- © Seismological Society of America
Global Navigation Satellite System (GNSS) position time series are used pervasively in earthquake science to measure the surface response to earthquake cycle deformation. Characteristic usage cases are focused on the temporal windowing of position data to isolate coseismic, postseismic, or interseismic deformation. Here, we present an interactive visualization approach for the temporal evolution of GNSS time session in 2D in which the position estimates are amplified relative to their true positions, or are amplified relative to a reference state. This approach enables a rapid visual assessment of deformation patterns across all phases of the earthquake cycle in relation to topographic structure and active faults including azimuth reversal of coseismic and interseismic deformation.
Over the last two decades, Global Navigation Satellite System (GNSS) position time‐series measurements have emerged as an integral part of earthquake science, enabling the imaging of coseismic slip distributions (e.g., Shen et al., 1996; Simons et al., 2011), quantification of slip deficit rates, and the discovery of silent earthquakes (e.g., Dragert et al., 2001; Graham et al., 2014). Classical approaches to visualize these data have fallen into two general categories: (1) map view of velocity/displacement vectors over a fixed time interval and (2) time versus position plots of GNSS component (east, north, and up) time series. Each of these approaches has proved to be informative ways of understanding the spatial distribution crustal movements and the time evolution of solid‐earth deformation.
Maps with arrow representations of GNSS velocities/displacements are used to visualize and understand both tectonic and earthquake cycle activity (e.g., Feigl et al., 1990, 1993; Hager et al., 1991; Sella et al., 2002; Sagiya, 2004; Kreemer et al., 2014; see Data and Resources). The velocities and displacements are derived from differential position measurements and represent snapshots of activity within a finite time interval (Fig. 1). With the recent rise of very dense GNSS data sets in Japan (Sagiya, 2004) and the western United States (see Data and Resources), it has become more challenging to use static arrow plots to meaningfully visualize all GNSS data in a given region (Fig. 1), as the velocity arrows plot over one another without using multiple velocity scales on a single figure (Wang et al., 2011). Time‐dependent arrow animations of GNSS displacements following the 2011 Mw 9 Tohoku‐Oki earthquake have revealed the spatially coherent propagation of both body and surface waves (Grapenthin and Freymueller, 2011, see Data and Resources). Time‐dependent vertical velocity changes have also been visualized as animated scatter plots (see Data and Resources).
More typically, time‐dependent GNSS time series are visualized as individual displacement components (east, north, and up) as a function of time (e.g., Savage and Svarc, 1997; Dragert et al., 2001, Ergintav et al., 2009; Mavrommatis et al., 2014; Loveless and Meade, 2016). This enables the identification of the temporal relationships and relative magnitudes of deformation between different phases of the earthquake cycle (Fig. 2). Interseismic deformation appears relatively steady in time with semiharmonic annual perturbations at rates of <100 mm/yr. Coseismic deformation is readily identified as jumps in daily (or subdaily) position estimates and postseismic appears as nonlinear variations in position estimates over the years to decades following large earthquakes. Additionally, slow or silent earthquakes may appear as motion reversals in interseismic velocity trends (e.g., Dragert et al., 2001) or as time‐dependent changes in the slope of interseismic velocity components (e.g., Nishimura et al., 2004; Meade and Loveless, 2009; Mavrommatis et al., 2014). Web‐based browsing of GNSS time series is available at numerous archival and data distribution sites (see Data and Resources) and the MATLAB‐based TSView tool (see Data and Resources, Herring, 2003) enables the interactive removal jumps and trends from locally hosted time‐series data are to isolate individual stages of the earthquake cycle.
A recent innovation in the visualization of GNSS position time series was the development of geodograms (Wernicke and Davis, 2010). Designed to illuminate low magnitude, spatially coherent behavior plots show positive and negative trends after a linear trend has been subtracted from GNSS position time series projecting along an azimuth. These visualizations have been used to understand nonlinear interseismic deformation trends and led to the inference of in the Basin and Range Province and led to the hypothesis inference of the occurrence of intracontinental slow‐slip events (Wernicke and Davis, 2010).
