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\documentclass[se,manuscript]{copernicus}
%PRINT VERSION
%\documentclass[extra]{gji}
\usepackage{setspace}
\usepackage{subfig}
\usepackage{graphicx}
%\doublespacing
\begin{document}
\title{Performance of high-rate GPS waveforms at long periods ($30 \ s
% \Author[affil]{given_name}{surname}
\author[1,2]{K. Kelevitz}
\author[1,2]{N., Houli\'{e}}
\author[1]{D., Giardini}
\author[2]{M., Rothacher}
\affil[1]{Institute of Geophysics, ETH Z{\"u}rich, Switzerland }
\affil[2]{Mathematical and Physical Geodesy, ETH Z{\"u}rich, Switzerland}
%% The [] brackets identify the author with the corresponding affiliation. 1, 2, 3, etc. should be inserted.
\runningtitle{Performance of high-rate GPS waveforms at long periods ($30 \ s
\runningauthor{Kelevitz et al.}
\correspondence{Krisztina Kelevitz (kkelevit@ ethz.ch)}
\received{}
\pubdiscuss{} %% only important for two-stage journals
\revised{}
\accepted{}
\published{}
%% These dates will be inserted by Copernicus Publications during the typesetting process.
\firstpage{1}
\maketitle
\begin{abstract}
We present the comparison of long period ($T > 30\ s$) 1$Hz$ GPS and synthetics waveforms with very broadband seismograms recorded in Japan during the 2003 Tokachi-Oki megathrust event ($M_w$ = 8.3, 2003 Sept 25). We show that GPS can provide valuable data between periods of $30 \ s$ and $1300 \ s$, but waveforms with periods between $120 \ s$ and $300 \ s$ have to be handled with caution, because these periods are more subject to multipath effects and ionosphere perturbations. In the light of the comparison with synthetic seismic displacement waveforms, the performance of GPS does not vary from $350 \ km$ to $1300 \ km$ (RMS $\sim 0.01 \ m$). GPS stations located within $350 \ km $ to the epicenter experience static offsets $ > 5 \ cm$, which cannot be predicted by synthetic seismograms, but still provide robust and reliable waveforms. We conclude that even for very long periods, GPS is well capable of recovering millimetre ground motion oscillations, potentially providing valuable information on the lithosphere and upper-mantle heterogeneities on a scale of $300 \ km$ to $3000 \ km$.
\end{abstract}
\linespread{2}
\introduction %% \introduction[modified heading if necessary]
The quality of tomographic models depends on the quality of data available, on the distribution of instruments, and on our capability to invert these data with high accuracy. Thanks to both the large amount of data collected by dense seismic networks and the increasing computational resources, global Earth velocity models are continuously improving. For regions located beneath the crust and down to depths of $\simeq 400 \ km$, most global seismic velocity models \citep{kennett1991,becker2002,panning2006} are in agreement \citep{ritsema2011}. The consistency of these models is nevertheless guaranteed by the inclusion of long-period records of large seismic events. Indeed, these waveforms participate in constraining the rheology of the crust and upper-mantle and normal modes of the Earth \citep{park2005}.
Today, long-period data are recorded by very broadband seismometers of regional (e.g. Berkeley Seismological network, USArray \citep{usarray}) or global (e.g. GEOSCOPE, Global Seismic Network \citep{geoscope,peterson1989}) networks. The installation and maintenance costs of such instruments being very high make these data very precious and the networks difficult to expand. The best-performing instruments to record surface motion followed by earthquakes are very broadband seismometers (such as STS-1, STS-2 \citep{wielandt1982} among others). They are capable of recording seismic waves over a wide range of periods (from $0.1s$ to $1200 \ s$) that enables us to map the subsurface at various resolutions \citep{romanowicz2001,montagner2008}. However, because of their great sensitivity, very broadband seismometers suffer of limitations related to signal saturation if the acceleration of the ground is too strong. As a consequence, few long-period data are available in the near-field of large earthquakes. Therefore long-period data recorded by high-accuracy instruments are limited to remote locations or to the days that follow the recovery of the instruments. This lack of data results in a lower resolution of the seismic finite fault models for large event ($Mw > 8$) and a divergence of seismic velocity models for depths $>400 \ km$ \citep{ritsema2011}.
