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Introduction
Global Positioning System (GPS) technology has been widely used for more than 25 years for measuring crustal coseismic displacement due to earthquakes, which is so-called GPS Seismology. In fact, the first earthquake, whose displacement was measured by GPS, is the Loma Prieta (California) earthquake with moment magnitude (Mw 6.9) occurred in 1989 (Williams and Segall, 1996). After this earthquake, hundreds of papers have been published following the occurrence of moderate to large magnitude earthquakes. The GPS Seismology is also used along with other space and seismological tools (i.e. InSAR and strong motion) to understand the crustal deformation due to earthquakes. The coseismic displacement, derived by GPS, is of importance to seismic hazard assessment studies. It can support both the modeling of causative fault rupture and seismic moment (source parameters), as well as contributing to tsunami warning systems (e.g. Branzanti et al., 2013). The magnitude and epicenter information is determined immediately after a destructive earthquake. However, the damage distribution is not a simple function of these two parameters alone. More detailed information, such as the horizontal coseismic displacement, is needed. Therefore, it is highly desirable to identify this displacement in the damaged area.
The aim of this work is to investigate a potential relationship between the horizontal GPS coseismic displacement and the earthquake parameters such as the magnitude. A data set of horizontal GPS coseismic displacement in the near-field has been collected around the world. The data is, then, processed by regression analyses to estimate the empirical relationship linking the near field horizontal GPS coseismic displacement as a function of other independent variables, such as the moment magnitude (Mw). This work can be directed to seismic hazard applications, especially in areas of a low level of instrumental seismic activity such as Syria, where the empirical relationship might be applied on data coming from a macroseismic analysis in the pre-instrumental period. In this perspective, the new empirical relationship could be helpful to predicate the coseismic displacements associated with the large historical earthquakes that occurred along the Dead Sea fault system (DSFS) along the northwestern plate boundary between the Arabian and Sinai plates. Furthermore, in most cases, where the GPS data are not available for all regions in the world, the empirical relations could be helpful in these regions. The importance of the work is that, to the best of our knowledge, there are no published works dealing with such a topic. Therefore, it could be the first attempt in this trend.
Data and Methods
The derivation of the GPS coseismic displacements empirical relationship has been carried out through the three following steps. The first step is the data gathering and selection, whereas the worldwide GPS seismology data have been collected in the near-field of the earthquakes. The second step is the data analysis with the validation of the data set and the application of appropriate regression analysis to derive the target empirical relationship. The third step is a preliminary application of the derived empirical relationship for large historical and some instrumental earthquakes occurred along the DSFS.
In the first step, the data set has been selected according to the following criteria: 1) GPS station should be located in the near field and the epicentral distance less than 100 km; 2) Earthquake focus should be shallow and its depth less than 70 km; and 3) Moment magnitude should be moderate to large one. According to these selection criteria, 120 events occurred within the period from 1989 to 2017 have been selected. This data set includes mainly the GPS coseismic displacements due to the interplate earthquakes. The data set is reviewed gradually to get the seismological and geodetic parameters and the necessary information for each earthquake. Recently, the GPS coseismic displacement database has been made available via so many websites and published in a lot of papers. Our data has been collected from 125 relevant papers and documented results at few related websites. The compiled database, selected according to the above criteria, includes for each event the earthquake parameters such as date, epicenter, focal depth (h) and moment magnitude (Mw), and the faulting type (normal, strike-slip and thrust). In addition, it includes the relevant GPS data such as the near-field GPS station code (ID), the distance between the epicenter and the nearest GPS station (Δ), near-field GPS coseismic horizontal displacement (DGPS), type of measurement (e.g. survey GPS or continuous GPS). Appendix 1 lists the seismological-GPS parameters used in this study for 120 events within the period from 1989 to 2017. Note that GPS coseismic displacements were measured for the first time for the (Mw 6.9) Loma Prieta, California, earthquake in 1989. The last event in Appendix 1 is an earthquake of (Mw 6.6) that occurred in 2017 in the Aegean Sea between Turkey and Greece. Fig. 1 shows the distribution of the earthquakes listed in Appendix 1. We can observe that most of these earthquakes are distributed along the plate boundaries.
Figure 1 Simplified world map showing the spatial distribution of the 120 earthquakes occurred along the plate boundaries, listed in Appendix 1. The map shows locations of selected GPS stations and their velocity vectors to give an idea on the general directions of the tectonic plates. The rectangle is the location of the DSFS. GPS stations and its velocity vectors are plotted based on NASA database of present-day plate motions (Heflin, n.d.), according to the IGS08 reference frame and the reference ellipsoid of GRS80.
