CARIB 18 : A Stable Geodetic Reference Frame for Geological Hazard Monitoring in the Caribbean Region

We have developed a Stable Caribbean Reference Frame 2018 (CARIB18) using long-term continuous observations from 18 continuously operating Global Positioning System (GPS) stations fixed on the margins of the stable portion of the Caribbean plate. The frame stability of CARIB18 is approximately 0.7 mm/year in the horizontal direction and 0.9 mm/year in the vertical direction. A method that employs a total of seven parameters for transforming positional time series from a global reference frame (IGS14) to a regional reference frame is introduced. The major products from this study include the seven parameters for realizing CARIB18 coordinates and three-component site velocities of 250 continuous GPS stations (>3 years) with respect to CARIB18. Geological hazard monitoring using GPS has traditionally been performed using the carrier-phase differential method that requires single or multiple reference stations to be simultaneously operated in the field. CARIB18 allows for precise geological hazard monitoring using stand-alone GPS, which substantially reduces field costs and simplifies logistics for long-term geological hazard monitoring. Applications of CARIB18 in plate motion, post-seismic, and volcano monitoring and research are demonstrated in this article. The regional reference frame will be periodically updated every few years with more reference stations and longer periods of observations to mitigate the degradation of the frame over time and will be synchronized with the updates of the International GNSS Service (IGS) IGS reference frame.


Introduction
The Caribbean region is one of the earliest regions worldwide to employ Global Positioning System (GPS) for geological hazard studies.Due to its active tectonic and tropical environment, the Caribbean region is rife with natural hazards, such as earthquakes, volcanoes, landslides, flooding, tsunamis, hurricanes, and coastal erosions.GPS stations were installed in the Caribbean region since the middle of the 1980s for studying plate motions [1][2][3][4], almost one decade earlier than the full operation of GPS in 1995.The Caribbean region, as defined by this study, comprises the Caribbean Sea and its surrounding islands, including Central America to the west, the Greater Antilles to the north, the Lesser Antilles to the east, and parts of adjacent South America to the south (Figure 1).The tectonic entity that we refer to as the "Caribbean plate" comprises the Caribbean Ocean Plateau and the Plate Boundary Zones (PBZs) between the Caribbean Ocean Plateau and its neighbor tectonic plates, including the North American plate to the north, the North Andes plate to the south, the South American plate to the southeast and east, and the Cocos plate and Nazca plate to the west.Figure 1 depicts the PBZs outlined based on the early concept of Caribbean PBZs proposed by Burke and Mann [5,6].The plate boundaries are defined by Bird [7] and the GPS-derived site velocities obtained from this study.The width of PBZs varies from approximately 200 km in the western PBZ to over 600 km in the eastern PBZ.The Caribbean Ocean Plateau is often regarded as the internal and stable portion of the Caribbean plate.The PBZs surrounding the interior of the Caribbean plate are comprised of numerous microplates that have recently garnered much attention from the scientific and politico-economic communities due to the hazard risks posed to the surrounding populated island countries [8][9][10][11][12][13].
Remote Sens. 2019, 11, x FOR PEER REVIEW 2 of 31 the Plate Boundary Zones (PBZs) between the Caribbean Ocean Plateau and its neighbor tectonic plates, including the North American plate to the north, the North Andes plate to the south, the South American plate to the southeast and east, and the Cocos plate and Nazca plate to the west.Figure 1 depicts the PBZs outlined based on the early concept of Caribbean PBZs proposed by Burke and Mann [5,6].The plate boundaries are defined by Bird [7] and the GPS-derived site velocities obtained from this study.The width of PBZs varies from approximately 200 km in the western PBZ to over 600 km in the eastern PBZ.The Caribbean Ocean Plateau is often regarded as the internal and stable portion of the Caribbean plate.The PBZs surrounding the interior of the Caribbean plate are comprised of numerous microplates that have recently garnered much attention from the scientific and politico-economic communities due to the hazard risks posed to the surrounding populated island countries [8][9][10][11][12][13].Currently, there are over 250 permanent long-term (>3 years as December of 2018) GPS stations within the Caribbean region that share raw data to the public through data archive facilities operated by UNAVCO, International Global Navigation Satellite System (GNSS) Service (IGS), Crustal Dynamics Data Information System (CDDIS) of National Aeronautics and Space Administration (NASA), National Geodetic Survey (NGS), Scripps Orbit and Permanent Array Center (SOPAC), and several other institutions.Positional time series with respect to certain regional or global reference frames are also provided by several institutions to the research community, such as the Geodesy Advancing Geosciences and EarthScope (GAGE) Facility at UNAVCO [14] and the Nevada Geodetic Laboratory (NGL) at the University of Nevada [15].The GPS antennas are mounted on monuments fixed on the ground or on one-to two-story concrete buildings.According to a recent investigation Currently, there are over 250 permanent long-term (>3 years as December of 2018) GPS stations within the Caribbean region that share raw data to the public through data archive facilities operated by UNAVCO, International Global Navigation Satellite System (GNSS) Service (IGS), Crustal Dynamics Data Information System (CDDIS) of National Aeronautics and Space Administration (NASA), National Geodetic Survey (NGS), Scripps Orbit and Permanent Array Center (SOPAC), and several other institutions.Positional time series with respect to certain regional or global reference frames are also provided by several institutions to the research community, such as the Geodesy Advancing Geosciences and EarthScope (GAGE) Facility at UNAVCO [14] and the Nevada Geodetic Laboratory (NGL) at the University of Nevada [15].The GPS antennas are mounted on monuments fixed on the ground or on one-to two-story concrete buildings.According to a recent investigation on closely-spaced Continuously Operating Reference Stations (CORS) in the Puerto Rico and Virgin Islands region, there is no considerable difference between building-based (one-to two-story concrete buildings) and ground-based GPS observations with regard to the precision or repeatability of daily positions and reliability of long-term site velocities as long as the buildings are stable [16].Accordingly, we regard velocities derived from one-to two-story building-based GPS stations as free-field site velocities.
Large GPS networks in the Caribbean region include the Continuously Operating Caribbean Observational Network (COCONET, http://coconet.unavco.org), the Puerto Rico and Virgin Islands GPS network (PRVINET, http://redsismica.uprm.edu), the Nicoya Peninsula GPS Network in Costa Rica (Principal Investigator: Tim Dixon), the Sistema de Referencia Geocéntrico para las Américas (SIRGAS) Reference Network (http://www.sirgas.org),Caribbean Hurricane Prediction and Geodetic Network (PI: John Braun), Montserrat Volcano Observatory GPS Network (MVO), and other local networks.These long-term permanent GPS stations were installed by joint efforts of academic institutions, local government agencies, and land surveying companies.Unfortunately, many GPS stations within the Caribbean region were damaged by Hurricanes Irma and Maria in 2017.Some stations have not been recovered since August 2017.
The GPS dataset from a single station is not sufficient by itself to precisely measure the change of positions.GPS geological hazard monitoring projects have traditionally been conducted with a carrier-phase differential method that requires simultaneous GPS observations at rover and reference sites.Nevertheless, the instability of the reference GPS will ultimately affect the accuracy of the entire survey.Furthermore, it is not cost effective for a survey project to operate extra GPS stations outside its monitoring object, and it becomes exceedingly difficult to get ideal sites for installing reference GPS stations in urban environments.This study intends to introduce a method that utilizes stand-alone GPS for long-term geological hazard monitoring.
The need for a unified stable geodetic reference frame has become desperately urgent in the Caribbean region with the completion of the Continuously Operating Caribbean GPS Observational Network (COCONET) project along with an increasing public awareness in natural hazard monitoring using GPS.COCONET was funded by the National Science Foundation (NSF) of the U.S. in 2010 [17].As of 2018, COCONET is comprised of 85 new and refurbished stations and over 70 existing GPS stations distributed across 26 Caribbean nations.Several COCONET stations were installed on islands sitting on the margins of the stable portion of the Caribbean plate (Figure 1).Those stations have provided fundamental datasets for realizing a stable Caribbean reference frame.This study aims to establish a stable geodetic reference frame within the Caribbean region.Publicly available GPS datasets spanning to the end of 2018 are utilized to realize the regional reference frame.Accordingly, the reference frame is called the Stable Caribbean Reference Frame 2018 (CARIB18).