Because of its high accuracy at long-periods (detecting ground motions larger than 2 mm) and its lower maintenance costs, the Global Positioning System (GPS) networks could be used to support broadband seismometer and strong-motions networks to record surface motion close to seismic sources \citep{bilich2008,houlie2011,houlie2014} by providing high-quality displacement waveforms. As any other instruments, the detection of motion by GPS depends on the magnitude of the event, of the sensitivity of the instrument (i.e. sampling rate) and of its distance to the epicenter. High-rate GPS has been proven to be sensitive to ground motions that are induced by large earthquakes hundreds of kilometres from the epicentre \citep{larson2003} but its capability to recover long-period oscillations after the static offset is stabilized is not yet determined.
GPS observations have been shown to be reliable in providing surface displacement waveforms for periods ranging from $3 \ s$ to $\simeq 120 \ s$ \citep{elosegui2006,blewitt2008,bock2011,houlie2011,psimoulis2014}. As opposed to seismometers and superconducting gravimeters that record velocity or acceleration, GPS instruments provide displacement waveforms directly. Accuracy and performance of GPS data at longer periods ($50 - 1300 \ s$) still need to be assessed.
Here, we assess the performance of high-rate GPS waveforms for period bands that are relevant to the various applications of long-period seismology ($T > 30 \ s$) we compare them with synthetic seismograms computed using SPECFEM3D GLOBE \citep{komatitsch2002} and YSPEC \citep{alattar2008} algorithms.
%
\nocite{bock1993}
\section{Data}
\subsection{GPS displacement waveforms}
The Tokachi-Oki earthquake occurred $\simeq 80 \ km$ offshore the Hokkaido island on 2003 September 25 at 19:50:07 (UTC) (Figure~\ref{fig:intro_figure}). The magnitude of the earthquake is $Mw = 8.1$\citep{miyazaki2004} and $8.3$ \citep{houlie2011}, and produced ground motion that were large enough to clip all high-frequency and broadband seismometers all across Japan \citep{clinton2004}. As its rupture is fairly uncomplicated compared to its magnitude \citep{miyazaki2004,koketsu2004} a point source approximation was validated to model this event for long distances \citep{houlie2011}. For this mega-earthquake the regional displacement (between $0.05 - 0.15 \ m$, Table \ref{fig:intro_figure}) is above the noise level of GPS measurements ($\simeq2 \ mm$) \citep{elosegui2006}.
We have processed data of 91 GPS sites (out of $\sim$ 800 available) of the GEONET network. We have selected those sites because of their proximity to F-NET seismometers \citep{okada2004}. We also included in the GPS dataset, data recorded by two receivers (MIZU and USUD) that belong to the International GPS Service (IGS) tracking network.
One of the GEONET GPS (0292) is colocated with a GEOSCOPE seismometer INU (STS-1 sensor). All seismometers and GPS stations mentioned in the text are displayed in Figure~\ref{fig:intro_figure}. All data have been processed using GAMIT GPS data processing software \citep{king2011}. We then used the ionosphere-free phase residuals to invert for the local displacement histories assuming all the phase residuals are due to the motion of the GPS antennas.
The GPS data processing is done in a network, where the solution of each station is not the absolute position, but rather a relative displacement compared to the average position of the entire network over the processing time period \citep{houlie2011}. After completion of the data processing using the double-difference approach, we extract the corresponding one-way residuals for each station-satellite pair. One way residuals equal the dot product of the antenna motion and the unit vector representing the line of sight (LOS) between each satellite (Figure \ref{fig:prn}.
Before the inversion LOS time-series, in order to minimize the contribution of multipath to the GPS phase, we took into account only data corresponding to satellites that were at least $ 10^\circ$ above the horizon.
%Satellites are moving continuously with respect to each GPS antenna, we also show another version of the same figure with varying satellite elevation (Supplementary Materials). In the following description of data processing we assume that the elevation and azimuth angles of each satellite were constant during the time of interest.