The data set has been adopted, where the seismological data includes many types of magnitude. In this regard, we have adopted the moment magnitude (Mw) since it is considered a more reliable measure of the energy released during an earthquake. Some earthquakes in our data set have surface wave magnitude. Since we have preferred (Mw), the surface wave magnitude (Ms) has been converted to (Mw) using the following empirical relation (Scordilis, 2006):
The data sets are restricted to earthquakes with (Mw) greater than and equal to 4.8. Most coseismic displacements, shown in Appendix 1, are taken directly from published papers, while, in few cases, they have been calculated by the authors through the geometric sum of the 2 horizontal components (east-west and north-south). Although the coverage is not uniform neither time nor area due to availability of GPS seismology data in the near field, we believe that the data in Appendix 1 could be adequate for derivation a relationship between GPS coseismic displacement and magnitude and the hypocentral distance to the GPS stations.
In the second step, a preliminary statistical analysis for deriving the intended relationship has been performed using Microsoft Excel in order to estimate its general form. Professional statistical analysis is, then, applied using the Number Cruncher Statistical System (NCSS) in order to get an adequate relationship. The NCSS provides a multi regression analysis for studying the relationships among a dependent (Y) variable in the function of one or more independent (Xs) variables (NCSS, 2016). Regression analysis is one of the most important tools widely used in statistical modeling of the data, i.e. deriving the relationships among variables. It helps in understanding how a dependent variable changes when one or more independent variables are varied. The idea behind the derivation of the relationship has emerged from a general seismological-geodetic observation that is at a single near-field GPS station of any earthquake, the larger the earthquake magnitude, the bigger the GPS coseismic displacement. Therefore, we selected the GPS coseismic displacement (DGPS) to be a dependent variable, and the moment magnitude (Mw) to be an independent variable. We also added, later on, the distance between the near-field GPS site and the earthquake hypocenter (Rhyp= (Δ2+h2)0.5) as a second independent variable. More details on the statistical processing have been presented in the next section.
Results
1 Derived Empirical Relationship
A preliminary analysis for estimation the general form of the target empirical relationship was performed using simple linear regression, provided by the “Microsoft Excel”. It has indicated that there is no obvious linearity among (DGPS) and (Mw). This result is confirmed by the weakness of the correlation coefficient (R2=0.46). Another trial test was performed using the exponential regression, where the trending line is more compatible with the experimental points (Fig. 2) than whose of linear regression with a moderate correlation coefficient (R2=0.52). The last estimated relationship is:
Both previous correlation coefficients could be considered very low for establishing a reasonable empirical relationship. The reasons for the small level of the correlation coefficients could be interpreted by interfering other affecting factors or independent variables such as: 1) the hypocentral distance of earthquakes; 2) the effect of local geology “site effect” on the GPS displacement; 3) the faulting mechanisms; 4) the directivity effect due to the slip on the fault; 5) the differences of the ITRF used; 6) the differences between the processing software. Therefore, it is predicted that the target relationship will not be of a naive form and a simple regression will not be effective to give a reasonable correlation coefficient. A sophisticated form can be obtained using a multi regression analysis, where many affecting factors could be taken into consideration. In this case, the correlation coefficient could be close to 1.0. In this regard, an advanced professional program “Number Cruncher Statistical System (NCSS) (NCSS, 2016)” has been used for the improvement of our data set modeling. The exponential model should be modified to take the logarithms of the dependent variable (Mw). The relationship (2) becomes a simple linear regression (Figure 3):
with (R2=0.52). This relationship is still inappropriate because of the moderate correlation coefficient. However, the last relationship needs more improvement using an advance analysis model and additional variables, such as the distance between the GPS station and the focus of the earthquake (Rhyp). A good solution has been obtained by multiple linear regression, which gives the optimum fit and results in the following relationship:
with the correlation coefficient (R2=0.66) and the root mean square of error (RMS=0.45) representing the uncertainty in (log DGPS). Thanks to the second independent variable, the relationship has been visibly improved. In the relationship (4), the (DGPS) unit is cm and (Rhyp) is hypocenter-to- GPS station distance in km.
