Comprehensive Analysis of 2 years of SG Data from Table Mountain, Colorado D.J. Crossley and Su Xu (Department of Earth and Atmospheric Sciences, St. Louis University, St. Louis, MO 63108) and T. van Dam (NOAA/NOS/NGS Geosciences Research Laboratory and CIRES, Campus Box 216, University of Colorado, Boulder, Co., 80309). Abstract We present an analysis of more than 2 years of data from the Superconducting Gravimeter CO24 at Table Mountain near Boulder, Colorado. The analysis is done in several steps: the gravity data, sampled at 5s, is cleaned for gaps, disturbances and offsets and then decimated to 1hr, an ETERNA analysis is done to determine the tidal gravimetric factors and phases, during which the atmospheric pressure loading and the period and damping of the FCN are obtained. A short period analysis of the five quietest days in the seismic mode band (200-600s) shows the combined instrument/site noise to be one of the quietest of all SGs analyzed to date. For the long periods, a local tide, including various ocean loading models, is subtracted from the data and the residual gravity is corrected for IERS polar motion and drift. The final residual gravity agrees well with data from 2 FG5 Absolute Gravimeters. Local rainfall data, when converted to pseudo-groundwater using a simple horizontal aquifer model, yields a recharge time of 4 hrs and a discharge time of 91 days. TMGO is an extremely stable site with excellent noise characteristics. Introduction GWR CO24 is a Superconducting Gravimeter (SG) that has been operating since 1995 at Table Mountain Gravity Observatory (TMGO), about 10km northeast of Boulder, Colorado. The station coordinates are: north latitude 40.1308deg, east longitude 254.7672deg and elevation 1682m. The instrument is a compact dewar model with a 0.5" niobium sphere. Table Mountain is a permanent geodetic observatory operated by NOAA; in addition to the SG, NOAA operates and maintains two FG5 absolute gravimeters and a continuous GPS site. We have selected two years of observations for this study, from days 95104 (14 April, 1995) to 97107 (17 April, 1997). The purpose of the study is to evaluate the site and instrument in conjunction with the Global Geodynamics Project (GGP, Crossley and Hinderer, 1995). Data Processing Atmospheric pressure is recorded every minute; gaps and obvious disturbances are filled by linear interpolation. The raw data, recorded every 5s, is flagged for missing values, or gaps, with the arbitrary value 99.0. It is decimated using a Chebyshev filter to 1 min samples and decimated again to 1 hour using a Butterworth filter to produce the time series shown in Fig. 1. The data is reasonably clean, with relatively few gaps, spikes and offsets, and no obvious drift. To fill gaps and repair other bad data, we need a synthetic tide for the station. Because we do not yet have local tidal factors, we construct tides for a standard elastic earth model using the program GWAVE (Merriam, personal communication), and include whole-Earth gravimetric factors and the Free Core Nutation (FCN) resonance. We add to the synthetic tide an atmospheric pressure signal, interpolated linearly from 1 min, using a nominal scalar admittance of -0.3 mugal mbar^{-1}. For gaps filled with a 99.0 value we substitute a synthetic tide (+pressure) signal, further adjusted by an arbitrary linear slope that ensures no offset at the beginning and end of the gap. We use two methods to examine the remaining problems in the data. The first is to decimate the gap-filled data to 1 minute and combine all 1 minute days into a single file. We subtract a nominal 1 minute elastic tide (+pressure) for the entire period and examine the residuals. Problems can be easily identified for treatment at either the 5 sec raw data or directly on the 1 minute data. For detailed analysis, we take each day of 5s residuals and subtract a nominal 5 sec tide and visually inspect the data for problems. Both approaches are useful for identifying disturbances such as clipped earthquakes, helium filling, data problems and obvious offsets in the data. In the present study, we correct all problems in the 5 sec data except for 3 days of bad data near the end of the record that were fixed on the 1 minute samples. The offset history recovered from this analysis of the two years data is shown in Fig. 2. There is only one large offset, on September 21, 1995, amplitude 37 mugal, due to loss of power to the system; it lasts 7 days. There are many smaller offsets, less than 0.3 mugal, which we chose not to remove and several other pseudo-offsets that were left because we suspect they have a non-geophysical origin. With the disturbances and offsets identified, we again replace the residual gravity, defined as observed gravity - synthetic local tide + pressure, with either a linear slope, or with a constant value plus offset, depending on our judgment. The total amount of data replaced by all of the above procedures is 6.8%. The fixed gravity data is then decimated