GPS Data Processing
A complex aspect of GPS is that it initially provides positional coordinates with respect to a global reference frame, since the positions of satellites are defined with respect to a global reference frame.For high-accuracy positioning relying on post-processing, satellite ephemerides are always determined based on ground-based GPS observations from selected International GNSS Service (IGS) tracking stations.IGS08 was adopted in 2011 and then, due to the growing number of unusable stations within the IGS08 frame, was updated to IGb08 on 7 October 2012 [18].In January 2017, IGS14 frame was adopted in parallel with the redefinition of the International Terrestrial Reference Frame 2014 (ITRF2014) [19].The ITRF is a standard frame for referencing positions at different times and places around the world and provides the foundation for ground-based and space-based observations in Earth system sciences.IGS14 is the latest in a series of GNSS reference frames (e.g., IGS00, IGS05, IGS08) adopted by IGS [20].In general, a global reference frame is realized with an approach of minimizing the overall horizontal movements of a group of selected frame stations distributed worldwide.For example, the IGS08 reference stations are comprised of 232 permanent GPS stations; IGb08 reference stations are comprised of 235 permanent GPS stations [18], and IGS14 reference stations are comprised of 252 permanent GPS stations [20].The positional coordinates for most of the GPS stations change over time with respect to global reference frames as shown in Figure 1.The site velocities with respect to a global reference frame are often dominated by the long-term drift and rotations of tectonic plates.Localized ground deformation, such as the ground motions associated with volcano activities (swelling, sinking, and cracking), fault creeping, landslides, and subsidence, could be obscured or biased by long-term plate drifts.
Accuracy and precision of GPS positioning have been improved dramatically over the past two decades due to advances in GPS hardware, software, and reference frames.The accuracy of GPS measurements (positions or displacements) does not solely rely on GPS equipment (antenna and receiver) but largely depends on how the data are collected in the field and how the data are processed [21][22][23][24].GPS data processing algorithms generally implement two approaches: relative positioning and absolute positioning.The relative positioning approach uses simultaneous observations from two or more GPS units.One GPS unit is considered as a fixed station, also called a reference station.The relative positions are calculated using a carrier-phase differential method, which inherits high accuracy from the fact that the closely-spaced GPS units experience very similar errors and biases.The absolute positioning method determines the position of a single GPS station without using any simultaneous observations from other ground GPS stations.Precise Point Positioning (PPP) is a typical absolute positioning method [25].The PPP method has attracted broad interests in land surface displacements and structural deformation monitoring because of its operational simplicity and consistent accuracy over time and space [26,27].
This study applied the single-receiver phase ambiguity-fixed PPP method employed by the GIPSY-OASIS (V6.4) software package, simplified as GIPSY, for calculating 24-h average (daily) positions.The GIPSY software package was developed by the Jet Propulsion Laboratory (JPL).GIPSY employs the single-receiver phase ambiguity-fixed PPP method that incorporates the Wide-Lane and Phase-Bias (WLPB) estimates from a global network of ground GPS stations to fix phase ambiguities [28].JPL's final satellite orbit and clock products with respect to IGS14 and the WLPB estimates are used for the GIPSY processing.As of December 2018, JPL has not released its final orbit and clock products with respect to IGS14 for the years before 2002.Therefore, the GPS observations before epoch 2002.0 are not processed in this study.The other major parameters and key correction models applied during the GIPSY processing are the same as those reported in Wang et al. [29].An outlier-detection-and-removal algorithm was applied to the positional time series derived from the PPP solutions.The details of the outlier rejection method were addressed in Wang [23] and Firuzabadi and King [30].On average, six percent of the total measurements are removed as outliers in this study.
The PPP solutions are defined in an Earth-Centered-Earth-Fixed (ECEF) Cartesian coordinate (XYZ) system with its origin in the Earth's center of mass.In order to study ground deformation at the Earth's surface, the ECEF-XYZ coordinates are converted to a geodetic orthogonal curvilinear coordinate system (longitude, latitude, and ellipsoid height) referencing the GRS80 ellipsoid.The geodetic coordinates with respect to CARIB18 are then projected to a two-dimensional (2D) local horizontal plane.This enabled us to track superficial ground deformation in the north-south (NS) and east-west (EW) directions at each site.The vertical displacement derived from the ellipsoid heights is used to depict land subsidence and uplift in this study.According to the investigation by Wang and Soler [31], the vertical displacement derived from ellipsoid heights retains the same value as those derived from orthometric heights.
It is worth noting, however, that JPL combined numerous redundant regional GPS networks to calculate precise GPS orbit and clock corrections as well as the WLPB estimates that are used by GIPSY during the PPP processing for fixing phase ambiguities.Accordingly, the PPP method essentially relies on observations from a huge number of ground GPS stations, although the end users do not need to include any data from other ground GPS stations in their PPP processing.There are nine IGS track stations within the Caribbean region (Figure 1), which are used to determine the final satellite orbits and clock corrections by IGS.

A Method for Realizing a Stable Reference Frame
The determination of site position at a specific epoch, and in turn, the change of the position over time (site velocity), is the primary task in geological hazard monitoring using GPS.The position and velocity are always determined in a specific reference frame.A stable reference frame indicates that regional "common" movements have been removed or minimized.The regional common movements may include a combination of secular plate motions, glacial isostatic adjustment, surface mass loading, and other minor secular effects [32].

Seven-Parametric Positional Time Series Transformation
The main physical and mathematical properties of a reference frame are the origin, the scale, the orientation, and the change of these parameters over time.In the geodesy community, a regional reference frame is often developed through a simultaneous transformation from a well-established and broadly used global reference frame, such as IGS reference frames.A group of common points (reference stations) are used to tie these two reference frames.The Helmert coordinate transformation method is often used to produce a distortion-free transformation between two reference frames.The transformation can be realized by a daily 7-parametric transformation method or a 14-parametric transformation method.The 7-parameters include three translations, three rotations, and one scale for each epoch (mostly each day); the 14-parameters include three translations, three rotations, one scale, and their one-time derivatives.For example, a daily 7-parametric method is employed by Blewitt et al. [33] in transforming IGb08 coordinates to the North American Reference Frame of 2012 (NA12) coordinates; a 14-parametric method is employed by NGS in transforming IGS08 coordinates to NAD83 coordinates [34].The Helmert coordinate transformation method also provides an approach of realizing a regional reference frame by obtaining daily 7-parameters or by obtaining a total of 14-parameters.
The coordinate transformation of a point at a specific epoch from a global (G) reference frame to a regional (R) reference frame can be realized by a combination of rotation, scaling, and translation: where P G represents the positional vector with respect to the global reference frame (e.g., IGS14); P R represents the transformed positional vector with respect to the regional reference frame (e.g., CARIB18); T is a vector consisting of three translation parameters along the x, y, and z axes; R is a rotation matrix consisting of three rotations around the x, y, and z axes; and s is a scale factor for adjusting the overall distortion that could occur during the transformation.A regional reference frame is often configured to retain the same origin and scale with a global reference frame.Thus, the scale factor s in Equation ( 1) is often set to zero [34,35].Accordingly, Equation (1) can be simplified as which can be written in an explicit format: where X(t) G , Y(t) G , and Z(t) G are the ECEF-XYZ coordinates (at epoch t) of a site with respect to the global reference frame; X(t) R , Y(t) R , and Z(t) R are the ECEF-XYZ coordinates of the site with respect to the regional reference frame; T x , T y , and T z are three translational shifts between two reference frames along the x, y, and z coordinate axes; and R x , R y , and R z are three rotations around the x, y, and z coordinate axes.These six parameters (T x , T y , T z , R x , R x , R x ) can be calculated using selected common points (reference sites) with known coordinates with respect to both the regional and global reference frames.In theory, three references are enough to obtain those six parameters.However, more reference points are often helpful to solve the inverse problem by using the least-squares method and result in a better fitting and more robust coordinate transformation.The selection of reference stations is critical for realizing a stable regional reference frame.A detailed approach for selecting reference stations will be addressed in the next section.This section will focus on the mathematical aspects of realizing a stable reference frame.
According to numerous investigations [36,37], the time series of these six transformation parameters also retain a linear relationship over time.This can be proven by a strict mathematical induction as long as reference points retain linear displacements with regard to the original global reference frame.Thus, the time series of each of these six transformation parameters can be obtained by linear regression, for example: The translational and rotational parameters at t 0 are zeros since these two reference frames are aligned at epoch t 0 and are referred to the same ECEF-XYZ coordinate system.There are no translations and rotations for coordinates at this epoch.Thus, the coordinate transformation from a global reference to a regional reference frame described in Equation (3) can be rewritten as where T x , T y , T z , R x , R y , and R z are the one-time derivative of T x (t), T y (t), T z (t), R x (t), R y (t), and R z (t), respectively.X(t) G ,Y(t) G , and Z(t) G can be obtained by the PPP processing.Accordingly, the coordinate transformation at any epoch from a global to a regional reference frame can be accomplished by knowing a total of seven parameters: t 0 , T x , T y , T z , R x , R y , and R z .The detailed method for getting these seven parameters will be introduced in the following.
Since T x (t), T y (t), T z (t), R x (t), R y (t), and R z (t) retain a linear regression over time, T x , T y , T z , R x , R y , and R z can be obtained by just knowing the values at any two specific epochs, such as t 0 and t 1 .Fox example, T x can be calculated by the following equation: As aforementioned, the translational and rotational parameters at t 0 are zero since there are no translations and rotations of coordinates at t 0 .Thus, knowing those six transformation parameters (three translations, three rotations) at one epoch (t 1 ) is enough to estimate T x , T y , T z , R x , R y , and R z .A strict stable reference frame means that a stable site would retain a zero site velocity over time.Since the stable regional reference frame is tied to a global reference frame at t 0 (e.g., 2015.0), the ECEF-XYZ coordinates of the selected reference sites at epoch t 1 (e.g., 2018.0) with respect to the regional reference frame can be estimated by the following equations: X G (t 0 ), Y G (t 0 ), Z G (t 0 ), and X G (t 1 ), Y G (t 1 ), Z G (t 1 ) can be obtained by the PPP processing.Thus, these six parameters (T x , T y , T z , R x , R y , and R z ) at epoch t 1 can be obtained according to Equation (5).Finally, T x , T y , T z , R x , R y , and R z can be estimated according to the method illustrated by Equation (6).

