Very Long Baseline Interferometry Baseline Research Articles

Least-squares Wavelet and Cross-wavelet Analyses of VLBI Baseline Length and Temperature Time Series: Fortaleza–Hartebeesthoek–Westford–Wettzell

Extensive least-squares wavelet and cross-wavelet analyses are performed on the Very Long Baseline Interferometry (VLBI) baseline length and temperature time series for a network of four VLBI antennas located in different continents. These analyses do not rely on any pre-processing of the measurements including interpolations or gap-filling, and they can provide accurate instantaneous frequency information along with phase differences in the time–frequency domain. Out of four antennas mounted in Fortaleza, Hartebeesthoek, Westford, and Wettzell, the most and the least possibly impacted VLBI time series by the annual temperature variation are Westford–Wettzell and Fortaleza–Hartebeesthoek, respectively. Furthermore, the annual components of the temperature time series in Westford and Wettzell lead the ones in the corresponding VLBI time series by nearly one month, where one of the baseline sides is either in Westford or Wettzell.

Combination of GPS and VLBI on the observation level during CONT11—common parameters, ties and inter-technique biases

Multi-technique space geodetic analysis software has been developed which allows to combine data on the observation level. In addition to local tie information, site-wise common parameters, i.e., troposphere and clocks, can be estimated with this software. Thus, it will be discussed how common parameters have to be estimated and where biases/offsets need to be taken into account. To test such a novel concept, Global Positioning System (GPS) and Very Long Baseline Interferometry (VLBI) data from the CONT11 campaign are being utilized. Since the VLBI baselines of this campaign extend over several thousands of kilometers, GPS data are processed in precise-point positioning mode and satellite orbits and clocks are kept fixed to the IGS final products. From the obtained results, it can be shown that the combination of space geodetic data on the observation level leads to a consistent improvement of station position repeatability as well as nuisance parameters like troposphere estimates. Furthermore, estimation of common parameters (troposphere or clocks) at co-located sites helps to improve the solution further and derive an utmost physically consistent model of the concerned parameters.

INFERENCES OF -STABLE DISTRIBUTION OF THE UNDERLYING NOISE COMPONENTS IN GEODETIC DATA

We investigate the use of distribution functions to characterise the geophysical signals and noise components embedded in the geodetic Very Long Baseline Interferometry (VLBI) data sets across some of the International VLBI Service (IVS) stations. The rationale of using α-stable distributions as a tool to model the noise components in geodetic observables is due to the existence of impulsive signals/noise bursts (which often take the form of excursions with intermittent occurrences) in the data sets suggesting deviations from Gaussian distribution. A deviation from Gaussian distribution type would therefore suggest that statistical techniques such as least squares analysis, often used for analyzing the geodetic data (which are often based on Gaussian assumptions) could not be robust. In this paper, the properties of a long-range α-stable distribution with long tails and infinite moments in geodetic data are investigated by way of statistically testing their distribution using a family of stable distributions. The choice of stable distributions is based on the ease with which the statistical properties of the non-Gaussian processes are defined. Results indicate that the independent geophysical noise components reconstructed from geodetic VLBI baseline data exhibit distributions that have asymptotic power-law decay (albeit variable power indices) whose underlying process can be modelled as a long-range dependent process with an α-stable distribution (i.e., the stable varieties have small characteristic exponents).

1.3 mm WAVELENGTH VLBI OF SAGITTARIUS A*: DETECTION OF TIME-VARIABLE EMISSION ON EVENT HORIZON SCALES

Sagittarius A*, the ∼4 × 106 M☉ black hole candidate at the Galactic center, can be studied on Schwarzschild radius scales with (sub)millimeter wavelength very long baseline interferometry (VLBI). We report on 1.3 mm wavelength observations of Sgr A* using a VLBI array consisting of the JCMT on Mauna Kea, the Arizona Radio Observatory's Submillimeter Telescope on Mt. Graham in Arizona, and two telescopes of the CARMA array at Cedar Flat in California. Both Sgr A* and the quasar calibrator 1924−292 were observed over three consecutive nights, and both sources were clearly detected on all baselines. For the first time, we are able to extract 1.3 mm VLBI interferometer phase information on Sgr A* through measurement of closure phase on the triangle of baselines. On the third night of observing, the correlated flux density of Sgr A* on all VLBI baselines increased relative to the first two nights, providing strong evidence for time-variable change on scales of a few Schwarzschild radii. These results suggest that future VLBI observations with greater sensitivity and additional baselines will play a valuable role in determining the structure of emission near the event horizon of Sgr A*.

