Abstract
Dayscale Earth's free oscillation after large earthquakes has been detected by underground instruments such as strainmeters, gravimeters and seismometers, to investigate Earth's internal structure, geodynamics and source properties of earthquakes. Here we show that Global Positioning System (GPS) can also detect the signals of the Earth's free oscillation. A dense GPS array in Japan (GEONET) recorded the surface deformation following the 2011 Tohoku megathrust earthquake. A simple array analysis over 300 stations reduces local noise in GPS time series. We find that the dense GPS array truly detected both spheroidal and toroidal fundamental modes in threedirection displacement. This new tool has a strong potential to investigate the free oscillations particularly in lowfrequency bands.
Introduction
Vibration of an elastic sphere has been theoretically calculated from the 19^{th} century and Earth's free oscillation was first observed after the 1960 Chilean earthquake^{1,2}. Many following studies revealed the Earth's internal structure, geodynamics and source properties of earthquakes by using the free oscillation signals^{3,4,5,6}. Recently it was found that the Earth's free oscillation continuously occurs in limited modes^{7,8,9}.
Strainmeters, gravimeters and broadband seismometers served a role in observing the free oscillation signals. These instruments have good signaltonoise ratios in corresponding frequency bands. However, Global Positioning System (GPS) has not been used for the purpose despite its advantages of threecomponent observation in displacement and flat frequency response to 0 Hz. If we reduce much noise contained in GPS time series, GPS would be a powerful tool to detect small displacement signals by the free oscillation as well as seismic waves^{10,11}.
Here we focus on the Earth's free oscillation after the 2011 Tohoku megathrust earthquake^{12,13,14}. A dense GPS array in Japan, called GEONET, continuously observed postseismic land deformation^{15,16} after the occurrence of the mainshock (JST 14:46 on March 11). Using timeseries data at GEONET stations, we look for the signals of the Earth's free oscillation in a lowfrequency range (> 250 seconds). Since the lowfrequency range corresponds to a longwavelength range over several hundred kilometers, we can stack spectral data at many stations to improve signaltonoise ratios. Figure 1 shows 341 GEONET stations near the source region of the 2011 Tohoku earthquake that we focus on. The period to obtain Fourier amplitude spectra is 18 hours (from JST 15:00 on March 11 to 9:00 on March 12).
Results
Figure 2 presents the absolute values of the stacked amplitude spectra in three directions (NorthSouth, EastWest and vertical components) over the 341 stations. The systematic increases of the amplitude toward 0 Hz reflect the postseismic deformation owing to afterslip at the plate interface^{15,16} and tides. We confirm many spectral peaks, corresponding to fundamental spheroidal (_{0}S_{n}, n = 0, 2, 3, 4, et al.) and toroidal (_{0}T_{n}, n = 2, 3, 4, et al.) modes.
The spheroidal modes should appear in both vertical and horizontal components^{20}. In Figure 2, we can identify all of the fundamental spheroidal modes excluding _{0}S_{2} from the vertical component. The mean signal amplitudes during the 18 hours correspond to steady oscillations with submillimeter amplitudes. By contrast, the toroidal modes principally appear in horizontal components^{20}. The signals of the toroidal modes mainly contribute to the NS movement inferred from the location of the GPS stations and the earthquake mechanism (Figure 1). Focusing on the spectral peaks of the NS component in Figure 2, we can recognize good consistency with _{0}T_{2} and possible other toroidal modes, e.g., _{0}T_{10, 0}T_{11}. The characteristic frequencies of the toroidal modes actually do not correspond to the observed spectral peaks of the vertical component. To focus on a specific mode, longer datasets than 18 hours or coordinate rotation in the timeseries data would be useful.
In order to compare the GPS results with other instruments, we also analyse timeseries data of broadband seismometer (STS1^{21}) during the same period. Figure 3 shows the comparative results of the GPS array and the seismometer. For the GPS spectra (left figure), the original timeseries data in displacement are transformed into velocity. The STS1 seismometer that we use is located at Yamizo station of the Fnet broadband seismograph network. The instrument response of the STS1 seismometer is corrected.