Selection of Reference Stations
In general, there is no rigorous criterion for selecting reference stations.Some useful guidelines for selecting reference stations have been addressed by a great number of publications [38][39][40].The essential criterion is that a reference site should have long-term continuous GPS observations that will allow precise delineations of long-term secular plate motions.However, there is no unified definition for "long-term".According to our experience for realizing stable reference frames within the Houston metropolitan area [41,42] and the North China region [29], a minimum of 3 years continuous observational time span is needed for assessing the linearity of the GPS-derived displacement time series.Linearity is a term that is often used to assess the quality of a potential reference station, which reflects how well the motions can be described by a constant velocity over a period of time.
In practice, the selection of reference stations largely depends on what is available.Different versions of Caribbean reference frames had been realized and applied in previous tectonic studies.For example, DeMets et al. [43] used site velocities from 13 GPS sites to model the movement of the Caribbean plate with respect to ITRF2000; the model was updated with site velocities from 16 GPS sites (12 are campaign stations; 4 are continuous stations) by DeMets et al. [44].Symithe et al. [45] used more GPS stations to establish a Caribbean reference frame.Those reference frames were designed to map the strain in the Earth's crust at plate boundaries and to "observe" long-term plate or sub-plate motions.They do not provide easy access for non-expert users.Since the advent of GPS, expert users in geodesy often realize their own Caribbean reference frames to define site positions and velocities for tectonic studies; non-experts in geodesy just use individual references to get relative positions.As a consequence, it is difficult to compare and integrate GPS-derived results (e.g., faulting, micro-plate motions, post-seismic deformation) from different researchers obtained during different periods.
The stable portion of the Caribbean plate is covered by water.Sites within the PBZs experience complex stress and retain different site velocities as a result of inter-and intra-plate interactions.As a consequence, defining and implementing a strict plate-fixed reference frame within the Caribbean region could be a great challenge.The boundaries between the stable portion and the PBZs can rarely be defined with high precision.In general, sites closer to the interior portion of the Caribbean plate are less affected by inter-plate interactions compared to sites further away from the interior portion.Accordingly, the initial screening of reference stations is targeted on those stations that are close to the margins of the interior portion of the Caribbean plate.The stability of a GPS site is difficult to be determined at the level of a few millimeters per year prior to having a stable regional reference frame.For this reason, the initial selection of reference stations is mainly based on the geographic distribution and data history rather than "tectonic stability".
Initially, thirty-two stations adjacent to the margins of the interior portion of the Caribbean plate are selected as reference stations (Figure 2a).Stations with an observational period less than three years or have large data gaps have been excluded from the initial selection.The seven parameters (t 0 , T X , T Y , T Z , R X , R Y , and R Z ) for transforming the positional time series from IGS14 to the interim reference frame are calculated according to the method introduced in the previous section.The XYZ coordinates of each reference station with respect to IGS14 are transformed to the interim reference frame according to Equation (5).The horizontal and vertical site velocity vectors of these 32 reference stations are plotted in Figure 2a.The velocities are referred to the interim reference frame.It is clear that several stations (VRAI, ACP1, CN34, CN36, and SAMA) in the western and southwestern PBZs experienced significantly larger horizontal and/or vertical velocities than the other stations.These stations are affected by the thrust of the Nazca and North Andes plates towards the Caribbean plate (Figure 1).Four stations (CN12, JME2, BAR2, and RDSD) in the northern PBZ also experienced significant horizontal movements with respect to the interim reference frame.Those stations with large velocities are removed from the group of reference stations and those six parameters (T Y , T Y , T Z , R X , R Y , and R Z ) were recalculated.A trial-and-error approach is employed to refine the selection.Stations that have a horizontal velocity higher than 1.5 mm/year or have a vertical velocity higher than 2 mm/year with respect to the new reference frame were removed from the group of reference stations.Finally, eighteen continuous GPS stations were selected as reference stations after several trials and considering the overall geographic distribution of the network of reference stations.Figure 2b depicts the locations of these 18 reference stations and their horizontal and vertical velocity vectors with respect to CARIB18.Four (RDSD, CRO1, LMMF, ABMF) among these 18 reference stations are the IGS tracking stations.The locations of these 18 reference stations, their site velocities with respect to CARB18, and the root-mean-square (RMS) of the detrended displacement time series are listed in Table 1.RMS indicates the precision of the PPP solutions in the Caribbean region.The horizontal precision is approximately 4 mm and the vertical precision is 9 mm.These seven parameters (t 0 , T X , T Y , T Z , R X , R Y , and R Z ) for transforming the GPS-derived positional time series from IGS14 to CARIB18 are listed in Table 2.   Figure 3 illustrates the observational history and data continuity of 16 among these 18 reference stations utilized to realize CARIB18.All reference stations have a history of over five years except two COCONET stations: CN29 and CN35.The three-component positional time series of the other two reference stations, CART and CN11, are illustrated in Figures 4 and 5, respectively.CART is a long history (2002-2018) GPS station operated by the Geographic Institute Agustín Codazzi of Colombia (IGAC).CART is kept as a reference station because of its critical geographic location, lying on the continental shelf of South America plate, and filling a large gap of the reference network in the south-west PBZ.CART is not considerably affected by the thrust of the North Andes plate and the Nazca plate towards the Caribbean plate.All other nearby stations in the southwestern PBZ are significantly affected by the thrust of the two tectonic plates as shown in Figure 2a.and ISCO (2011-2018) with respect to IGS14 and CARIB18.CN11, one of the reference stations for realizing CARIB18, is a COCONET station located on the San Pedro Caye, Jamaica.The 7-year observations indicate that this site moves to the northeast direction with a velocity of approximately 12 mm/year with respect to IGS14.Its three-component velocities (<1 mm/year) with respect to CARIB18 indicate that this site is fixed to the stable portion of the Caribbean plate and is not affected by local faulting activities.ISCO is a COCONET regional station located on the Isla del Coco (Coco Island), the only land mass of the Cocos plate that emerges above sea level.ISCO recorded the largest horizontal velocities with respect to both IGS14 (NS: 73.8 ± 0.5 mm/year; EW: 49.2 ± 0.5 mm/year) and CARIB18 (NS: 69.6 ± 0.5 mm/year; EW: 34.3 ± 0.5 mm/year) within the Caribbean region.The horizontal velocity vector with respect to CARIB18 indicates that the convergence rate of Cocos plate with the Caribbean plate at this site is at 77.6 ± 0.5 mm/year with an azimuth of 26.23 degrees (clockwise direction of North).The observed convergence rate at this site agrees well with the convergence rate estimated by the MORVEL plate motion model [44]: 77.7 ± 2.7 mm/year with an azimuth of 26.9 degrees.The MORVEL-estimated relative velocity between the Cocos plate and the Caribbean plate is based on an average over the last 780,000 years (the width of the central magnetic anomaly).MORVEL is primarily a geological estimate of plate motions.The consistency between the geological-estimate and the 8-year GPS estimate suggests that the collision between the Cocos and Caribbean plates have been continuing over seven hundred thousand years with a steady velocity.) with respect to IGS14 and CARIB18.CN11, one of the reference stations for realizing CARIB18, is a COCONET station located on the San Pedro Caye, Jamaica.The 7-year observations indicate that this site moves to the northeast direction with a velocity of approximately 12 mm/year with respect to IGS14.Its three-component velocities (<1 mm/year) with respect to CARIB18 indicate that this site is fixed to the stable portion of the Caribbean plate and is not affected by local faulting activities.ISCO is a COCONET regional station located on the Isla del Coco (Coco Island), the only land mass of the Cocos plate that emerges above sea level.ISCO recorded the largest horizontal velocities with respect to both IGS14 (NS: 73.8 ± 0.5 mm/year; EW: 49.2 ± 0.5 mm/year) and CARIB18 (NS: 69.6 ± 0.5 mm/year; EW: 34.3 ± 0.5 mm/year) within the Caribbean region.The horizontal velocity vector with respect to CARIB18 indicates that the convergence rate of Cocos plate with the Caribbean plate at this site is at 77.6 ± 0.5 mm/year with an azimuth of 26.23 degrees (clockwise direction of North).The observed convergence rate at this site agrees well with the convergence rate estimated by the MORVEL plate motion model [44]: 77.7 ± 2.7 mm/year with an azimuth of 26.9 degrees.
The MORVEL-estimated relative velocity between the Cocos plate and the Caribbean plate is based on an average over the last 780,000 years (the width of the central magnetic anomaly).MORVEL is primarily a geological estimate of plate motions.The consistency between the geological-estimate and the 8-year GPS estimate suggests that the collision between the Cocos and Caribbean plates have been continuing over seven hundred thousand years with a steady velocity.This explains why there are few stable sites within the western PBZ with respect to the interior of the Caribbean plate.This explains why there are few stable sites within the western PBZ with respect to the interior of the Caribbean plate.This explains why there are few stable sites within the western PBZ with respect to the interior of the Caribbean plate.