Identification of Potential Weak Target Radio Quasars for ASTRO-G In-Beam Phase-Referencing

Abstract We apply an efficient selection method to identify potential weak Very Long Baseline Interferometry (VLBI) target quasars simply using optical (SDSS) and low-resolution radio (FIRST) catalogue data. Our search is restricted to within 12 from known compact radio sources that are detectable as phase-reference calibrators for ASTRO-G at 8.4 GHz frequency. These calibrators have estimated correlated flux density $>$20 mJy on the longest ground–space VLBI baselines. The search radius corresponds to the primary beam size of the ASTRO-G antenna. We show that $\sim$20 quasars with at least mJy-level expected flux density can be pre-selected as potential in-beam phase-reference targets for ASTRO-G at 8.4 GHz frequency. Most of them have never been imaged with VLBI. The sample of these dominantly weak sources offers a good opportunity to study their radio structures with unprecedented angular resolution provided by Space VLBI. The method of in-beam phase-referencing is independent from the ability of the orbiting radio telescope to do rapid position-switching manoeuvres between the calibrators and the nearby reference sources, and less sensitive to the satellite orbit determination uncertainties.

Millimetron—a large Russian-European submillimeter space observatory

Millimetron is a Russian-led 12 m diameter submillimeter and far-infrared space observatory which is included in the Space Plan of the Russian Federation for launch around 2017. With its large collecting area and state-of-the-art receivers, it will enable unique science and allow at least one order of magnitude improvement with respect to the Herschel Space Observatory. Millimetron will be operated in two basic observing modes: as a single-dish observatory, and as an element of a ground-space very long baseline interferometry (VLBI) system. As single-dish, angular resolutions on the order of 3 to 12 arc sec will be achieved and spectral resolutions of up to a million employing heterodyne techniques. As VLBI antenna, the chosen elliptical orbit will provide extremely large VLBI baselines (beyond 300,000 km) resulting in micro-arc second angular resolution.

The impact of radio source structure on European geodetic VLBI measurements

European geodetic very long baseline interferometry (VLBI) sessions (also known as EUROPE sessions) have been carried out on a regular basis for the past 15 years to study relative crustal motions within Europe. These sessions are based on observations of extragalactic radio sources, which serve as distant fiducial marks to establish an accurate and stable celestial reference frame for long-term geodetic measurements. The radio sources, however, are not always point-like on milliarcsecond scales, as VLBI imaging has revealed. In this work, we quantify the magnitude of the expected effect of intrinsic source structure on geodetic bandwidth synthesis delay VLBI measurements for a subset of 14 sources regularly observed during the EUROPE sessions. These sources have been imaged at both X-band (8.4 GHz) and S-band (2.3 GHz) based on dedicated observations acquired with the European VLBI Network (EVN) in November 1996. The results of this calculation indicate that the reference source 0457+024 causes significant structural effects in measurements obtained on European VLBI baselines (about 10 picoseconds on average), whereas most of the other sources produce effects that are only occasionally larger than a few picoseconds. Applying the derived source structure models to the data of the EUROPE5-96 session carried out at the same epoch as the EVN experiment shows no noticeable changes in the estimated VLBI station locations.

Troposphere gradients from the ECMWF in VLBI analysis

Modeling path delays in the neutral atmosphere for the analysis of Very Long Baseline Interferometry (VLBI) observations has been improved significantly in recent years by the use of elevation-dependent mapping functions based on data from numerical weather models. In this paper, we present a fast way of extracting both, hydrostatic and wet, linear horizontal gradients for the troposphere from data of the European Centre for Medium-range Weather Forecasts (ECMWF) model, as it is realized at the Vienna University of Technology on a routine basis for all stations of the International GNSS (Global Navigation Satellite Systems) Service (IGS) and International VLBI Service for Geodesy and Astrometry (IVS) stations. This approach only uses information about the refractivity gradients at the site vertical, but no information from the line-of-sight. VLBI analysis of the CONT02 and CONT05 campaigns, as well as all IVS-R1 and IVS-R4 sessions in the first half of 2006, shows that fixing these a priori gradients improves the repeatability for 74% (40 out of 54) of the VLBI baseline lengths compared to fixing zero or constant a priori gradients, and improves the repeatability for the majority of baselines compared to estimating 24-h offsets for the gradients. Only if 6-h offsets are estimated, the baseline length repeatabilities significantly improve, no matter which a priori gradients are used.

