COMET’s Marek Ziebart and Chris Atkins, both at UCL, have been using sidereal filtering to detect geohazards in near-real time. This article describes how they have applied this to earthquakes in the Aleutian Islands, Alaska.
Geodetic quality GPS (Global Positioning System) data – fundamentally high precision range measurements made between orbiting spacecraft and tracking stations, often rigidly attached to bedrock – is one of the key observables available to us to analyse plate tectonics and the earthquake cycle. Such tracking stations now often make measurements at 1 Hz or higher. This enables us to calculate high rate position time series for the tracking stations, revealing various kinds of motion related to seismic waves and other forms of deformation.
One such time series is shown below, calculated by a standard processing method called PPP (precise point positioning). The plot shows the change in position in the north-south direction. When do you think the earthquake seismic waves begin to arrive?
GPS Seismology
How can we use this type of data? The time series in figure 2 shows an estimate of the GPS antenna movement in the North-South direction during the 2011 magnitude 9.0 Tohoku earthquake over a period of 25 minutes. This is a measurement of the ground shaking – the data is used to understand the nature of the earthquake and to compare it to other earthquakes in different places around the world. Earthquakes often cause a change in the shape of the ground that is retained after the earthquake is over, and which can be determined from a time series. This kind of information can be used to estimate the size of the earthquake, how much energy was released and tells us about the earthquake’s epicentre location.
Another kind of instrument, a seismometer, can be used to determine similar information. The drawback of seismometers is that they can ‘clip’ when the seismic waves become too large to handle. A GPS antenna, on the other hand, has no such limitation – no matter how big the amplitude of the seismic waves, they can still be measured using GPS technology. Because of this, GPS antennas such as the ones shown in figures 1 and 6 below are sometimes called broadband GPS seismometers. In practice we combine information from both GPS antennas and seismometers – they are complimentary. There are now thousands of such GPS antennas installed around the world, connected to the internet and taking measurements 24 hours a day.
So what’s the problem? The problem is Multipath – this is akin to radio interference where the signals transmitted by the orbiting satellites have more than one way of getting to the antenna. The strongest, direct signal – which is the one we want to measure – is distorted by signals bouncing off adjacent reflecting surfaces in the antenna’s vicinity. This causes spurious patterns of motion in the receiver time series. These can vary rapidly over a few seconds in a noise-like way (with amplitudes at the few mm level), or they can appear as a random walk – a slowly varying position error (with changes at the level of a few centimetres). Both these effects limit our ability to use GPS data for seismometry. To get some feel for the effect consider Figure 4.
On the day of the earthquake (shown as the black time series) the onset of the arrival of the largest seismic waves is shown clearly at around 6:03:00. A not dissimilar signature is also visible around 5:50:00. However, that same signature (an apparent ground movement of some 25mm over a few minutes, shaking and then reducing in magnitude) is visible at almost the same time on the previous day (in the grey time series). It doesn’t mean the earthquake was repeating – these are multipath distortions. They appear indistinguishable from seismic waves. Our problem, then, is how to remove the spurious, apparent motion from the time series, whilst retaining the actual signature of the earthquake. So what’s the solution?
Sidereal Filtering
Sidereal filtering is a technique used to reduce errors caused by multipath in the positioning of GPS receivers. It relies upon the receiver remaining static from one day to the next relative to its surrounding environment and takes advantage of the ground track repeat time of the GPS satellites, which is just less than a sidereal day (usually around 23 hours, 55 minutes, 55 seconds). The repeating multipath error can thus be identified and largely removed from the following day by subtraction.
A conventional position-domain sidereal filter (PDSF) identifies and removes this repeating pattern from a position time series. However, the ground track repeat time of individual GPS satellites can differ from each other by a few seconds, whereas a PDSF has to assume that all satellites have the same repeat time. This can cause problems for the PDSF, especially when the oscillations caused by multipath interference are particularly high. We have developed an observation-domain sidereal filter (ODSF) that identifies and removes multipath errors from the GPS phase measurements themselves.
Unlike the PDSF, it can account for the fact that the ground track repeat times of the GPS satellites differ by a few seconds from one another. This means that it is more effective at removing the effects of high-frequency multipath error and is less sensitive to satellite outages. For each phase measurement, the ODSF algorithm searches for an appropriate correction based on the azimuth and elevation of the relevant satellite. That correction is derived from the measurement residuals on the previous day that most closely correspond to that azimuth and elevation. The precision of these measures of azimuth and elevation needs to be high – a hundredth of a degree or better. This is readily achievable in our algorithm.
Figure 5 shows the same 25-minute time series of 1 Hz displacements in northing as shown in Figure 4. Also plotted in red and green are the time series that result after applying the two types of sidereal filter: the PDSF and ODSF respectively. Notice that both the PDSF and the ODSF are largely successful at removing these oscillating errors. They reveal a surface wave arrival time of about 06:00 with the largest Love waves arriving at around 06:03. These events would not have been so easy to distinguish in the original unfiltered time series.
Figure 7 similarly shows 1 Hz displacements at station AV27 which is only 11 km from AV24. One would therefore expect a very similar displacement signal. However, it is clear that the standard PPP time series, plotted in black and grey, are severely affected by strong short-period (~11 s) multipath error. In this case, the PDSF was unable to remove such a high-frequency error and instead increased the amplitude of these oscillations. The ODSF on the other hand was far more effective because it could take into account the differing repeat times of the satellites.
Conclusions
The precision of GPS technology has improved dramatically since 1995 when the system reached FOC (full operational capability). It is an effective tool for measuring geohazards and other geophysical phenomena in near real-time. However, data processing and interpretation must be handled carefully. Multipath effects on position time series can introduce spurious signatures that resemble seismic events and hamper our ability to exploit the technology. Sidereal filtering offers a very effective way to clean up GPS positioning time series to reveal more clearly geophysical events, effectively in real-time.
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