The time series of phase changes along the line of sight directions were inverted into displacement in east, north and vertical directions using a least-squares approach:
\begin{equation}
\begin{bmatrix}
north\\
east\\
vert
\end{bmatrix}= (G^{T}\cdot W_{d}\cdot G)^{-1}\cdot G^{T}\cdot W_{d}\cdot \begin{bmatrix}
\phi_{1}\\
\phi_{2}\\
\vdots \\
\phi_{n}
\end{bmatrix}
\label{eq:disp}
\end{equation}
\noindent where the matrix G is:
\begin{equation}
G= \begin{pmatrix}
\cos el_{1}\cdot \cos az_{1} & \cos el_{1}\cdot \sin az_{1} & \sin el_{1}\\
\cos el_{2}\cdot \cos az_{2} & \cos el_{2}\cdot \sin az_{2} & \sin el_{2}\\
\vdots & \vdots & \vdots \\
\cos el_{n}\cdot \cos az_{n} & \cos el_{n}\cdot \sin az_{n} & \sin el_{n}
\end{pmatrix}
\label{eq:G}
\end{equation}
\noindent where $el_{n}$ and $az_{n}$ are the elevation and azimuth of the $n^{th}$ satellite at each epoch, respectively. The matrix $W_{d}$ is the inverse of the variance-covariance matrix of the data:
\begin{equation}
W_{d}=\left ( \sigma _{d}^{2} \right )^{-1}\cdot I
\label{eq:Wd}
\end{equation}
\noindent where $\sigma$ is $2 \ mm$, in agreement with many studies assessing the accuracy of GPS measurements \citep{elosegui2006,houlie2005,houlie2011,psimoulis2014}. The satellite phase information after correction for ionosphere effects is denoted by $[\phi_{n}]$. The resulting displacement waveforms are shown in Figure~\ref{fig:gps_components}.
For easier interpretation we also consider the motion of the ground in a source - GPS antenna space frame by rotating the horizontal north and east components into a more meaningful radial and tangential direction:
\begin{equation}
\begin{bmatrix}
radial\\
tangential
\end{bmatrix}= \begin{bmatrix}
cos\theta & -sin\theta\\
sin\theta & cos\theta
\end{bmatrix}\cdot \begin{bmatrix}
east\\
north
\end{bmatrix}
\label{eq:rotating}
\end{equation}
%
As shown by Houli\'e et al. (2011), due to the satellite distribution in the sky, the vertical motion of the GPS observations is the most reliable of the three components presented \nocite{houlie2011}. This can be well explained that 1) we are not estimating absolute coordinates, but only position changes and 2) all satellites contribute to constraining the vertical motion, while their contribution to the horizontal components depends on the azimuthal distribution of the satellites during the time of the wave propagation. The accuracy of horizontal components is, however, not only determined by the position of satellites, but also by the position of the source with respect to the GPS antenna. Decomposing the ground motion into radial and tangential components allows to separate Rayleigh and Love waves.
\subsection{Seismic and synthetic seismic waveforms}
During the event, it appeared that almost all F-NET and Hi-net seismometers clipped \citep{clinton2004}. \citet{houlie2011} showed that the data recorded by the GEOSCOPE \citep{geoscope} STS-1 very broadband seismometer located in Inuyama, Japan (code INU, Figure~\ref{fig:intro_figure}) could be used for the periods ranging from 30 to 60s. In this study, as we are interested by periods longer than 200s in whole Japan, we supplemented this data with sets of synthetics seismograms.
% The sensitivity of these instruments is the greatest between periods of $0.2$ and $300 \ s$ with linearly decreasing sensitivity up to $1200 \ s$. This factory instrument response has been improved by the GEOSCOPE team using both tides and remote seismic events \citep{geoscope}. We obtain displacement waveforms using the SAC2000 (Seismic Analysis Code ) package\citep{sac}.
%When long-period seismic data are not available close to the GPS antenna, we generate synthetic seismic waveforms to simulate the arrivals of the propagating seismic waves. Considering the periods investigated in this paper, the Tokachi-Oki event has a very compact ($\simeq 50 \times 50 \ km$, average slip $\simeq 5 \ m$) source \citep{miyazaki2004}.
Synthetic seismic waveforms have been computed with the SPECFEM3D GLOBE (REF) and YSPEC (REF) packages taken for assumed the seismic source to be a point source solution. We consider this assumption to be reasonable at least in the far field as according to \citep{miyazaki2004} the Tokachi-Oki rupture was very compact ($\simeq 50 \times 50 \ km$). SPECFEM3D GLOBE is a continuous Galerkin spectral-element method, which simulates acoustic (fluid), elastic (solid), coupled acoustic/elastic, poroelastic or seismic wave propagation on a global or regional scale \citep{komatitsch2002}. It gives great flexibility on the settings and it is capable of modelling long-period waves up to a period of $\simeq 500 \ s$. We present synthetic seismic waveforms computed by SPECFEM3D GLOBE using the 3D S40RTS mantle model \citep{ritsema2011}, and the built-in CRUST2.0 crustal model \citep{bassin2000}. The YSPEC synthetics package calculates synthetic seismograms in spherically symmetric earth models using the direct radial integration method introduced by \citep{friedrich1995}, and extended in \citep{alattar2008} to incorporate the effects of self-gravitation. YSPEC synthetic seismograms are computed using the 1D PREM model \citep{dziewonski1981}. For a full scale of comparisons, we also have computed SPECFEM synthetic seismograms with PREM model.