Contributions of GPS and VLBI for understanding station motions

Abstract The occurrence of non-secular signals in site positions is well known. Since a few years, a main objective of research has been the separation of apparent motions from real geophysical motions and deformations. We investigated eight weekly Global Positioning System (GPS), one daily solution from Scripps Orbit and Permanent Array Center (SOPAC), and two Very Long Baseline Interferometry (VLBI) station coordinate time series and the corresponding baselines. One major hurdle in our investigation was the handling of constraints imposed on the GPS solutions. Seasonal signals in the height component with amplitudes of up to 9 mm for a few sites on the Asian continent were recovered. For baselines longer than 5000 km, the precision of the GPS technique is superior to the VLBI technique from the point of view of repeatability. The improvement on VLBI baseline repeatability after applying the atmospheric pressure loading time series provided by the Goddard Space Flight Center (GSFC) VLBI group reaches 3.3% (median value). Coordinate time series or baseline lengths derived from GPS and VLBI Analysis Centers (ACs) solutions have not yet achieved an unambiguously assessment of sub-cm agreement.

Degree‐1 Earth deformation from very long baseline interferometry measurements

The presence of degree‐1 deformations in very long baseline interferometry (VLBI) measurements is detected for the first time. We compare VLBI measurements with the deformation field predicted using a GPS‐determined load moment. Degree‐1 series in the center of figure frame have root mean square values up to 3 and 1.5 mm in the up and horizontal components respectively. The predicted baseline series are compared with VLBI baseline series where there are >50 matching points. For the period 1996–2001, 14 baselines out of 35 are significantly correlated (5% significance level). For the period 1985–2001, a sinusoidal fit to the GPS load‐moment series predicts baseline series at all VLBI epochs, 49 out of 110 baselines are significantly correlated (5% significance level). Comparison between annual signals estimated from the VLBI and predicted baseline series shows that degree‐1 deformation most likely dominates the annual phase of the VLBI series.

Coupling of long oceanic waves in the Pacific Ocean and the rotating elastic Earth during the 1986–1987 El Niño

We investigate interannual coupling between the rotating elastic Earth and the ocean during the 1986–1987 El Niño. We find the E‐W component of the ground tilt at the Esashi Earth Tides Station up toward the east about 50 milliarc seconds (mas), a rise of sea level about 5 cm at Chichijima and Oshima in the northwestern Pacific Ocean, and an increase of ∼1 cm in the very long baseline interferometry (VLBI) baseline distance between Kashima (Japan) and Kauai (Hawaiian Islands) as well as the residual length of day (LOD) changes of ∼50 μs during the 1986–1987 El Niño. The residual LOD is derived from elimination of changes in atmospheric angular momentum. Our discussions are based on the coupling between torsional motions of the elastic Earth and reflection of the eastward traveling equatorial Kelvin waves at the eastern boundary of the Pacific Ocean. These equatorial waves exchange the momentum and the axial and zonal component of vorticity with the elastic Earth. During the 1986–1987 El Niño, reflection of the Kelvin wave is expected to excite torsional motions and to couple with differential zonal rotation in the elastic Earth and to generate anomalies of ∼1.6 μs in LOD. The differential zonal rotation due to the torsional motion can produce the same order of the magnitude of changes in the VLBI baseline distance between Kashima and Kauai. Variations of the E‐W component of the tilt cannot be explained by torsional motion. We infer that the midlatitude Rossby waves are generated in the central Pacific Ocean. This conclusion is consistent with sea level changes at Chichijima and Oshima and changes of the tilt at Esashi.

