For the past decade, the USGS has been monitoring deformation at various locations in the western United States using continuous GPS. The main focus of these measurements are estimates of displacement averaged over one day. Essentially, these consist of recording at 30 seconds intervals the carrier-frequency phase-data (equivalent to travel-time) between a GPS receiver and the GPS satellite network. In turn, these observations, which are converted to pseudo—ranges, are processed using one of the “research grade” programs (GIPSY, Zumberge et al., or GAMIT, wwwgpsg.mit.edu/~simon/gtgk) to estimate the position of the GPS receiver averaged over 24 hours. However, it is possible and desirable to estimate the position of the receiver (actually the antenna) more frequently and to do this within a few seconds of the time actual measurement (known as real-time). A recent example, the 2004 Magnitude 6, Parkfield, California earthquake, demonstrated that having GPS estimates of position more frequently than simply a daily average is required if one requires discrimination between co-seismic and post-seismic deformation (Langbein et al., 2006). The high-rate estimates of position obtained at Parkfield show that post-seismic deformation started less than one-hour after the mainshock and that this deformation was roughly the same magnitude as the co-seismic deformation. The high-rate solutions for Parkfield were done by others including Yehuda Bock at UCSD and Kristine Larson at U. of Colorado, but not the USGS.

The Parkfield experience points out the need for an in-house capability by the USGS to be able to accurately measure co-seismic displacements and other rapid, deformation signals using GPS. This applies to both the Earthquake and Volcano Hazard programs. Although at many locations where we monitor deformation, we have strainmeters and tiltmeters in addition to GPS which, in principle, are far more sensitive to rapid deformation over periods of less than a day (Langbein and Bock, 2004). But, not all locales include strain and tiltmeters. Thus, having the capability to extract signals with periods of less than a day is desirable since the distribution of GPS is more extensive than strain and tilt.

At both Parkfield and Long Valley, the USGS has been using other software packages to process the GPS data at sub-daily intervals and in real-time. The underlying goal of these types of measurements is to detect any deformation event as it evolves; the 24 hour processing might not provide timely results if such a deformation event is precursory to a geologic hazard (an earthquake for Parkfield and either a volcanic event or an earthquake for Long Valley).

In Long Valley, We use the software package called 3DTracker (http://www.3dtracker.com, http://www.condorearth.com) to estimate the changes of in position of a remote site relative to a “fixed” site. The 3DTracker software uses double difference GPS code measurements and receiversatellite-time triple differences from one epoch to the next of the GPS phase data (a proxy for travel-time measurements) and employs a Kalman filter to obtain stability in the estimate of position. That is, the estimate of the current position depends upon the estimate of the prior position. Hence, a time series of position looks fairly smooth depending upon the coefficient selected for the Kalman filter. With triple differences, the sometimes troublesome initial integer cycle ambiguity terms cancel (number of wavelengths between the receiver and each satellite), but only the incremental change in position is calculated. This triple difference Kalman filter solution is slow to converge and less accurate than a double difference (e.g., RTD, Track) solution, but it is robust and computationally efficient (Remondi and Brown, 2000). 3D-Tracker allows use of various single-frequency and dual-frequency GPS phase and code observables including the ionospheric-free combinations (known as LC or L3 and P(L3)) formed from an linear combination of the L1 and L2 carrier phase and code data. The lowest noise observable is the L1 carrier, but it is biased by ionospheric refraction that has amplitudes of about 1 to 10 ppm. This results in a systematic scale error in the relative positions. The L3 phase noise is about 3 times greater than the L1 phase noise, but it is generally used to solve for all but the shortest baselines (< 5 km). In addition, the software does output the position changes is a standard format that can be used for other analysis.

At Parkfield, we use the software package called RTD (http://www.geodetics.com). The RTD software has been described in the literature (Bock et al., 2000) but basically, it estimates the position without the constraint of a Kalman filter. It uses double differences (in our studies the LC or ionospheric free observable is used) and the integer ambiguities are resolved independently for each 1-second measurement; Most GPS software that use double-differences require several epochs of measurements to resolve the integer ambiguities. The data files use a proprietary format and can not be read by me or others; rather, Yehuda Bock at UCSD (and author of RTD) translates these files into a standard format that can be read by me.

Recently, Tom Herring of MIT has modified the GAMIT software to process kinematically GPS data (www-gpsg.mit.edu/~simon/gtgk/tutorial/Lecture_13.pdf). At this time, the software, known as TRACK, does not process the observations in real-time. Consequently, the latency between the time of the observation and the time when a position estimate is available depends upon the frequency that the data are downloaded and the speed of actually processing the observations; there could be a delay of an hour or two before the a position estimates are available. Unlike RTD and 3DTracker, TRACK comes with GAMIT (which is distributed freely) and is currently operating in a test mode at the USGS office in Pasadena. The LC or ionosphere free observable is used in our TRACK solutions.