Effects of Network Geometry
The geometry of the network of reference stations has been recognized as a major element affecting the overall stability of a regional reference frame [35,46,47].Ideally, the selected reference stations should be evenly distributed over the whole area of interest.Figure 2b indicates that over one-third of these 18 reference stations are located within the eastern PBZ; few reference stations are located within the western and southwestern PBZs.The dense reference stations within the eastern PBZ may predominate the reference network and affect the behavior of the reference frame transformation.
In order to assess the potential effect of the geometry of reference stations on the overall performance of the reference frame, we recalculate these seven parameters by removing two stations (RDON and SVGB) in the eastern PBZ from the network of 18 reference stations and by adding one station (CN20) in the western PBZ to the reference network.CN20 is a COCONET station located on Bocas Island, Panama (Figure 2a).It is close to the interior of the Caribbean plate and is less affected by the thrust of the Cocos plate compared to other stations within the western PBZ. Figure 7 depicts the three-component displacement time series of CN20 with respect to four reference frames realized by 32 reference stations (Figure 2a), 18 reference stations (Figure 2b), 16 reference stations (excluding RDON and SVGB from those 18 stations), and 19 reference stations (adding CN20 to those 18 reference stations).We also checked velocity vectors of other stations with respect to these different reference frames.It is confirmed that adding one station in the western PBZ or removing two or more stations in the eastern PBZ does not considerably degrade the overall stability of the reference frame.The stability of the reference frame will be defined in the next section.

Effects of Network Geometry
The geometry of the network of reference stations has been recognized as a major element affecting the overall stability of a regional reference frame [35,46,47].Ideally, the selected reference stations should be evenly distributed over the whole area of interest.Figure 2b indicates that over one-third of these 18 reference stations are located within the eastern PBZ; few reference stations are located within the western and southwestern PBZs.The dense reference stations within the eastern PBZ may predominate the reference network and affect the behavior of the reference frame transformation.
In order to assess the potential effect of the geometry of reference stations on the overall performance of the reference frame, we recalculate these seven parameters by removing two stations (RDON and SVGB) in the eastern PBZ from the network of 18 reference stations and by adding one station (CN20) in the western PBZ to the reference network.CN20 is a COCONET station located on Bocas Island, Panama (Figure 2a).It is close to the interior of the Caribbean plate and is less affected by the thrust of the Cocos plate compared to other stations within the western PBZ. Figure 7 depicts the three-component displacement time series of CN20 with respect to four reference frames realized by 32 reference stations (Figure 2a), 18 reference stations (Figure 2b), 16 reference stations (excluding RDON and SVGB from those 18 stations), and 19 reference stations (adding CN20 to those 18 reference stations).We also checked velocity vectors of other stations with respect to these different reference frames.It is confirmed that adding one station in the western PBZ or removing two or more stations in the eastern PBZ does not considerably degrade the overall stability of the reference frame.The stability of the reference frame will be defined in the next section.Plots depicting the effect of geometry of reference stations to the stability of the regional reference frame.COCONET station CN20 is located on Bocas Island in Panama (see Figure 2a).(a) The three-component displacement time series with respect to the initial reference frame realized by 32 reference stations (Figure 2a) and 18 reference stations (CARIB18, Figure 2b); (b) the threecomponent displacement time series with respect to reference frames realized by 18 reference stations (CARIB18, Figure 2b), 16 reference stations (removing RDON and SVGB from these 18 reference stations), and 19 reference stations (adding CN20 to these 18 reference stations).

Stability of CARIB18
In practice, a stable site may not retain a near-zero velocity (e.g., <1 mm/year) in 3D space with respect to a stable regional reference frame.For example, stable sites within the Houston, Texas area retain approximately 2 to 3 mm/year horizontal movement towards the northeast direction with respect to NAD83 [48].NAD83 is regarded as a North American plate fixed reference frame and has been widely applied in both surveying and research communities as a stable reference frame.The 2 to 3 mm/year "background velocity" makes it difficult to use NAD83 as a reference to monitor faulting activities at a few millimeters-per-year level.Since a tectonic plate is not rigid, there is no way to achieve a strictly stable reference frame.To the most stringent users, the stability of a reference frame defines the essence of a successful reference frame.In practice, the stability or precision of a regional reference frame is often evaluated by averaging the velocities of all reference stations with respect to the reference frame [33].The stability indicates the ability to extrapolate station coordinates accurately into the past and the future beyond the frame range.For CARIB18, the frame range is approximately from 2008 to 2018 as shown in Figure 3.The useful lifetime of a regional reference frame depends on its stability, which is also referred to as predictability.According to the statistics listed in Table 1, the precision of PPP solutions is approximately 4 mm in the horizontal directions and 9 mm in the vertical direction within the Caribbean region; the stability of CARIB18 is at a level of 0.7 mm/year in the horizontal direction and approximately 0.9 mm/year in the vertical direction.That means the reference frame may result in an accumulated positional-error (uncertainty) of 4 mm in the horizontal direction and 5 mm in the vertical direction within a five-year period, which are still below the precision (repeatability) of the PPP daily solutions.That is to say, the regional reference can be confidently used for at least five years beyond the frame window (2008-2018) without causing any considerable positional errors.The stability may be further improved in future updates when a longer time span of observations and more reference stations are used in realizing the regional reference frame.
Ultimately, the stability of a regional reference frame is determined by the rigidity of the block of crust that the reference stations are mounted on.The rigidity of tectonic plates is an important assumption for plate reconstructions and geodynamic modeling [38,49].The assumption is useful but Figure 7. Plots depicting the effect of geometry of reference stations to the stability of the regional reference frame.COCONET station CN20 is located on Bocas Island in Panama (see Figure 2a).(a) The three-component displacement time series with respect to the initial reference frame realized by 32 reference stations (Figure 2a) and 18 reference stations (CARIB18, Figure 2b); (b) the three-component displacement time series with respect to reference frames realized by 18 reference stations (CARIB18, Figure 2b), 16 reference stations (removing RDON and SVGB from these 18 reference stations), and 19 reference stations (adding CN20 to these 18 reference stations).