% using the parallel computing resources available at ETH-Zurich (BRUTUS)
% you do not support this statement by any reference
%Comparisons have been made with the YSPEC package to assess the long period signals of SPECFEM3D GLOBE that are not reliable of recovering long-period ground motion at periods longer than $500 \ s$, as the software is designed to model seismograms of broadband seismometers, with recordings typically below $\simeq~360 \ s$.
Both SPECFEM3D GLOBE and YSPEC synthetic simulations are set to start at the origin time $t_0$ of the earthquake. We adopt this time as a reference time for each dataset, since the very broadband seismometers (STS-1 and STS-2) are following UTC (Coordinated Universal Time), while the GPS system has its own time reference. The offset of time between UTC and the GPS time at the time of the Tokachi-Oki earthquake has been corrected for a difference of 13 leap seconds.
The amplitudes of the presented synthetic waveforms have been scaled to match the GPS waveform amplitudes. This allows a comparison between the phases of the GPS and synthetic datasets. We justify the scaling of the amplitudes with unknown uncertainties of the source size and the different Earth models used when generating synthetic datasets.
\section{Results}
\subsection{Comparison at the INU GEOSCOPE site}
We present the comparison between the seismic records (GEOSCOPE station at Inuyama, INU) synthetic seismograms and GPS time-series in displacement (station 0292, Figure \ref{fig:gps_components_comparison}).
As records lengths are longer than 5000s (10 minutes of data before the event) they allow documenting periods as long as 1300s. To assess the GPS waveforms performance as thoroughly as possible, we filtered each waveform into 5 period bands: $30 - 50 \ s$, $50 - 120 \ s$, $120 - 300 \ s$, $300 - 500 \ s$ and $500 - 1300 \ s$. These corners frequencies correspond to the corner periods (30 and 50s) of the ground motion at 0292 according to \citet{houlie2011}, to the corners periods (120 and 300s) of STS-2 and STS-1 seismometers and at least to the frequency of the normal mode 0S0 (~1200s). The additional period (500s) is used to make sure a band is defined for periods beyond the 4th corner frequency of the STS-1 sensor. For all data, we use band-pass Butterworth second-order a-causal filters included into SAC \citep{sac} to the vertical components of the different datasets (Figure~\ref{fig:hokk_filters}). Such filter being a-causal, the effect of the ground motion cannot be seen before the arrival time.
We first compare east, north and vertical components of GPS time-series with the corresponding component of both real and synthetic seismograms.
For the short period bands ($30 - 50 \ s$ and $50 - 120 \ s$), we observe a good agreement between the different GPS and seismic waveforms (Figure\ref{fig:gps_components_comparison}). Such agreement has been noticed already for the first band by \citet{houlie2011}. We tested this comparison in two geometries (East, North, Vertical and Radial, Tangential, Vertical). The fit between dataset in R,T,V geometry is however better than in E,N, V geometry as few satellites are present in the sky near azimuths 0 and 180 at the time of the event.
The GPS data in the period band of $120 - 300 \ s$ seems less reliable, possibly due to the contribution of radio wave multipath (reflection of GPS radio waves on a object before its arrival at the antenna) but also possibly by the arrival of new satellite in the constellation. Such effect has been identified as the possible cause for steps in the time-series. This band should be the case for a future research effort to both understand the cause (ionosphere scintillation, multipath, bad distribution of satellite in the sky.
For the long period bands ($300 - 1300 \ s$), even if the amplitudes are smaller (peak to peak amplitude of ~0.5cm) we observe a good agreement between GPS and synthetic waveforms, even if a slight shift in phase in visible. The seismogram
start of the oscillation detected by the GPS is in phase with the seismic synthetics but not with the seismogram of GEOSCOPE sensor INU. Due to the large shake (>1cm/s) it likely quasi-static saturation was responsible for the misfit between real and synthetic seismograms.
\subsection{Comparison with synthetic seismograms}
All long-period (T>30s ) signals do have a component that is related to specific locations of sensors.