JPL has a version of their GIPSY software called “Real-time GIPSY (RTG)” (gipsy.jpl.nasa.gov/orms/rtg), which, like TRACK, can process the pseudo-range data “off—line”. However, this software is not freely distributed. Instead, at least one company, NAVCOM, has teamed with JPL to integrate RTG with GPS receivers and telemetry that yields positions in realtime.

Kristine Larson of University of Colorado has modified the original GIPSY to estimate positions kinematically. Again, like TRACK, the positions are estimated off—line. Much of her research is described in Larson et al. (2003), and Choi et al. (2004).

For Long Valley, out of the 17 GPS sites, we monitor 5 baselines within the caldera at 5 second intervals relative to the Bald Mountain site at the edge of the caldera using 3DTracker. The baseline measurement using 3DTracker consists of determination of the 3 dimensional positions of the 5 remote points (GPS receivers) relative to a GPS site at Bald. A second, independent system collects and downloads once a day the 30-second data used for the 24-hour solutions for the 12 sites not monitored with 3DTracker. For the sites monitored with 3DTracker, the pseudo—range data are decimated to 30 seconds and converted to a form used for the 24-hour solutions. Both sets of telemetry employ 900 MHz spread spectrum radios which require line of site between all of the links. The telemetry for the 3DTracker sites require a dedicated radios at each end and intermediate repeaters as needed, while the telemetry required for the other sites use a single master radio, repeaters as needed, and a radio at each remote site. (The 5 sites being monitored with 3DTracker require 13 radios.)

At Parkfield, RTD is used to measure the position changes all 12 baselines at 1 second intervals relative to a site, Pomm, adjacent to the San Andreas Fault. The complete RTD package (hardware and software) collects all of the data and determines the position of each site relative to Pomm. In addition, the system stores both the 1-second and 30-second pseudo-range data for later downloading which are ultimately used in the 24-hour solutions. To do this, each site has a 2.4 GHz radio and a telemetry buffer. The telemetry buffer holds 24-hours of data (in the event that the telemetry link is broken) and converts the RS232 data stream from the GPS receiver into a form compatible with an IP (Internet protocol) network connection. In contrast with the Long Valley system, the telemetry link for GPS at Parkfield consists of a single radio at each remote sites and a single radio at the central site. Although position estimates are produced within 1-second of the observations, these results are not immediately available because there is no high speed Internet connection to Parkfield. Instead, the data are stored on a removable disk and sent to UCSD once per month.

Below, I describe the results of a simple experiment to examine the response of some of these systems to simulated deformation that could be an analogue of a tectonic or volcanic event. In many engineering applications, the system response is tested by inputting a step to the system and measuring the output of the system. Essentially, this is what I've done. The experiment described below moves the GPS antenna from its original position to a new position within 1 second; the software tracks the translation. These measurements were conducted in August 2004 with the RTD software at Parkfield, and twice in Long Valley. The first Long Valley test was conducted in September 2004 using 3DTracker on a single baseline. The test was repeated in September 2005 using 3DTracker on two baselines and, importantly, saving the RINEX files of the data so that the data could be replayed through 3DTracker using other options in the program and, using other software packages including TRACK.

In addition, we observed a short-term event at the Three Sisters volcano in Oregon. This event was snow melt at a remote GPS site which gave an apparent 15 cm displacement in vertical in less than one-day. 3DTracker is used to monitor this site, and the event was captured with this software. In addition, with the assistance of others, I got additional estimates of position using other software packages; those results are presented.

Finally, the precision of both 3DTracker and RTD are compared using a power spectrum. Those results would suggest that 3DTracker using appropriate Kalman filter coefficients would have better precision than RTD; instead, the lower noise level from 3DTracker is a result of smoothing from the Kalman filter.

Given the results described in this report, high-rate GPS is certainly capable of accurately measuring displacements of 1 centimeter with a high degree of statistical confidence. Plotting these results show that the time of the displacement can be visually determined to that of the sampling interval of the data. However, especially with small amplitude signals, any of the software packages can yield erroneous deformation “signals” that are either due excess travel-time of the GPS carrier frequency from multipath or a limitation in the software. Thus, the time series of displacements must be viewed with caution and knowledge of external circumstances that might cause a change in position. 

The casual reader should continue with the next section describing the methods then jump to the last two sections for the discussion and conclusions. I have made some recommendations there.