INTERACTIVE VISUALIZATION OF GNSS‐AMPLIFIED POSITION TIME SERIES IN SPACE
The central idea is to take the initial GNSS coordinates of each station and draw lines connecting their daily position estimates, in which the change in daily longitude and latitude is amplified by a factor of α. The first coordinate of each track is the initial longitude and latitude position of each GNSS time series t0. A first‐order approximation of the amplified longitude and latitude track positions is given by and λp(t)=λ(t0)+α(λ(t)−λ(t0)), in which and λ(t) give the longitude and latitude of a GNSS station at time t. The amplified station longitudes and latitudes, relative to initial coordinates and λ(t0), are given by and λp(t), and these are the quantities that are plotted as the position tracks for each station. These amplified position tracks (Fig. 3) directly show the position history of each GNSS station and allow for the visual estimation of both linear velocity trends and deviations away from linear trends. Additionally, we encode time into the visual representation of the position track visualization by coloring each track with a smooth gradation from a starting color (indicating t0) through a smooth variation to an ending color representing the final time in the position track. A disadvantage to the simple track amplification method described here is that it does not adequately track across nonmonotonic variations in longitude and latitude (i.e., poles, prime meridian).
INTERACTING WITH TIME‐SERIES POSITION TRACKS
“lon”: [139.06990407, 139.069904, 139.06990413, …],
“lat”: [34.949757897, 34.949757882, 34.949757941, …]
in which name is a string specifying the name of the GNSS station (should be unique), start is an integer specifying the Unix timestamp of the first GNSS reading, and lon and lat are arrays of floating point numbers giving the station longitude and latitude positions at daily intervals. The longitude and latitude arrays must be of the same length for each station, but they may be distinct at different stations. Zero longitude and latitude are treated as special values indicating missing data. A JSON file with these data can be loaded by clicking on the “Load local file” button. For an example of data sets derived from the GEONET array in Japan and PBO array in the United States, see Data and Resources.
In addition to the standard Google Maps navigation features, the interactive nature of this GNSS position track visualization is characterized by four main features: (1) temporal windowing, (2) control of amplification scale, (3) median position corrections, and (4) color encoding of time. The temporal window of the displayed tracks is not fixed at the first and last date of the available data. Instead, it can be specified and controlled by a time line at the bottom of the visualization (Fig. 3). This enables the track visualization to be temporally localized on an event of interest (e.g., the 2011 Tohoku‐Oki earthquake). At smaller time intervals, GNSS tracks may appear relatively short in the absence of significant coseismic activity or too long as a result of large coseismic displacements. The track scaling magnitude α can be adjusted by dragging the “multiplier” slider. Larger and smaller multiplier values produce longer and shorter track lengths, respectively. Position estimates may be modified by a “median correction,” ranging from 0 to 1, in which 0 indicates no median correction. This adjustment to the time series subtracts the median position from each component time series on a station‐by‐station basis. In some cases, this may lead to less noisy visualizations of interseismic tracks. Selectable colors (“start color”, “end color”) can be used to encode the relative time along a GNSS track. For example, in Figure 3, yellow indicates the start of selected epoch, and the color grades to red which characterizes the end of the selected epoch. Additionally, the GNSS position tracks may be animated by selecting the “enable” check box under the “Animation” tab. This feature will continually draw day‐by‐day track updates, returning to the starting date once the end date has been reached.
We described a web‐based application for analyzing time‐dependent GNSS position time series in their geographic context that provides a way to simultaneously visualize the temporal and spatial evolution of these complex fields. As these data sets continue to grow ever larger, from tens to thousands of stations, there is an increasing need to be able to interactively interrogate these data to understand the spatial relationships between deformation across the entire earthquake cycle and to enable the discovery of new types of deformation at the Earth’s surface.
DATA AND RESOURCES
We thank Zhigang Peng and two anonymous reviewers for offering comments on this article.