To assess the quality of GPS time-series across the entire network, we calculate the RMS deviation between each component of synthetics seismograms and GPS time-series.
For each band, the Root Mean Square Deviation (RMSD) has been computed (Table {\bf XX}):
\begin{equation}
RMSD = \sqrt {\frac{1}{N} \cdot \sum {(d_1 - d_2)^{2}}}
\label{eq:rms1}
\end{equation}
\noindent where $N$ is the number of points used for the RMS deviation analysis. The two datasets considered are denoted by $d_1$ and $d_2$.
All RMSD are shown in Figure \ref{fig:rms_bands} for different band pass filters and for the three components, respectively.
%\begin{figure}[t]
%\includegraphics[width=10cm]{10_rms_components_normalised_rotated.eps}
%\caption{RMS fit between GPS data and YSPEC synthetics (crosses) and GPS data and SPECFEM synthetics (circles) for vertical, east and north components.}
%\label{fig:rms_components}
%\end{figure}
%\begin{figure}[t]
%\includegraphics[width=12cm]{08_conclusion_map_rotated.eps}
%\caption{The GEONET stations and their static displacement in the near-field.}
%\label{fig:rms_map}
%\end{figure}
The RMS error between GPS and both synthetic datasets are satisfactory, especially at epicentral distances larger than $\simeq 350 \ km$. Stations closer than $320 \ km$ to the epicentre appear to be more noisy compared to synthetic datasets. These stations are mostly located in and around the sedimentary basins of Hokkaido island \citep{miyazaki2004}. The presence of large sedimentary basins and the source being so close to these stations explain the larger RMS fit values. These are also the stations that experience static displacement which contributes to the larger RMS between data and synthetic waveforms.
The comparisons between GPS and the two different types of synthetics differ from each other due to the different method of generating synthetic waveforms and the different Earth models that are used. YSPEC synthetics are based on a self-gravitating Earth model, therefore including gravitational effects that start to rise at long period surface waves. It uses a simple 1D model, PREM, therefore it is not expected to capture the finer details. SPECFEM synthetics on the other hand are generated using s40rts, a more detailed 3D model, but there is no self gravitation applied. As expected, SPECFEM synthetics fit the GPS data better at shorter periods, and the two fits are getting closer to each other as we increase the period range.
The vertical component proves to give the best fit across the period ranges. This is expected due to the satellite constellation as explained in section 3. We see a trend of decreasing RMS error with increasing period ranges, with the exception of the period band of $120 - 300 \ s$, that seems to be contaminated by multipath error at most stations.
To put our study in context, we compare the accuracy of the GPS waveforms presented here with previously published results. In Table~\ref{tab_xy} we show the uncertainties of the processed GPS waveforms at different period ranges, as well as the uncertainties of GPS waveforms from other published works. These uncertainties were determined from the GPS waveforms recorded the day before the earthquake when the satellite constellations are exactly the same (23 hours and 56 minutes before) and there is no expected ground motion. We fit the time windows of these calculations to the different period-bands so that the window contains the arrival of the surface waves at those periods.
\begin{table}
%\begin{minipage}{80mm}
\caption{Uncertainties of the GPS measurements compared to other studies.}
\label{tab_xy}
\begin{tabular}{lrrrr}
Dataset & Period (s) & Accuracy (mm) & Reference \\
\hline
Radial displacement & 30-50 & $\pm \ 2$ & This study \\
Tangential displacement& 30-50 & $\pm \ 2$ & This study \\
Vertical displacement &30-50 & $\pm \ 1.5$ & This study \\
Vertical displacement &50-120 & $\pm \ 2$ & This study \\
Vertical displacement &120-300 & $\pm \ 2$ & This study \\
Vertical displacement &300-500 & $\pm \ 2$ & This study \\
Vertical displacement &500-1300 & $\pm \ 0.5$ & This study \\
Vertical displacement &30-50 & $\pm \ 2$ & \citep{houlie2011} \\
Absolute displacement & $\infty$ & $2.5 \pm 2.5$ & \citep{elosegui2006} \\
Spectral displacement &3-10 & $4.5 \pm 2.3$ & \citep{psimoulis2014} \\
Spectral displacement &10-100 & $5.1 \pm 2.1$ & \citep{psimoulis2014} \\
\end{tabular}
%\end{minipage}
\end{table}
\section{Conclusion}
We compare high-rate GPS waveforms with broadband seismometer waveforms and 3D synthetic seismic waveforms computed with SPECFEM3D GLOBE \citep{komatitsch2002} and YSPEC \citep{alattar2008}. We determine displacement {\bf waveforms with periods ranging from $30 \ s$ to $1300 \ s$ for a } selection of high-rate GPS sites.