Global postseismic rebound of a viscoelastic Earth: Theory for finite faults and application to the 1964 Alaska earthquake

A spherically symmetric Earth model with viscoelastic rheology is used to study the postseismic rebound associated with finite lithospheric dislocations. We perform a systematic study of surface deformations due to sources characterized by two‐ and three‐dimensional faults, modeled by a linear and planar distribution of point sources. Our approach is based on the normal mode technique for a layered Earth with linear viscoelastic rheology and allows for a self‐consistent description of the time evolution of postseismic displacements due to strike‐ and dip‐slip faults. As a case study, we compare the predicted horizontal displacements due to the 1964 Alaska earthquake with very long baseline interferometry (VLBI) baselines changes observed in this region in the period 1984–1989. Although subduction and postglacial isostatic adjustment are expected to contribute significantly to present‐day velocities, our results show that the postseismic rebound due to the 1964 Alaska earthquake plays a relevant role in the changes of several VLBI baselines. The last section is devoted to the analysis of the evolution of other North American baselines. As suggested by recent investigations based on forward approaches, isostatic readjustment of the Earth's crust in response to the melting of the last Pleistocene ice sheets is a major contributor to baseline variations in this area. Our results indicate that a correct interpretation of VLBI baseline changes in North America should account also for the effects of postseismic deformation.

Ionospheric calibration of single frequency VLBI and GPS observations using dual GPS data

The ionospheric effect is one of the main sources of error in Very Long Baseline Interferometry (VLBI) and Global Positioning System (GPS) high precision geodesy. Although the use of two frequencies allows the estimation of this effect, in some cases dual observations are not possible due to the available equipment or the type of observation. This paper presents the ionospheric calibration of single frequency VLBI and GPS observations based on the ionospheric electron content estimated from dual frequency GPS data. The ionospheric delays obtained with this procedure and the VLBI baseline length results have been compared with those obtained with dual frequency data. For the European geodetic VLBI baselines, both solutions agree at the 3–5 parts in 10−9 level. The noise introduced by the GPS-based calibration is in the order of 3 cm for the VLBI observables and of 10 cm for the GPS observables.

A comparison of VLBI data with the Ice‐3G Glacial Rebound Model

Crustal motion predicted by the ICE‐3G glacial rebound model exhibits a pattern of tangential (horizontal) divergence away from the centres of uplift, which in North America and Europe are located around Hudson Bay and the Gulf of Bothnia. Tangential velocities reach peak magnitudes of 1–2 mm/yr, and must be included when predicting Very‐Long‐Baseline‐Interferometry (VLBI) baseline‐length change rates due to post‐glacial rebound. Out of 18 observed VLBI baselines examined 3 are situated such that their predicted length rates are around their 2σ uncertainties or greater. It is encouraging that 2 of these baselines exhibit predicted length rates within 2σ of the observed rates.

Radiointerferometric polar motion observations with high temporal resolution

For several years polar motion has been routinely monitored with the technique of geodetic Very Long Baseline Interferometry (VLBI) at five-day intervals. Here we present the results of the first two series of VLBI measurements for polar motion monitoring observed on a quasi daily basis employing only a single baseline. The high sensitivity of the long north-south baseline between radio telescopes at Wettzell in Germany and Hartebeesthock in South Africa for both components of polar motion permitted relatively short and inexpensive measurements of only two hours duration per session. The results of this series agree very well with the pole path determined with the IRIS network using 4 observatories in each observing session of 24 hour duration. With the polar motion results of the two series spanning about 35 days each, spectral analyses were performed which have shown a fortnightly period with a high degree of probability. These measurements demonstrate the potential of long north-south VLBI baselines for monitoring polar motion with very high temporal resolution for studies of short period fluctuations.

An evaluation of water vapor radiometer data for calibration of the wet path delay in very long baseline interferometry experiments

The internal consistency of the baseline length measurements derived from analysis of several independent very long baseline interferometry (VLBI) experiments is an estimate of the measurement precision. In this paper we investigate whether the inclusion of water vapor radiometer (WVR) data as an absolute calibration of the propagation delay due to water vapor improves the precision of VLBI baseline length measurements. We analyzed 28 International Radio Interferometric Surveying runs between June 1988 and January 1989; WVR measurements were made at the G. R. Agassiz Station of the Harvard College Observatory in Ft. Davis, Texas, during each session. We found that the addition of WVR data decreased the scatter of the length measurements of Ft. Davis baselines by 5–10%. The observed reduction in the scatter of the baseline lengths is less than what we would expect from the behavior of the formal errors, which suggest that the baseline length measurement precision should improve 10–20% if WVR data at Ft. Davis are included in the analysis. The discrepancy between the formal errors and the baseline length results could be explained as the consequence of systematic errors in the dry‐mapping function parameters, instrumental biases in the WVR and Ft. Davis barometer, or both.

