm/√yr, respectively. The implications of this are twofold: first, it may be difficult to derive good estimates for random walk noise less than 5 years in length; and second, if the expected velocity signal is small, as is the case for the NMFZ, then monument design and site location become critical, if we expect to obtain geophysically meaningful results within the next 20 years.

Our objectives are:
• to install two sets of two monuments each along a baseline < 10 km long in the NMSZ to measure monument instability:
• to determine if monument motion for existing pillars in the NMSZ is similar in magnitude to that of the reference sites through analysis of colored noise and random walk motion;
• to assess potential errors associated with different spatial subsets of the total NMSZ network;
• to compare results from measurements in the NMSZ with those from the Caribbean region for both bedrock and unconsolidated sediment sites to determine if the magnitude of errors are comparable in the two regions and
• to evaluate the contribution of seasonal effects and tropospheric wet delay variability to data uncertainties.

Current funding provided by USGS-NEHRP, NASA.

GPS geodesy in the New Madrid Seismic Zone: an investigation of monument stability and error sources

In the winter of 1811-12, three of the most powerful earthquakes in U.S. history struck the New Madrid region of the central United States. Because events similar to these have tremendous destructive power were they to occur today, much work has been done in recent years to assess recurrence intervals, strain accumulation, and fault displacements within the New Madrid seismic zone (NMSZ). Paleoseismological field evidence is consistent with significant earthquakes occurring every 500 to 800 years. Using these recurrence intervals, the predicted peak ground acceleration expected in 50 years at 2% probability for the NMSZ exceeds that of San Francisco. To assess surface strain accumulation in the New Madrid seismic zone, investigators began Global Positioning System (GPS) geodetic studies in the region in the 1990’s. Recent results are consistent with little or no motion within error. The apparent low rates are difficult to reconcile with interpretations of high earthquake recurrence intervals from paleoseismology (Figure 1). Recently, attention has been directed to models in which far-field stresses act on either a lower crustal detachment fault or zone of weakness. Both models predict small average strain rates, ~1x10-8 per year, that are difficult to detect with geodetic techniques despite the significant probability of another large-magnitude event in the next few to several hundred years. To compound the problem, errors associated with monument instability, atmospheric variability, measurement accuracy, observation interval, and site distribution may overwhelm the tectonic signal. Monument motion is likely significant in the NMSZ, which is dominated by unconsolidated sediments of the Lower Mississippi Valley. Detailed study of the error budget, however, has not been undertaken to date within the NMSZ. We are conducting a systematic analysis of monument stability and noise characteristics for selected sites in the NMSZ to constrain errors associated with continuous and campaign sites. The purpose is twofold: 1) to assess quantitatively noise related to monument motion in different geological substrates; and 2) to evaluate the suitability of different monument types in low strain environments. Work is done in collaboration with Bob Smalley of CERI (Center for Earthquake Research and Information) at the University of Memphis who maintains a network of continuous GPS stations within the NMSZ (Figure 2). All geodetic data, including GPS velocity estimates, contain both colored, or time-correlated, and white, or time independent, noise. Because several years may be required to obtain accurate site velocity estimates from GPS data time series in areas of small strain, a variety of errors with different timescales may corrupt the data. In addition, the nature of the error source may change with time. Time-correlated noise includes effects associated with potential monument motion, satellite orbit uncertainties, and atmospheric and local environmental variables. Although frequent measurement and averaging can minimize white noise, these methods are less useful for time-correlated noise. Models that incorporate only white noise, however, underestimate the uncertainty. Regionally correlated noise can be reduced by implementation of a filtering algorithm that subtracts the common mode, nontectonic signals from the GPS time series. This method is most applicable to a relatively dense network of continuous sites. Monument instability is an important noise source in geodetic studies and is likely a substantial source of time-correlated noise in long-term GPS experiments, introducing spurious position shifts unrelated to tectonic signals. Assumptions of monument behavior generally are not well constrained, particularly for different types of monuments in various geologic settings. We examined data from the International GPS Service for Geodynamics global tracking site at North Liberty, Iowa (NLIB) (Figure 3) located ~700 km NW of the NMSZ, which should reflect in a general way some of the time-correlated noise characteristics, such as those related to seasonal atmospheric variability and orbit precession, that we would expect for new and existing NMSZ CGPS sites. In order to examine the potential error sources in the NLIB time series, several methods were employed. First, the residual time series were subjected to spectral analysis using standard Fast Fourier Transform (FFT) techniques implemented as software modules in GMT. FFT techniques are optimal for finite datasets with uniformly spaced continuous samples. In the case of NLIB, nearly 93% of the possible daily solution residuals are available for spectral analysis, making it well-suited for the FFT method. Spectral power was calculated in 512 discrete frequency bins from 185.18 cycles/yr (0.0054 yr or ~2 days) to 0.36 cycles/yr (2.78 yr) for each geodetic component residual (Figure 4). The resultant power spectrum was then fit over this frequency range, assuming that it follows a simple power law relationship of the form y=ax-k. The exponent, k, is often referred to as the spectral index of the phenomenon and high values indicate relative smoothness of the process being studied. For example, it is well known that classical white (time invariant) noise has a k of 0, while flicker (time-correlated) noise has a k of 1. Values between 0 and 1 are commonly referred to as “colored noise,” as it has characteristics of both end-members. Brownian, or random walk, processes have a k of 2. As seen in Figure 4, our derived k for NLIB is ~0.5±0.2. The k’s are similar for all three components, suggesting that a common phenomenon is responsible for the noise characteristics in all three geodetic components. We note, however, that our analysis treats each component residual as independent, when, in fact, they are highly correlated. We illustrate the impact of a range of 1.5 to 4 mm/√yr for random walk noise on the total error budget for the NLIB north component. We used white noise and flicker noise values derived from a maximum likelihood estimator (MLE) algorithm (Figure 5). The MLE code module returns the average of the 5 maximum values calculated for the entire NLIB dataset. The data are binned according to the total number of available observations; for the 5.77 yr NLIB time series, 126 estimates are generated. Using the calculated white noise of 3.3 mm/yr and flicker noiseof 4.9 mm/yr and a conservative maximum estimate of white noise of 4.0 mm/√yr, we can see that the total noise remains above 5 mm/yr even after 10 years of continuous GPS observations. The total noise of the east and vertical components will be 1.5 to 3 times worse. As shown in Figure 5, the random walk component in the overall error will become dominant after 0.72 and 5.14 years if random walk noise is 4.0 mm/√yr or 1.5 mm/√yr, respectively. The implications of this are twofold: first, it may be difficult to derive good estimates for random walk noise less than 5 years in length; and second, if the expected velocity signal is small, as is the case for the NMFZ, then monument design and site location become critical, if we expect to obtain geophysically meaningful results within the next 20 years. Our objectives are: • to install two sets of two monuments each along a baseline < 10 km long in the NMSZ to measure monument instability: • to determine if monument motion for existing pillars in the NMSZ is similar in magnitude to that of the reference sites through analysis of colored noise and random walk motion; • to assess potential errors associated with different spatial subsets of the total NMSZ network; • to compare results from measurements in the NMSZ with those from the Caribbean region for both bedrock and unconsolidated sediment sites to determine if the magnitude of errors are comparable in the two regions and • to evaluate the contribution of seasonal effects and tropospheric wet delay variability to data uncertainties. Current funding provided by USGS-NEHRP, NASA.