Evidence from processed high-rate GPS data of the 2003 Tokachi-Oki earthquake shows that the long-period GPS waveforms are re are in agreement with the synthetic seismic waveforms for at least the first $1200 \ km$ around the epicenter for $T > 30 \ s$.
Such long-period surface waves (30-1300s) sample the crust and the upper mantle {\bf(depth range?)}.
We conclude that GPS instruments have the potential to supplement networks of broadband seismometers and to enhance the imaging of large-scale structures in the upper- and mid-mantle in the next generation of seismic tomographic models.
%RMS deviation between GPS and synthetics are as high as the RMSD between synthetic datasets. This is due to the use of different Earth velocity models, different approaches in term of gravity modelling.
Next generation of velocity models can include data recorded by GPS receivers in the near-field, and they might be able to better recover static offsets ($> 2 \ cm$) for sites located near the source ($d < 2x \ fault \ segment$). GPS would complement seismic dataset together in order to improve simultaneously seismic sources and Earth velocity models.
QUESTIONS: Does Hokkaido event generate long-periods? up to what period?
%\conclusions %% \conclusions[modified heading if necessary]
%TEXT
\clearpage
% Figure 1
\begin{figure}
\includegraphics[width=12cm]{figures/01_intro_map_rotated_wprofile_NH.eps}
\caption{a) Location of the GPS GEONET network with respect to the extended rupture of the Tokachi-Oki earthquake. Location of the 0292 GPS and the co-located INU broadband seismometer stations; and the two IGS stations, MIZU and USUD are labeled. b) Horizontal displacements versus epicentral distance. Level of 0 and 2 cm displacement are indicated using grey lines. From this profile, we constrain a threshold distance at 320km. This distance corresponds to the double of the fault segment width as defined by \citep{miyazaki2004}}
\label{fig:intro_figure}
\end{figure}
\newpage
% Figure 2
\begin{figure}
%\includegraphics[width=12cm]{02a_prn_plot.eps}
%\includegraphics[width=12cm]{02b_vert_no_filter.eps}
\includegraphics[width=12cm]{figures/02a_prn_plot_02b_vert_no_filter.eps}
\caption{a) Line of Sight (LOS) ionosphere-free phase for site 0292 (see Figure~\ref{fig:intro_figure}) around the passage time of the seismic wavefield generated by the Tokachi-Oki earthquake. b) Vertical and horizontal (north and east) displacement waveforms at 0292 GPS station of the Hokkaido earthquake with a $30 - 50 \ s$ Butterworth filter applied. The blue star indicates the origin time of the earthquake.}
\label{fig:prn}
\label{fig:gps_components}
\end{figure}
\newpage
% Figure 3
\begin{figure}
%\includegraphics[width=12cm]{03_hokkaido_components_rotated.eps}
\includegraphics[width=12cm]{figures/04_hokkaido_rad_tang_components_normalised_NH.eps}
%\caption{a)Vertical, and horizontal (north and east) displacement waveforms at 0292 GPS station of the Hokkaido earthquake with a $30 - 50 \ s$ Butterworth filter applied. The blue star indicates the origin time of the earthquake.