The Long Term Stability of VLBI Earth Orientation Measurements

Tectonic motions will, in general, change the orientation as well as the length of baselines used in Very Long Baseline Interferometry (VLBI), and will thus cause slow divergences between Earth orientation results obtained with different VLBI networks, as well as between VLBI results and those obtained by Satellite Laser Ranging (SLR) and Lunar Laser Ranging (LLR). Such drifts (on the order of a milliarcsecond /year) are inherently interesting as well as being significant in combinations of orientation results from different sources. The geodetic study of tectonic motions is also closely connected to research into the nature and causes of systematic errors in data from the modern techniques of space geodesy. We describe both a special coordinate system found to be of use in the analysis of VLBI data and tectonic motion estimates for a VLBI baseline stretching from California to Australia.

Mobile Very Long Baseline Interferometry and Global Positioning System measurement of vertical crustal motion

Mobile very long baseline interferometry (VLBI) and Global Positioning System (GPS) geodetic measurements have many error sources in common. Calibration of the effects of water vapor on signal transmission through the atmosphere, however, remains the primary limitation to the accuracy of vertical crustal motion measurements made by either technique. We have evaluated the two primary methods of water vapor calibration currently in use for mobile VLBI baseline measurements: radiometric measurements of the sky brightness near the 22–GHz emission line of free water molecules and surface meteorological measurements used as input to an atmospheric model. Based upon a limited set of nine baselines, it is shown that VLBI data calibrated with water vapor radiometer measurements can, in some cases, provide a significantly better fit to the theoretical delay model than the same data calibrated with surface meteorological measurements. A detailed error model for the vertical baseline component indicates that current mobile VLBI technology should allow accuracies of order 5 cm with water vapor radiometer calibration and 10 cm when surface meteorological calibration is used. A statistical analysis of the results of repeated measurements of the 336‐km baseline from Big Pine, California, to Pasadena, California, shows the scatter in the vertical baseline component to be consistent with this model. A similar model for a hypothetical GPS baseline measurement is presented. A covariance analysis based upon this model shows current GPS technology to be capable of accuracies in the vertical baseline component comparable to present mobile VLBI measurements. Expected improvements in system components for both technologies should allow reduction of the uncertainty in the vertical component to less than 3 cm by 1989.

A comparison between LAGEOS laser ranging and very long baseline interferometry determined baseline lengths

The NASA Crustal Dynamics Project uses satellite laser ranging (SLR) and very long baseline interferometry (VLBI) data collected and analyzed by the Goddard Space Flight Center and the Jet Propulsion Laboratory for the measurement of geodynamic and geodetic parameters. An important parameter is the determination of the baseline length or intersite distance. Since October 1979, baselines determined from SLR data and VLBI data have been compared to help assess the accuracy of the baseline measurements from these independent techniques. Eight locations in the continental United States participated in the comparison: Westford, Massachusetts; Fort Davis, Texas; Platteville, Colorado; and Quincy, Owens Valley, Goldstone, Pasadena, and Monument Peak, California. Twenty‐two baseline lengths between these locations, as determined by SLR, were differenced from the corresponding VLBI determinations. The rms scatter about zero for the length differences is 5.2 cm with a mean of 1.0±1.1 cm, and there is no apparent scale factor between these two distance determinations. For this result, the Monument Peak‐Quincy baseline has been adjusted for tectonic plate motion by using the SLR‐determined baseline rate. For the eight other baselines crossing a plate boundary, tectonic motion was not modeled. If a model for this motion based upon baseline changes derived from strain rates is applied, the rms scatter about zero for the 22 differences becomes 7.2 cm, with a mean of 1.0±1.1 cm. The above results are within the combined error budgets of the SLR and VLBI baseline length determinations.