Stability of CARIB18
In practice, a stable site may not retain a near-zero velocity (e.g., <1 mm/year) in 3D space with respect to a stable regional reference frame.For example, stable sites within the Houston, Texas area retain approximately 2 to 3 mm/year horizontal movement towards the northeast direction with respect to NAD83 [48].NAD83 is regarded as a North American plate fixed reference frame and has been widely applied in both surveying and research communities as a stable reference frame.The 2 to 3 mm/year "background velocity" makes it difficult to use NAD83 as a reference to monitor faulting activities at a few millimeters-per-year level.Since a tectonic plate is not rigid, there is no way to achieve a strictly stable reference frame.To the most stringent users, the stability of a reference frame defines the essence of a successful reference frame.In practice, the stability or precision of a regional reference frame is often evaluated by averaging the velocities of all reference stations with respect to the reference frame [33].The stability indicates the ability to extrapolate station coordinates accurately into the past and the future beyond the frame range.For CARIB18, the frame range is approximately from 2008 to 2018 as shown in Figure 3.The useful lifetime of a regional reference frame depends on its stability, which is also referred to as predictability.According to the statistics listed in Table 1, the precision of PPP solutions is approximately 4 mm in the horizontal directions and 9 mm in the vertical direction within the Caribbean region; the stability of CARIB18 is at a level of 0.7 mm/year in the horizontal direction and approximately 0.9 mm/year in the vertical direction.That means the reference frame may result in an accumulated positional-error (uncertainty) of 4 mm in the horizontal direction and 5 mm in the vertical direction within a five-year period, which are still below the precision (repeatability) of the PPP daily solutions.That is to say, the regional reference can be confidently used for at least five years beyond the frame window (2008-2018) without causing any considerable positional errors.The stability may be further improved in future updates when a longer time span of observations and more reference stations are used in realizing the regional reference frame.
Ultimately, the stability of a regional reference frame is determined by the rigidity of the block of crust that the reference stations are mounted on.The rigidity of tectonic plates is an important assumption for plate reconstructions and geodynamic modeling [38,49].The assumption is useful but not true.In general, a smaller portion of a plate is more appropriate to be considered as a rigid block than a larger portion.Thus, a local-scale reference frame may provide a more stable reference than a regional-scale reference frame and, in turn, is preferred for monitoring local-scale ground deformation over time and space.A dense GPS network has been operated in the Puerto Rico and Virgin Islands (PRVI) region for over ten years [46].A local-scale reference frame, stable Puerto Rico and Virgin Islands Reference Frame (PRVI12), was established by Wang et al. [34] for landslide monitoring.Seven reference stations with a history of five years were used to realize PRVI12, which achieved stabilities of approximately 1.5 mm/year in both horizontal and vertical directions.PRVI12 was updated to PRVI14 in 2016 by using three more reference stations and a longer period of GPS observations [46].The stability of PRVI14 was 0.4 mm/year in the horizontal direction and 0.6 mm/year in the vertical direction.We updated PRVI14 to PRVI18 through this study by using three more years of GPS observations and add CN03 to the network of reference stations (Figure 8).CN03 is a COCONET station that was installed on the Virgin Gorda Island in February 2013.The seven-parameters for transforming IGS14 coordinates to PRVI18 are listed in Table 2.The stabilities of PRVI18 are approximately 0.4 mm/year in the horizontal directions and 0.5 mm/year in the vertical direction.The update from PRVI14 to PRVI18 does not considerably improve the stability of the local reference frame, which implies that the stability of PRVI18 is approaching the rigidity of the PRVI block.Adding more reference stations and/or using longer periods of observations may not considerably improve the stability of the local reference frame.The stability of PRVI18 is approximately two times better than the stabilities of CARIB18.This confirms that a reference frame covering a smaller area retains higher stability than a reference frame covering a larger area.

Applications of CARIB18
CARIB18 provides a unified stable reference to study inter-plate motions between the Caribbean plate and its surrounding plates and micro-plate motions within the PBZs. Figure 9 depicts horizontal and vertical velocity vectors derived from GPS observations within the Caribbean region with respect to CARIB18.To ensure reliable tectonic interpretation, we only retain sites that have been continuously recording over three years.The velocities are calculated with the Median Interannual Difference Adjusted for Skewness (MIDAS) method introduced by Blewitt et al. [53].We visually inspected each displacement time series and corrected obvious errors associated with antenna changes and outliers.We also compared the site velocities calculated by the MIDAS method and the conventional least-squares method.It is found that the velocities obtained by the two methods agree well in general and the MIDAS method does a better job in minimizing the effects of outliers and step discontinuities associated with antenna changes or co-seismic displacements.Locations, observational histories, and three-component velocities with respect to CARIB18 of these 250 stations are listed in Table A1.Site velocities of stations on the Nicoya Peninsula, northwest Costa Rico are derived from GPS observations since 2015.The positional time series during the period from 2012.5 to 2015.0 are significantly affected by the pre-seismic, co-seismic, and post-seismic events associated with the 5 September 2012 Nicoya, Costa Rica earthquake (Mw 7.6) as shown in Figure 10. Figure 8 depicts the horizontal velocity vectors of those PRVI GPS stations (>5 years) with respect to CARIB18 (red) and PRVI18 (blue).The magnitudes and directions of the velocity vectors with respect to PRVI18 clearly indicate that those sites (PRMI, PRLT, PRGY) at the southwest corner of the Puerto Rico main island experience substantially larger motions compared to other stations.The horizontal velocities of other GPS stations are at a level of below 0.5 mm/year.However, the horizontal velocities of PRMI and PRLT are at the level of 1.5 to 2 mm/year.PRMI moves southwest against the PRVI block and PRLT moves to the northwest.PRMI is located on Magueyes Island, a small island 2 km south to the southern boundary of Lajas Valley, which is a 30-km-long east-west trending depression zone bounded by hills on its northern and southern edges.This area has the most frequent onshore microseismicity in the PRVI region [50].Previous researchers have recognized possible Quaternary fault controls for the Lajas Valley on the basis of geomorphology and seismic reflection profiles [51,52].
The velocity anomalies (both magnitude and direction) at PRMI and PRLT confirms ongoing faulting activities within the Lajas Valley.It appears that the Lajas Valley currently experiences a north-south direction extension (1.5 mm/year) and minor right-lateral strike slip.However, the faulting movements are not so obvious with respect to CARIB18 since all stations in the PRVI region retain a horizontal velocity of approximately 1.5 to 2 mm/year.PRVI18 is definitely a better reference frame than CARIB18 for precisely tracking faulting activities and for assessing present seismic risk within the PRVI region.

Applications of CARIB18
CARIB18 provides a unified stable reference to study inter-plate motions between the Caribbean plate and its surrounding plates and micro-plate motions within the PBZs. Figure 9 depicts horizontal and vertical velocity vectors derived from GPS observations within the Caribbean region with respect to CARIB18.To ensure reliable tectonic interpretation, we only retain sites that have been continuously recording over three years.The velocities are calculated with the Median Interannual Difference Adjusted for Skewness (MIDAS) method introduced by et al. [53].We visually inspected each displacement time series and corrected obvious errors associated with antenna changes and outliers.We also compared the site velocities calculated by the MIDAS method and the conventional least-squares method.It is found that the velocities obtained by the two methods agree well in general and the MIDAS method does a better job in minimizing the effects of outliers and step discontinuities associated with antenna changes or co-seismic displacements.Locations, observational histories, and three-component velocities with respect to CARIB18 of these 250 stations are listed in Table A1.Site velocities of stations on the Nicoya Peninsula, northwest Costa Rico are derived from GPS observations since 2015.The positional time series during the period from 2012.5 to 2015.0 are significantly affected by the pre-seismic, co-seismic, and post-seismic events associated with the 5 September 2012 Nicoya, Costa Rica earthquake (M w 7.6) as shown in Figure 10.The resulting velocities depicted in Figure 9 show a number of important features.There are strike-slip faults along the northern and southeastern boundaries of the Caribbean plate, allowing westward movements of the North American and South American plates relative to the Caribbean plate.There are little relative motions presently between North and South American plates.The northern PBZ is affected by a left-lateral motion between the Caribbean and North American plates.The southern PBZ is affected by right-lateral motion between South American plate and Caribbean plate, and by northwest thrust movements between the North Andes plate and the Caribbean plate.The western PBZ is occupied by Central America.The Cocos plate and Nazca plate in the Pacific   The resulting velocities depicted in Figure 9 show a number of important features.There are strike-slip faults along the northern and southeastern boundaries of the Caribbean plate, allowing westward movements of the North American and South American plates relative to the Caribbean plate.There are little relative motions presently between North and South American plates.The northern PBZ is affected by a left-lateral motion between the Caribbean and North American plates.The southern PBZ is affected by right-lateral motion between South American plate and Caribbean plate, and by northwest thrust movements between the North Andes plate and the Caribbean plate.The western PBZ is occupied by Central America.The Cocos plate and Nazca plate in the Pacific Ocean thrust towards the Caribbean plate.The stations within the western PBZ experience a steady horizontal movement (1-2 cm/year) towards the interior of the Caribbean plate.The eastern PBZ is an island arc which follows the line of the subduction zone where Atlantic plate is being pushed under the Caribbean plate.The site velocities with respect to CARIB18 within the eastern PBZ are less than 1 mm/year except on Monserrat island.Overall, the eastern PBZ shows little movement with respect to the interior of the Caribbean plate.Thus, CARIB18 would be able to serve as a rigorous reference frame for landslide, faulting, subsidence, and volcano and structure health monitoring on these islands, and would be particularly important for land surveying projects on those islands that do not have long-history GPS stations, such as Dominica, St. Vincent and the Grenadines, and Grenada.The site velocities within the northern, southern, and western PBZs vary from a few millimeters per year to a couple of centimeters per year, which depicts significant microplate motions.Accordingly, CARIB18 may not be a precise reference frame for tracking localized horizontal ground deformations within the northern, southern, and western PBZs.Local-scale reference frames are needed to conduct precise faulting and landslide monitoring on these islands.
Intra-plate motions within the PBZs have been heavily investigated by numerous researchers using GPS observations [54][55][56][57][58].With the continuous accumulation of COCONET and other GPS observations in and around the Caribbean plate, the research community will soon gain a better understanding of the tectonic motions within the PBZs.Instead of exploring the details of plate tectonic motions, this study will demonstrate the applications of CARIB18 in tracking localized ground deformation for geological hazard monitoring purposes.