%b) Vertical, and horizontal (radial and tangential) displacement waveforms of 0292 GPS station (red), co-located INU STS-1 seismic station (blue) and synthetic seismic waveforms (green) of the Hokkaido earthquake with a $30 - 50 \ s$ Butterworth filter applied. The blue star indicates the origin time of the earthquake.}
\caption{Vertical, and horizontal (radial and tangential) displacement waveforms of 0292 GPS station (red), co-located INU STS-1 seismic station (blue) and synthetic seismic waveforms (green) of the Hokkaido earthquake with a $30 - 50 \ s$ Butterworth filter applied. The blue star indicates the origin time of the earthquake.}
%\label{fig:gps_components}
\label{fig:gps_components_comparison}
\end{figure}
\newpage
% Figure 4
\begin{figure}[t]
\includegraphics[width=12cm]{figures/05_hokkaido_filters_normalised.eps}
\caption{Vertical displacement waveforms of 0292 GPS station (red), co-located INU STS-1 seismic station (blue) and synthetic seismic waveforms calculated with SPECFEM (green) and YSPEC (blue) of the Hokkaido earthquake with different Butterworth filters applied. The blue star indicates the origin time of the earthquake.}
\label{fig:hokk_filters}
\end{figure}
\newpage
%\begin{figure}[t]
%\includegraphics[width=12cm]{v2_06_hokkaido_30-50s_normalised.eps}
%\caption{Collection of vertical components of GEONET station waveforms filtered at $30 - 50 \ s$.}
%\label{fig:hokk_selection_1}
%\end{figure}
%\newpage
%\begin{figure}
%\centerline{
%\subfloat[50
%\includegraphics[width=.45\linewidth]{v2_06_hokkaido_50-120s_normalised.eps}}
%\hspace{1cm}
%\subfloat[120s
%}
%
%\vspace{.5cm}
%\centerline{
%\subfloat[300 s
%\hspace{1cm}
%\subfloat[500 s < T < 1300 s]{\includegraphics[width=.45\linewidth]{v2_06_hokkaido_500-1300s_normalised.eps}}
%}
%%\label{fig:hokk_selection_1}
%\label{fig:hokk_selection_2}
%%\label{fig:hokk_selection_3}
%%\label{fig:hokk_selection_4}
%%\label{fig:hokk_selection_5}
%\caption{Comparison between GPS and synthetic (YSPEC) time series}
%\end{figure}
%Figure 5
\begin{figure}
%\centerline{
\subfloat[30 - 50 s; 50 - 80 s]{
\includegraphics[width=.85\linewidth]{figures/regional_20_hokkaido_filters_selected_vert.eps}}
%\hspace{1cm}
\subfloat[80 - 120 s; 120 - 160 s]{\includegraphics[width=.85\linewidth]{figures/regional_20_hokkaido_filters_selected_vert_long.eps}}
%}
%\vspace{.5cm}
%\centerline{
%\subfloat[160 - 200 s; 200 - 300 s]{\includegraphics[width=.35\linewidth]{figures/regional_20_hokkaido_filters_selected_vert_long_2.eps}}
%\hspace{1cm}
%\subfloat[300 - 400 s; 400 - 500 s]{\includegraphics[width=.35\linewidth]{figures/regional_20_hokkaido_filters_selected_vert_long_3.eps}}
%}
%\label{fig:hokk_selection_1}
%\label{fig:hokk_selection_2}
%\label{fig:hokk_selection_3}
%\label{fig:hokk_selection_4}
%\label{fig:hokk_selection_5}
\label{fig:hokk_waveforms_SPECFEM}
\caption{{Comparison between GPS and synthetic (SPECFEM) time series at the following period bands: a) $30 - 50 \ s$ and $ 50 - 80 \ s$; b) $80 - 120 \ s$ and $ 120 - 160 \ s$; c) $160 - 200 \ s$ and $ 200 - 300 \ s$; d) $300 - 400 \ s$ and $ 400 - 500 \ s$. The blue star marks the PDE time: 19:50:38}}
\end{figure}
\newpage
\begin{figure}[t]
\includegraphics[width=8cm]{figures/09b_rms_bands_comparison_with_new_data.eps}
\caption{RMS fit between GPS data and YSPEC synthetics (crosses) and GPS data and SPECFEM synthetics (circles) at the band-pass filtered period ranges presented.}
\label{fig:rms_bands}
\end{figure}
\newpage
%\input{spectrograms_LP}
%\newpage
%\input{spectrograms_mesh_LP}
%\appendix
%\section{} %% Appendix A
%\subsection{} %% Appendix A1, A2, etc.
\clearpage
\authorcontribution{K. Kelevitz performed the data processing and analyses described in the Data and Results sections. All authors contributed to the interpretation of the results and prepared the manuscript }
\begin{acknowledgements}
The project is funded by SNF (Swiss National Fund), under the project code 200021\_143605. We would like to thank Tarje Nissen-Meyer and Lapo Boschi for helpful discussions and comments on the paper; and Daniel Peter for advices on synthetic seismic waveforms. The SPECFEM3D GLOBE simulations presented here were performed using the BRUTUS cluster at ETH Z{\"u}rich. All authors thank the GEONET GSI for recording, archiving the datasets.
\end{acknowledgements}
\clearpage
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\bibliographystyle{copernicus}
\end{document}