to 1 minute, and then to 1 hour. High Frequency Noise Analysis One measure of the quality of the site+instrument is the high frequency noise level. We construct a Seismic Noise Magnitude (SNM), introduced by Banka (1997), which is a measure of the residual noise in the seismic normal mode band between 200s and 600s. In this band, SGs generally perform slightly worse than modern seismometers, but are still acceptable for normal mode studies. To obtain this parameter, we examine each day in the two year record and subtract a synthetic tide (+pressure) and a 9'th order polynomial (to remove the remaining long periods) and find the RMS time deviation of the residual. We then pick the five quietest days and compute the periodogram (FFT) of each by padding by a factor of at least two and use a 10% cosine bell data window. These 5 FFTs are averaged in the frequency domain to produce a single spectral estimate, shown in Fig. 3. A significant peak appears towards the end of this portion of the spectrum at a period of about 114s. This is the resonance of the niobium sphere which is typical of most SGs; it is excited by disturbances and is particularly noticeable after large horizontal acceleration. The fact that this resonance appears on all days of the record, even the quietest days where there are no obvious excitations, is interesting. As a means of comparing different instruments, the SNM is the log of the mean Power Spectral Density in the chosen frequency band, with an arbitrary scaling factor (2.5 for our system of units). A comparison of the Boulder site with the instruments discussed by Banka (1997), shown in Fig. 4, establishes Boulder as one of the quietest SG sites at this end of the frequency spectrum. ETERNA Analysis for Diurnal Periods From the 2 year record we determine local gravimetric amplitude and phase factors from the 1 hour gravity and pressure data from a tidal analysis using ETERNA (Wenzel, 1997; V2.1). We select 48 groups of waves and assume a single scalar coefficient for the pressure, a 2nd order Chebyshev polynomial for the instrument drift, and an instrumental phase lag of 0s. The output of the analysis is a list of amplitude and phase factors for the input wave groups; all waves longer than 1 year and shorter than 8 hr are set to (delta=1.16, kappa=0$). Waves at other frequencies are obtained by linear interpolation. These tidal factors include three components: the body tide, the ocean tide and the instrument phase delay. The amplitudes and phase factors are then used as the basis of a local synthetic tide for the station Boulder, and this replaces the nominal elastic tide used in filling gaps and disturbances (see above). Finally, we then go back and re-process all the data, as described in the data processing above, and repeat the ETERNA analysis a second time to produce a self-consistent table of local tidal parameters used in subsequent processing. Our second step is to re-process the 1 hour gravity and pressure data and perform a third ETERNA analysis, but this time using the known instrument phase delay of 30.0s for our station as input to ETERNA. This phase delay has been determined electronically by F. Klopping (personal communication). The resulting residual gravity is shown in Fig. 5. Note that the fitting of annual waves in ETERNA has absorbed most long period signals potentially present in the data. The scalar atmospheric admittance was found to be -0.27 mugal mbar^{-1}. A large positive increase in gravity near the beginning of the recording (~ day 40) initially appears to contain at least two offsets. A closer examination reveals that the gravity changes occur over several days and are of geophysical, rather than instrumental, origin. A similar 'offset' occurs at ~ day 400. Other than these, the residual gravity varies by only a few mugal over the entire two-year period. FCN Resonance The ocean loading parameters for Boulder were kindly supplied for us by Olivier Francis (International Center for Earth Tides, Brussels) for 5 different ocean load models. The parameters for waves psi_{1} and phi_{1} were obtained by scaling arguments. For the amplitudes, we determined the ratio of the theoretical tidal amplitudes and the given ocean loading factors for waves P_{1} and K_{1} and applying this factor to the theoretical tidal amplitudes for the two small waves. This method does not work for the phases since the theoretical phase is zero, so we took the ratio of the phases of psi_{1} and K_{1} for stations Cantley and Strasbourg (known to us from a previous analysis) and applied the similar ratios for Boulder. We corrected the observed tidal amplitudes for waves K_{1}, P_{1}, psi_{1} and phi_{1}, with O_{1} being the reference wave, for ocean loading. The corrected body wave gravimetric factors are then fitted by a simple resonance curve to determine the period T and damping Q of the Nearly Diurnal Free Wobble (and associated FCN) of the core, following a procedure described in Hinderer (1997). We find