Post-Seismic Monitoring
Post-seismic ground deformation following large earthquakes can occur many years to several decades and affect exceptionally large areas.For example, post-seismic ground deformation following the 1964 Alaska earthquake (27 March 1964, Mw 9.2) is still ongoing even a half-century after the main shock [59,60].Monitoring post-seismic deformation is critically important to understanding the process of earthquake cycles and improving risk assessment for large earthquakes and tsunami potential.GPS has become an important tool for monitoring post-seismic ground deformation due to after-slip, viscoelastic relaxation, poroelastic rebound, and other slow displacements following large earthquakes.Long-term GPS observations have advanced both the spatial and temporal characteristics of post-seismic deformation.
Earthquakes are the major destructive form of natural hazards in the Caribbean region.The most recent devastating earthquake occurred in the Caribbean region is the 2012 Nicoya, Costa Rica earthquake (M w 7.6, 5 September 2012).The epicenter of this earthquake was on the Nicoya Peninsula, 11 km east-southeast of Nicoya.This earthquake was felt all over Costa Rica as well as in Nicaragua, El Salvador, and Panama.It was the second strongest earthquake recorded in Costa Rica's history, following the 1991 Limon earthquake (M w 7.7, 22 April 1991).Figure 10 illustrates the application of CARIB18 in depicting pre-seismic, co-seismic, and post-seismic ground deformation associated with the mainshock.LAFE is located on the Nicoya Peninsula, northwestern Costa Rica.Ongoing post-seismic deformation and three slow-slip-events (SSE) can be clearly identified from the positional time series with respect to CARIB14.Unfortunately, the SSE events can be barely identified from the positional time series with respect to IGS14.The site velocities before and after this earthquake are considerably different, particularly in the north-south (NS) direction (21 mm/year vs. 8 mm/year), which suggests that the post-seismic deformation is still ongoing at this site.Post-seismic, episodic tremor, and SSE following the 2012 Nicoya earthquake had been investigated by different research groups using GPS data observed during different periods [61][62][63][64].Those results were referred to different reference stations or reference frames.As a consequence, it is difficult to align and compare those results.Figure 11 illustrates the application of CARIB18 in depicting spatial variations of horizontal and vertical ground deformation associated with the pre-seismic, co-seismic, post-seismic, and SSE.CARIB18 provides a unified platform for non-expert GPS users to conduct advanced post-seismic, co-seismic, and SSE modelling over time and space.

Volcano Monitoring
Volcanoes are distributed all over the Caribbean region.Most of the active volcanoes are located on the Lesser Antilles islands within the eastern PBZ and on the Central American Arc (CAVA) within the western PBZ.The Lesser Antilles has been described as a double island arc that is built largely by volcanism above a subduction zone [65].CAVA is a chain of volcanoes which extends parallel to the Pacific coastline from Guatemala, El Salvador, Honduras, Nicaragua, Costa Rica, and down to northern Panama.Presently, the most active volcanos within the Caribbean region are the Fuego Volcano in Guatemala within the western PBZ and the Soufriere Hills Volcano (SHV) on Montserrat Island within the eastern PBZ.Fuego has erupted more than 60 times since 1524, making it Central America's historically most active volcano [66].The most recent disastrous eruption occurred on 3 June 2018, which was the deadliest eruption in Guatemala since 1929.Unfortunately, there are few long-term permanent GPS stations near the Fuego Volcano.This study demonstrates the application of CARIB18 in monitoring SHV within the eastern PBZ (Figure 12).SHV has been one of the most intensively studied volcanoes in the worldwide [67][68][69].In the last century, SHV has experienced at least eight aborted eruption events: 1897-98, 1933-37, 1966-67, November 1995-March 1998; November 1999-July 2003; August 2005-April 2007; July 2008-January 2009; and most recently October 2009-February 2010 [70].Recent eruption events since 2005 can be clearly identified from the long-term continuous GPS observations as illustrated in Figure 13.Ground surface deflates when lava is extruding and then inflates in times of non-extrusion.Changes to the ground surface of a volcano can provide clues about what is happening deep below the surface and provide insightful information of a forthcoming eruption [71][72][73][74].Current ground inflation at a rate of 1 cm/year has continued over nine years since the last eruption in February 2010.interest in projecting when the next major volcanic eruption will occur.Continuous GPS monitoring is vital to understanding whether and when the volcano may become active.CARIB18 provides a coherent reference frame for excluding long-term tectonic drifts from localized ground deformation and enables "absolute" volcano-induced ground deformation monitoring.The absolute ground deformation information will provide a precise estimate of the volume of intrusion magma over time and space.

Discussion
This study introduced an approach of using stand-alone GPS and a stable reference frame to conduct long-term geological hazard and structural health monitoring.By transforming PPP solutions to a regional reference fame, users do not need to install any ground reference stations in the field and do not need to include any reference data in their data processing.The stand-alone GPS surveying method will substantially reduce field costs and logistics for conducting long-term ground and structural deformation monitoring and therefore will revolutionize the way for conducting geological hazard and structural health monitoring.Hydrologists may use CARIB18 for studying ground deformations resulting from fluid withdrawal, aquifer deformation, and seasonal hydrologic The GPS monitoring at SHV was started by the third author of this article (Dr.Mattioli)) in collaboration with the Montserrat Volcano Observatory (MVO) [75].Currently, MVO operates a GPS, seismic, and SO 2 integrated monitoring network on Montserrat Island.Figure 14 depicts the ongoing ground deformation velocity vectors (2011-2018) on Montserrat derived from six long-term GPS stations since the last eruption and dome collapse in February 2010.The velocity vectors are referred to CARIB18.Five stations on the north side of the volcano show significant horizontal movements toward the north direction.RCHY lies on the southeast side of the volcano and is close to the volcano mouth.RCHY remains almost stable horizontally (<2 mm/year) with respect to the interior of the Caribbean plate (CARIB18), which suggests that significant horizontal displacements recorded by other GPS stations on the island are induced by shallow magma accumulation under the ground surface rather than tectonic drift.The entire island is still inflating at a rate of approximately 1 cm/year, which suggests that Montserrat's volcano system remains active.There is an increasing interest in projecting when the next major volcanic eruption will occur.Continuous GPS monitoring is vital to understanding whether and when the volcano may become active.CARIB18 provides a coherent reference frame for excluding long-term tectonic drifts from localized ground deformation and enables "absolute" volcano-induced ground deformation monitoring.The absolute ground deformation information will provide a precise estimate of the volume of intrusion magma over time and space.

Discussion
This study introduced an approach of using stand-alone GPS and a stable reference frame to conduct long-term geological hazard and structural health monitoring.By transforming PPP solutions to a regional reference fame, users do not need to install any ground reference stations in the field and do not need to include any reference data in their data processing.The stand-alone GPS surveying method will substantially reduce field costs and logistics for conducting long-term ground and structural deformation monitoring and therefore will revolutionize the way for conducting geological hazard and structural health monitoring.Hydrologists may use CARIB18 for studying ground deformations resulting from fluid withdrawal, aquifer deformation, and seasonal hydrologic and atmospheric pressure loading; geomorphologists may use CARIB18 for studying coastal erosion and wetland loss problems along the Caribbean coasts; oceanographic and sea-level researchers may use CARIB18 for monitoring and calibrating long-term sea level changes along the Caribbean costs; civil engineers may use CARIB18 for monitoring long-term stabilities of dams, sea walls, levees, high-rise buildings, and long-span bridges.It is anticipated that the regional reference frame will promote the applications of GPS techniques in the practice of geological hazard mitigation within the Caribbean region.CARIB18 will also facilitate the applications of GPS technology in construction, land surveying, photogrammetric, coastal hydrography, flooding risk mapping, and natural resource management.A sophisticated regional geodetic infrastructure would comprise at least two components: a network of numerous permanent GPS stations and regional reference frame.This study realized a stable regional reference frame that will serve as the essential geodetic infrastructure for long-term geohazards monitoring within the Caribbean region.A longer period of data accumulation from more reference stations would provide more reliable site velocity estimations and, in turn, improve the stability of the reference frame.CARIB18 will be updated periodically with a longer period of data accumulation and additional reference stations to ensure its continuity and stability.There are several other COCONET stations adjacent to the interior of the Caribbean plate that have not been utilized as reference stations in this study because of their short observational histories, such as CN49 and CN42 (Figure 2b).CN49 is located on Aves Ridge, approximately 250 km west of the Lesser Antilles Volcanic Arc.It is much closer to the rigid portion of the Caribbean plate than other stations within the eastern PBZ.Previously, there was a campaign GPS station (AVES) on this island.AVES was used as a reference station by previous investigations [43].CN42 is located on Gran Roque Island in the southeastern Caribbean Sea, over 200 km off the northeastern coast of Venezuela.CN49 was installed in April 2016 and no data has been archived since the Hurricanes Irma and Maria in 2017.CN42 was installed in October 2015 and no data has been archived since 2017.Those two stations will be considered as reference stations when updating the regional reference frame in the future.
This study confirms that a reference frame covering a smaller area overall retains higher stability than a reference frame covering a larger area.CARIB18 is able to serve as a rigorous stable reference frame for ground and structural deformation monitoring over time and space on the islands of the Lesser Antilles (eastern PBZ).However, it may not be an ideal reference frame for precisely (e.g., <2 mm/year) tracking horizontal ground and structural deformation on the other Caribbean islands.For faulting, subsidence and earthquake monitoring, and risk assessment with the Puerto Rico and Virgin Islands region, we recommend using PRVI18 rather than CARIB18.Rigorous local-scale reference frames require the geodesy community to install and maintain more continuously operating GNSS stations.