The comparison between the GPS array and the broadband seismometer implies: (1) The GPS array detected the signals of the Earth's free oscillation comparable to the seismometer. (2) The background noise levels of the GPS array are higher than the seismometer, but the GPS array seems better in a very low frequency range (roughly < 0.3 mHz).
Discussion
We revealed that the dense GPS array truly caught the signals of the Earth's free oscillation after the megathrust earthquake, using the simple stacking method. Although the background noise of the GPS array were still higher than the broadband seismometer, the flat response to 0 Hz of GPS led to the relatively lower noise in the very low frequency range. In addition, compared with gravimeters, GPS has an advantage of threedirection observation (two horizontal directions in addition to vertical direction). These facts indicate that GPS has a strong potential to investigate subseismic lowfrequency bands^{22}. Using more datasets in the world with proper timeseries processing would be required to investigate a specific mode.
The GPS timeseries data were analysed by a kinematic Precise Point Positioning method^{23,24}, not by a baseline analysis method. This allowed us to detect the signals of the Earth's free oscillation with long wavelengths over several hundred kilometres. The phases of the lowfrequency waves at the GPS stations do not vary significantly. Thus the simple stacking method illuminated the free oscillation signals. To check the efficiency of the stacking, we show comparative examples of the allstacked result (341 stations), a partlystacked result (30 stations) and a nonstacked result (1 station) in Figure 4. The signals of the Earth's free oscillation may appear even in the nonstacked case, however, the flutters of the spectra tend to hide the free oscillation signals in the nonstacked and partlystacked cases.
Methods
First, we obtain the GPS timeseries data by the kinematic PPP method using RTnet software, from RINEX files provided by Geospatial Information Authority of Japan. The sampling rate Δt is 30 seconds. In the analysis, carrier phase data, ephemeris data and clock data are used. The ephemeris is the IGS final orbit (with an interval of 15 minutes) and the clock is also the IGS final orbit (with an interval of 30 seconds). Based on the precise ephemeris and clock, absolute coordinate at each station is sequentially estimated in parallel with tropospheric delay. Ionospheric delay is excluded by combination of dualfrequency carrier phase observations.
To look for the signals of the Earth's free oscillation, we use the displacement timeseries data during 18 hour after the mainshock in three directions: NorthSouth component, EastWest component and vertical component. No particular timeseries processing such as detrending has been done. We compute discrete Fourier transform of the timeseries data by an FFT method with the Hann window^{25} at all the stations for each component:
where D is the data in the frequency domain, Δt is the sampling rate (30 seconds), N is total number of the time series with zero padding and d is the original timeseries data. The Fourier amplitude spectrum is given by the absolute value of D. Then we simply stack the amplitude spectra over the stations for each component (NS, EW and vertical).
We also process the STS1 seismometer data by a similar method. The original timeseries data is provided by National Research Institute for Earth Science and Disaster Prevention (NIED). There are two different points from the GPS case in processing the data. The first is the correction of the instrument response. The Fourier amplitude spectrum for the seismometer data is given by the absolute value of D divided by a complex transfer function (whose poles and zeroes are supplied by NIED). The second is that the sampling rate Δt of the seismometer data is 0.01 seconds.
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Acknowledgements
We thank Tetsuya Iwabuchi about the analysis of the GPS timeseries data. We also appreciate Geospatial Information Authority of Japan, NGDS, the VERIPOS/APEX service, Hitz, GPS Solutions inc. and National Research Institute for Earth Science and Disaster Prevention providing the datasets. Generic Mapping Tools^{26} is used to draw maps.
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Y.M. computed the spectra and wrote the paper; K.H. proposed the initial idea and discussed the results.
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Mitsui, Y., Heki, K. Observation of Earth's free oscillation by dense GPS array: After the 2011 Tohoku megathrust earthquake. Sci Rep 2, 931 (2012). https://doi.org/10.1038/srep00931
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DOI: https://doi.org/10.1038/srep00931
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