T=418 days and 1688 < Q < 1640. Changing the instrument phase delay between 0-50s, and ocean load error between 10%-40% results in changes of < 0.3 days in T and < 50 in Q. Though 3% below estimates from stacked stations, T agrees with these within its formal error. Long-Period Analysis The ETERNA analysis is not suitable for long periods because the annual waves are freely fitted and therefore absorb long term variations. We therefore return to the hourly values in and subtract a local synthetic tide (+nominal pressure correction) to arrive at a tide-subtracted residual, shown in Fig. 6. It can be seen that this residual has a small positive `drift' plus a quasi-annual fluctuation, unlike these components that are absent from Fig. 5. We have computed the smoothed 1-day polar motion, conveniently provided through data on the IERS Web Site. The gravity effect, plotted in Fig. 6, shows a strong correlation with the residual gravity. The corrected gravity is displayed in Fig. 7 and we note that it is unusual to see an almost complete absence of annual periods. It is difficult to argue convincingly that an SG should have a particular drift behavior. The consensus of opinion is that the drift should be a simple exponential function, rather than a low-degree polynomial, that represents residual physical processes that follows magnetic initialization of the SG. Consequently we fit an exponential function, rather than the Chebyshev polynomials allowed by ETERNA, to the residual gravity and assume this is the instrument drift (Fig. 7). Subtraction of this drift curve gives the third residual gravity shown in Fig. 8. The drift function is d(t) = -32.7703 e^{-0.0008998t} + 18.76164 mugal, with t in days, which yields about 5 mugal yr^{-1} at the end of the record. Many SGs have drift rates below even this small amount. Comparison with Absolute Gravity We compare the final residual with absolute gravity, measured using several Axis FG5 instruments, plotted with error bars in Fig. 8. The agreement is excellent except for three absolute gravity determinations at ~ day 300 that appear low by about 4 mugal compared to the relative measurements. Otherwise the overall agreement is within a few mugal over the two-year period. This correlation emphasizes the necessity of recording both types of gravimeter data for fundamental geodetic purposes. Comparison with Hydrological Data There is no well-logged data available for the site area, but we do have rainfall data, in the form of daily determinations shown as the bottom panel of Fig. 9. The rainfall is seen to correlate with increases in residual gravity, shown in the top panel of Fig. 9; this is especially noticeable between days 20 and 60, and also at ~ day 400. These correlations suggest a simple groundwater accumulation and discharge model: h_{i} = r_{j} (1-e^{-(i-j)/tau_{1}}) e^{ -(i-j)/tau_{2}} g_{i} = 2 pi G rho h_{i} where r_{j} = amount of rain at hour j, h_{i} = depth of aquifer at hour i, g_{i} = gravity observation at hour i and rho = density contrast. Assuming water is replacing pore space, rho = 1.0 gm cm^{-3}. Using the above model we can integrate the rainfall to obtain a pseudo-groundwater aquifer thickness h (middle panel of Fig. 9), and from that the gravity effect assuming an infinite slab model (2). From an optimum search using the first 200 days of data (where the correlation is strongest), we find in (1) that tau_{1} = 4 hrs, the \it{recharge time constant}, and tau_{2} = 91 days, the \it{discharge time constant}. Finally it is possible to estimate the groundwater/gravity admittance. Using the first 200 days we obtain 0.0414 mugal mm^{-1}, whereas for the whole record we find 0.00925 mugal mm^{-1}. The value calculated for the Bouguer slab (2) is 0.0419 mugal mm^{-1}, so the agreement for the first 200 days is embarrassingly good! Conclusions TMGO is an excellent SG site for seismic studies and remarkably stable with respect to long term gravity variations. There are no unexplained annual signals in relative gravity and the polar motion is extremely well determined. It would be very useful to have groundwater measurements to further model the interaction between rainfall and gravity, but clearly the connection is well established by this data set. Acknowledgments We thank NOAA and NSF for grant support for the data acquisition and processing. References Banka, D., 1997. Noise levels of superconducting gravimeters at seismic frequencies, Ph.D. Thesis, Technical University Clausthal. Crossley, D. & Hinderer, J., 1995. Global Geodynamics Project - GGP Status Report 1994, Cahiers du Centre European de Geodynamique et de Sismologie, Luxemburg, \bf{11}, 244-274. Hinderer, J., 1997. Constraints on the Earth's deep interior and dynamics from superconducting gravimetry, in \it{Earth's Deep Interior}, ed. Crossley, D., Gordon & Breach, 453pp. Wenzel, H.G., 1997. The nanogal software: Earth tide data processing package ETERNA 3.3, 13th Intl. Symposium on Earth Tides, Brussels, July 22-25.