Conclusions
CARIB18 provides a platform to integrate observations from different remote sensing techniques (e.g., GPS, InSAR, LiDAR, Photogrammetry) to a unified geodetic reference and enables multidisciplinary and cross-disciplinary research.The primary products from this study are the 7-parameters (Table 2) for converting the positional time series from IGS14 to CARIB18 and the three-component velocities of 250 Caribbean GPS stations with respect to CARIB18 (Table A1).Researchers in plate tectonics may use these velocity vectors to study current inter-and intra-plate motions within the Caribbean region.The frame stability of CARIB18 is approximately 0.7 mm/year in the horizontal direction and 0.9 mm/year in the vertical direction.CARIB18 can be confidently used for at least five years beyond the frame window from 2008 to 2018.Current GPS geodesy infrastructure within the Caribbean region makes it possible to precisely track minor ground deformation at the level of 1 mm/year and above using stand-alone GPS.CARIB18 will be synchronized with the update of the IGS reference frame.
Author Contributions: G.W. and H.L. prepared the original draft.All authors edited, reviewed, and improved the manuscript.

Figure 1 .
Figure 1.A map showing tectonic plates within the Caribbean region and the plate boundary zones (PBZs) between the Caribbean Ocean Plateau (the stable portion of the Caribbean plate) and its surrounding plates.The horizontal velocity vectors depict the secular plate motions at 250 permanent Global Positioning System (GPS) stations within the Caribbean region with respect to IGS14.The velocities are derived from recent GPS observations (2012-2018).

Figure 1 .
Figure 1.A map showing tectonic plates within the Caribbean region and the plate boundary zones (PBZs) between the Caribbean Ocean Plateau (the stable portion of the Caribbean plate) and its surrounding plates.The horizontal velocity vectors depict the secular plate motions at 250 permanent Global Positioning System (GPS) stations within the Caribbean region with respect to IGS14.The velocities are derived from recent GPS observations (2012-2018).

Figure 2 .
Figure 2. (a) Locations of 32 initially selected reference stations for realizing a regional reference frame within the Caribbean region.The horizontal (red) and vertical (blue) velocity vectors are referred to the initial reference frame realized by these 32 reference stations.(b) Locations of 18 reference stations for realizing the stable Caribbean reference frame (CARIB18).The horizontal (red) and vertical (blue) velocity vectors are referred to CARIB18.

Figure 2 .
Figure 2. (a) Locations of 32 initially selected reference stations for realizing a regional reference frame within the Caribbean region.The horizontal (red) and vertical (blue) velocity vectors are referred to the initial reference frame realized by these 32 reference stations.(b) Locations of 18 reference stations for realizing the stable Caribbean reference frame (CARIB18).The horizontal (red) and vertical (blue) velocity vectors are referred to CARIB18.
Figure 6 illustrates the three-component displacement time series (CARIB18) of another long-term reference station CRO1 (2002-2018).CRO1 is located on St. Croix Island and retains a slightly larger vertical velocity (-1.9 mm/year) compared to other reference stations.A closely spaced permanent GPS station (VIKH) on St. Croix recorded an identical site velocity with CRO1.The slight subsidence recorded by CRO1 may imply minor relative tectonic motions between St. Croix Island and the stable portion of the Caribbean plate.Remote Sens. 2019, 11, x FOR PEER REVIEW 10 of 31 CRO1 (2002-2018).CRO1 is located on St. Croix Island and retains a slightly larger vertical velocity (-1.9 mm/year) compared to other reference stations.A closely spaced permanent GPS station (VIKH) on St. Croix recorded an identical site velocity with CRO1.The slight subsidence recorded by CRO1 may imply minor relative tectonic motions between St. Croix Island and the stable portion of the Caribbean plate.

Figure 3 .
Figure 3. Plots showing the observational history and data continuity of 16 among 18 reference stations for realizing the Stable Caribbean Reference Frame (CARIB18).

Figure 5
Figure 5 depicts the long-term three-component displacement time series at CN11 (2012-2018)andISCO (2011ISCO ( -2018) )  with respect to IGS14 and CARIB18.CN11, one of the reference stations for realizing CARIB18, is a COCONET station located on the San Pedro Caye, Jamaica.The 7-year observations indicate that this site moves to the northeast direction with a velocity of approximately 12 mm/year with respect to IGS14.Its three-component velocities (<1 mm/year) with respect to CARIB18 indicate that this site is fixed to the stable portion of the Caribbean plate and is not affected by local faulting activities.ISCO is a COCONET regional station located on the Isla del Coco (Coco Island), the only land mass of the Cocos plate that emerges above sea level.ISCO recorded the largest horizontal velocities with respect to both IGS14 (NS: 73.8 ± 0.5 mm/year; EW: 49.2 ± 0.5 mm/year) and CARIB18 (NS: 69.6 ± 0.5 mm/year; EW: 34.3 ± 0.5 mm/year) within the Caribbean region.The horizontal velocity vector with respect to CARIB18 indicates that the convergence rate of Cocos plate with the Caribbean plate at this site is at 77.6 ± 0.5 mm/year with an azimuth of 26.23 degrees (clockwise direction of North).The observed convergence rate at this site agrees well with the convergence rate estimated by the MORVEL plate motion model[44]: 77.7 ± 2.7 mm/year with an azimuth of 26.9 degrees.The MORVEL-estimated relative velocity between the Cocos plate and the Caribbean plate is based on an average over the last 780,000 years (the width of the central magnetic anomaly).MORVEL is primarily a geological estimate of plate motions.The consistency between the geological-estimate and the 8-year GPS estimate suggests that the collision between the Cocos and Caribbean plates have been continuing over seven hundred thousand years with a steady velocity.

Figure 3 .
Figure 3. Plots showing the observational history and data continuity of 16 among 18 reference stations for realizing the Stable Caribbean Reference Frame (CARIB18).

Figure 5
Figure 5 depicts the long-term three-component displacement time series at CN11 (2012-2018) andISCO (2011ISCO ( -2018) )  with respect to IGS14 and CARIB18.CN11, one of the reference stations for realizing CARIB18, is a COCONET station located on the San Pedro Caye, Jamaica.The 7-year observations indicate that this site moves to the northeast direction with a velocity of approximately 12 mm/year with respect to IGS14.Its three-component velocities (<1 mm/year) with respect to CARIB18 indicate that this site is fixed to the stable portion of the Caribbean plate and is not affected by local faulting activities.ISCO is a COCONET regional station located on the Isla del Coco (Coco Island), the only land mass of the Cocos plate that emerges above sea level.ISCO recorded the largest horizontal velocities with respect to both IGS14 (NS: 73.8 ± 0.5 mm/year; EW: 49.2 ± 0.5 mm/year) and CARIB18 (NS: 69.6 ± 0.5 mm/year; EW: 34.3 ± 0.5 mm/year) within the Caribbean region.The horizontal velocity vector with respect to CARIB18 indicates that the convergence rate of Cocos plate with the Caribbean plate at this site is at 77.6 ± 0.5 mm/year with an azimuth of 26.23 degrees (clockwise direction of North).The observed convergence rate at this site agrees well with the convergence rate estimated by the MORVEL plate motion model[44]: 77.7 ± 2.7 mm/year with an azimuth of 26.9 degrees.

Figure 4 .
Figure 4. Three-component displacement time series of the long-history GPS station CART with respect to CARIB18.CART is located in Cartagena, Colombia (Figure 2) and is operated by the Instituto Geografico Agustin Codazzi, Colombia.

