Response of Global Navigation Satellite System Receivers to Known Shaking between 0.2 and 20 Hertz

Introduction

Over the past decade, several technological advances have allowed Global Navigation Satellite Systems (GNSS) receivers to have the capability to record displacements at high frequencies, with sampling rates approaching 100 samples per second (sps). In addition, communication and computer hardware and software have allowed various institutions, including the U.S. Geological Survey (USGS), to retrieve, process, and display position changes recorded by a network of GNSS sites with small, less than 1-s delays between the time that the GNSS receiver records signals from a constellation of satellites and the time that the position is estimated (a method known as “real-time”). These improvements in hardware and software have allowed the USGS to process GNSS (or a subset of the GNSS, the Global Positioning System, GPS) data in real-time at 1 sps with the goal of determining displacements from earthquakes and volcanoes in real-time. However, the current set of GNSS equipment can record at rates of 100 sps, which allows the possibility of using this equipment to record earthquake displacements over the full range of frequencies that typically are recorded by acceleration and velocity transducers. The advantage of using GNSS to record earthquakes is that the displacement, rather than acceleration or velocity, is recorded, and for large earthquakes, the GNSS sensor stays on scale and will not distort the observations due to clipping of the signal at its highest amplitude. The direct observation of displacement is advantageous in estimating the size and spatial extent of the earthquake rupture. Otherwise, when using velocity or acceleration sensors, the displacements are determined by numerical integration of the observations, which can introduce significant uncertainty in the estimated displacements. However, GNSS technology can, at best, resolve displacements of a few millimeters, and for most earthquakes, their displacements are less than 1 mm. Consequently, to be useful, GNSS data are only relevant for the large earthquakes with magnitudes (M) exceeding M5.5 at best.

With the capability to record GNSS data at high-rate, at sampling rates typical for seismological applications, experiments are needed to quantify the response of GNSS to shaking from earthquakes. There have been a few studies that examine the response of GNSS to strong shaking. One of the first was Elosegui and others (2006), where they simulated surface waves from a distant earthquake and mechanically applied the shaking to a GPS antenna. They processed the 1 sps observations and compared the estimated displacements with the simulated displacements. They determined that the GPS could accurately track the simulated surface wave whose primary frequency spans from 0.01 to 0.1 Hertz (Hz), which spanned the frequency band of the simulation.

To test GNSS equipment due to shaking from a large earthquake in the near-field, Wang and others (2012) used a mechanical simulator or shake table with 6 degrees of freedom and studied two different inputs to the simulator—(1) the accelerometer record from one station that was located near the 2010 M8.8 Maule, Chile earthquake, and (2) a 2-Hz sinusoid. Wang and others (2012) analyzed the 2-Hz data with spectral analysis and determined that the displacements observed by the GPS included higher harmonics along with the 2-Hz signal. In addition, the background spectral amplitude was greater during periods of 2-Hz shaking than when at rest. With the simulated M 8.8 earthquake, Wang and others (2012) observed decreased signal to noise for L1 and L2 carrier frequencies of the GPS signal, at times corresponding to high acceleration and jerk (first derivative of acceleration).

One of the principal limitations of these experiments was that the displacements of the shake table itself could not be measured independently. Although with the 2-Hz sinusoidal measurements, the input displacements were purely translational, Wang and others (2012) analysis of the data showed that the shake table also included rotational motions which affect horizontal inertial sensors like accelerometers and seismometers at first order.

More recently, Ebinuma and Kato (2012) used a GPS simulator to electronically test several GNSS receivers and obtain the receiver characteristics at three frequencies: 1, 2, and 5 Hz. The results showed that the amplitude of 5-Hz displacements recorded by the GPS was, depending on the receiver model, between 30 and 125 percent more than the displacement input to the simulator. At low frequencies, the GPS displacement was nearly equal to the input displacement. In addition, Ebinuma and Kato (2012) examined how each receiver model amplified an earthquake displacement record in the 2–8 Hz band. The simulated earthquake was the 2008 moment magnitude (Mw) 6.8 Iwate-Miyagi earthquake where, for the simulated record, acceleration peaked at 1 G.

The study discussed here builds on the tests by Ebinuma and Kato (2012), but rather than using electronic simulation, the tests are setup outdoors and closer to actual field installations of GNSS equipment. We used a one-dimensional shake table capable of 400 mm of displacement and high acceleration; the shake table also is constrained by a precision linear slider to have very low tilt that would affect inertial sensors. In addition, the stage position can be accurately monitored independent of the GNSS hardware and, importantly, provides a reference to compare with the estimated displacements from the GNSS data. Our tests spanned a greater frequency range from 0.2 to 20 Hz and we used equipment from three different manufacturers covering five different combinations of receivers and antennas. In addition, we have been able to simulate the frequency response of the GNSS equipment using a simple, causal filter. The quality of the filter was tested using additional test data where a step function in displacement was applied to the shake table. The observed displacements from the GNSS data show an overshoot in displacement at the time of the step or transition of the stage. That overshoot was accurately predicted using the filter design derived from our sinusoidal displacement tests.

Similar to Wang and others (2012), we also examined the GPS displacement records using standard spectral techniques. However, we extended their work by evaluating several models of GNSS receivers using a variety of input frequencies. Because our shake table was limited on acceleration and displacement, we did not attempt to duplicate the high shaking associated with high magnitude earthquakes. However, because our shake table could measure the table displacement, we could directly compare the measured GPS displacements with the true displacements.

First posted January 9, 2014