Figure 5 .
Figure 5. (a) A comparison of the displacement time series of CN11 with respect to CARIB18 and IGS14; (b) a comparison of the displacement time series of ISCO with respect to CARIB18 and IGS14.The root-mean-square (RMS) of the displacements is calculated from the detrended PPP daily solutions.

Figure 4 .
Figure 4. Three-component displacement time series of the long-history GPS station CART with respect to CARIB18.CART is located in Cartagena, Colombia (Figure 2) and is operated by the Instituto Geografico Agustin Codazzi, Colombia.

Figure 4 .
Figure 4. Three-component displacement time series of the long-history GPS station CART with respect to CARIB18.CART is located in Cartagena, Colombia (Figure 2) and is operated by the Instituto Geografico Agustin Codazzi, Colombia.

Figure 5 .
Figure 5. (a) A comparison of the displacement time series of CN11 with respect to CARIB18 and IGS14; (b) a comparison of the displacement time series of ISCO with respect to CARIB18 and IGS14.The root-mean-square (RMS) of the displacements is calculated from the detrended PPP daily solutions.

Figure 5 .
Figure 5. (a) A comparison of the displacement time series of CN11 with respect to CARIB18 and IGS14; (b) a comparison of the displacement time series of ISCO with respect to CARIB18 and IGS14.The root-mean-square (RMS) of the displacements is calculated from the detrended PPP daily solutions.

Figure 6 .
Figure 6.Three-component site velocities with respect to CARIB18 recorded by two permanent GPS stations (CRO1 and VIKH) on St. Croix island.The distance between these two stations is approximately 23 km.

Figure 6 .
Figure 6.Three-component site velocities with respect to CARIB18 recorded by two permanent GPS stations (CRO1 and VIKH) on St. Croix island.The distance between these two stations is approximately 23 km.

Figure 7 .
Figure 7. Plots depicting the effect of geometry of reference stations to the stability of the regional reference frame.COCONET station CN20 is located on Bocas Island in Panama (see Figure2a).(a) The three-component displacement time series with respect to the initial reference frame realized by 32 reference stations (Figure2a) and 18 reference stations (CARIB18, Figure2b); (b) the threecomponent displacement time series with respect to reference frames realized by 18 reference stations (CARIB18, Figure2b), 16 reference stations (removing RDON and SVGB from these 18 reference stations), and 19 reference stations (adding CN20 to these 18 reference stations).

Figure 8 .
Figure 8. Site velocity vectors of permanent GPS stations on the Puerto Rico and Virgin Islands (PRVI) with respect to the local-scale reference frame PRVI18 (blue) and the regional-scale reference frame CARIB18 (red).The yellow dots represent these 10 reference stations used in realizing PRVI18.

Figure 8 .
Figure 8. Site velocity vectors of permanent GPS stations on the Puerto Rico and Virgin Islands (PRVI) with respect to the local-scale reference frame PRVI18 (blue) and the regional-scale reference frame CARIB18 (red).The yellow dots represent these 10 reference stations used in realizing PRVI18.

Figure 9 .
Figure 9. Map showing the horizontal (red) and vertical (blue) velocity vectors at 250 GPS stations with respect to CARIB18.The linearity of the positional time series of GPS stations on the Nicoya Peninsula, northwest of Costa Rica, is affected by the 2012 Nicoya, Costa Rico earthquake (Mw 7.6, 5 September 2012), post-seismic deformation, and slow slip events.Only the observations after 2014.5 are used to calculate the site velocities on the Nicoya Peninsula.

Figure 9 .
Figure 9. Map showing the horizontal (red) and vertical (blue) velocity vectors at 250 GPS stations with respect to CARIB18.The linearity of the positional time series of GPS stations on the Nicoya Peninsula, northwest of Costa Rica, is affected by the 2012 Nicoya, Costa Rico earthquake (M w 7.6, 5 September 2012), post-seismic deformation, and slow slip events.Only the observations after 2014.5 are used to calculate the site velocities on the Nicoya Peninsula.

Figure 10 .
Figure 10.Plots illustrating the application of CARIB18 in delineating pre-seismic, co-seismic, and post-seismic ground deformation associated with the 5 September 2012 Nicoya, Costa Rico earthquake (Mw 7.6), and slow-slip events (SSE).LAFE is located in the small town of Paquera on the Nicoya Peninsula, Costa Rica.

Figure 10 .
Figure 10.Plots illustrating the application of CARIB18 in delineating pre-seismic, co-seismic, and post-seismic ground deformation associated with the 5 September 2012 Nicoya, Costa Rico earthquake (M w 7.6), and slow-slip events (SSE).LAFE is located in the small town of Paquera on the Nicoya Peninsula, Costa Rica.

Figure 10 .
Figure 10.Plots illustrating the application of CARIB18 in delineating pre-seismic, co-seismic, and post-seismic ground deformation associated with the 5 September 2012 Nicoya, Costa Rico earthquake (Mw 7.6), and slow-slip events (SSE).LAFE is located in the small town of Paquera on the Nicoya Peninsula, Costa Rica.

Figure 11 .
Figure 11.Maps illustrating the application of CARIB18 in depicting spatial patterns of pre-seismic, co-seismic, and post-seismic ground surface deformation caused by the Nicoya, Costa Rica

Figure 11 .
Figure 11.Maps illustrating the application of CARIB18 in depicting spatial patterns of pre-seismic, co-seismic, and post-seismic ground surface deformation caused by the Nicoya, Costa Rica earthquake (5 September 2012; M w 7.6).(a) and (d): Horizontal and vertical velocity vectors at GPS stations on the Nicoya Peninsula before the 2012 earthquake; (b) and (e): Co-seismic displacements occurred during the day that earthquake happened; (c) and (f): Post-seismic velocity vectors since 2015.The co-seismic displacement is calculated by differencing the one-week average positions after the earthquake day (5 September 2012) and one-week average position before the earthquake day.

Figure 12 .
Figure 12.GPS-derived site velocity vectors (red: horizontal; blue: vertical) at permanent GPS stations within the eastern PBZ (Lesser Antilles islands) with respect to CARIB18.

Figure 13 .
Figure 13.GPS recorded ground deformation associated with the volcanic activities of the Soufriere Hills Volcano on Montserrat since 2004.Shaded A, B, and C periods represent three eruption events.The marked velocity is the linear regression of the displacement time series from 2010 to 2018.TRNT is located about 6 km NNE from the mouth of the volcano (see Figure14).

Figure 12 . 31 Figure 12 .
Figure 12.GPS-derived site velocity vectors (red: horizontal; blue: vertical) at permanent GPS stations within the eastern PBZ (Lesser Antilles islands) with respect to CARIB18.

Figure 13 .
Figure 13.GPS recorded ground deformation associated with the volcanic activities of the Soufriere Hills Volcano on Montserrat since 2004.Shaded A, B, and C periods represent three eruption events.The marked velocity is the linear regression of the displacement time series from 2010 to 2018.TRNT is located about 6 km NNE from the mouth of the volcano (see Figure14).

Figure 13 .
Figure 13.GPS recorded ground deformation associated with the volcanic activities of the Soufriere Hills Volcano on Montserrat since 2004.Shaded A, B, and C periods represent three eruption events.The marked velocity the linear regression of the displacement time series from 2010 to 2018.TRNT is located about 6 km NNE from the mouth of the volcano (see Figure14).

Figure 14 .
Figure 14.Velocity vectors (red: horizontal; blue: vertical) with respect to CARIB18 at six permanent GPS stations on Montserrat Island.The velocities are derived from GPS observations (2011-2018) after the last eruption of the Soufriere Hills Volcano.

Figure 14 .
Figure 14.Velocity vectors (red: horizontal; blue: vertical) with respect to CARIB18 at six permanent GPS stations on Montserrat Island.The velocities are derived from GPS observations (2011-2018) after the last eruption of the Soufriere Hills Volcano.

Table 1 .
Eighteen reference stations and their site velocities with respect to CARIB18.
* The velocity is obtained by a least-squares regression method.** The uncertainty represents the 95% confidence interval of the velocity estimate.*** The root-mean-square (RMS) is calculated from the detrended displacement time series.

Table 2 .
Seven parameters for realizing CARIB18 and PRVI18.
horizontal precision is approximately 4 mm and the vertical precision is 9 mm.These seven parameters ( ,  ,  ,  ,  ,  , and  ) for transforming the GPS-derived positional time series from IGS14 to CARIB18 are listed in Table2.

Table A1 .
Observational histories and site velocities (CARIB18) of 250 permanent GPS stations within the Caribbean region.

Table A1 .
[53].JPL had not released its IGS14 orbit and clock data products for epochs before 2002 at the time we processed data for this study (December 2018).For this reason, GPS observations before 2002 were not processed.**Thevelocity and uncertainty were estimated using the MIDAS method[53]. *