In the NCSS, the regression problem has been solved by the least-squares method, where the regression coefficients are selected so as to minimize the sum of the squared residuals. The multiple regression analysis, applied in this research, has studied the relationship between a dependent variable (DGPS) and two independent variables (Mw and Rhyp). In the relationship (4), the intercept (−4.8065) is the point at which the regression plane intersects the (log DGPS) axis. The regression coefficients (0.9269 and - 0.0127) are the slopes of the regression plane in the direction of axis (Mw) and (Rhyp), respectively. These coefficients are called the partial-regression coefficients. Each partial regression coefficient represents the net effect of its variable on the dependent variable, holding the remaining independent variables in the equation constant. Once the regression coefficients have been estimated, various indices are studied to determine the reliability of these estimates. One of the most popular of these reliability indices is the correlation coefficient (R2). The correlation coefficient is an index that ranges from -1 to 1. When the value is near zero, there is no linear relationship. As the correlation gets closer to plus or minus one, the relationship is stronger. A value of one (or negative one) indicates a perfect linear relationship between two variables. In the relationship (4), the correlation coefficient (R2=0.66) indicates an acceptable linear relationship between the dependent variable (log DGPS) and the two independent variables (Mw and Rhyp). In the regression analysis, the underlying assumptions include that the sample is representative of the population; the independent variables are measured with no errors. In fact, more than one variable may play an effective role in this idea.
The residual analysis is performed to evaluate the empirical equation, obtained from the regression analysis. The residuals can be graphically analyzed in numerous ways. Pertain to that, we examined three types of the residuals; they are the histogram, the normal probability plot, the scatter plot of the residuals versus the sequence of the observations. The histogram of the residuals is to evaluate whether they are normally distributed. On the histogram, shown in Figure 4, we can visually evaluate the normality of residuals. For visually evaluating normality of the residuals, the better choice could be the normal probability plot (Figure 5), where the majority of data points are fallen along a straight line through the origin with a slope of 1.0. Some deviations from this straight line reflect departures from normality. Stragglers at either end of the normal probability plot indicate outliers, and the curvature at both ends of the plot indicates long or short distributional tails. In addition, a plot of the dependent variable (log DGPS) versus the first independent variable (Mw), and versus the second independent variable (Rhyp) could be useful to show outliers (Figure 6).
2 Preliminary Application
The last step in this research is the preliminary application of the obtained empirical relationship (4) for some large earthquakes occurred along the DSFS. The recent instrumental seismicity of Syria has produced a little number of low magnitude events (Abdul-Wahed & Al-Tahan, 2010; Abdul-Wahed et. al., 2011; Abdul-Wahed et al., 2018). Therefore, no GPS Seismology data are available in the region even along the DSFS. However, several large well-documented historical earthquakes occurred along the DSFS (Table 1 and Figure 7). In this case, the obtained empirical relationship (4) could be helpful to estimate the coseismic displacement causing the historical earthquake destruction in Syria. The DSFS is a regional active left-lateral strike-slip fault system that runs for about 1000 km long from the Gulf of Aqaba in the south to the East Anatolian fault system (EAFS) in the north near Antakia. It forms a transform boundary between the Sinai plate (part of the larger African Plate) to the west and the Arabian plate to the east. Both plates are moving in a general north-northeast direction, but the Arabian plate is moving faster, resulting in the observed left lateral motion. A set of large historical earthquakes along the DSFS is shown in Figure 7 and listed in Table 1 with depth according to the published literature. The related magnitude (Ms) has been converted to moment magnitude (Mw) using the empirical relation (1). The horizontal coseismic displacements have been estimated using the relationship (4) at the epicenter, where Δ=0. The results, shown in Table 1, demonstrate that the larger the earthquake magnitude, the bigger the GPS coseismic displacement. It could be useful to compare these empirical results with the real measurements of GPS stations. This comparison is enabled for an instrumental Nuweibaa earthquake, which occurred on 22 Nov. 1995 in Aqaba Gulf at the southernmost of the southern DSFS (Figure 7). The Dahab GPS station (DHAB) located at 26 km in the south-west of the epicenter, has documented a coseismic displacement of 17 cm (Kimata et al., 1997). The empirical results, shown Table 1, demonstrate the estimated coseismic displacement to be 33.36 cm at the epicenter of Nuweibaa earthquake. Taking into consideration the epicentral distance to the Dahab GPS station, the relationship (4) yields to 20 cm as coseismic displacement. The difference between the observed displacement and the estimated one is about 3 cm, where the relative error is about 15%. Therefore, the empirical relationship (4), obtained in the current research, could be fairly acceptable regarding the influence of numerous affecting factors.
Figure 7 A digital elevation map of the easternmost Mediterranean showing distribution of the large historical earthquakes and some selected instrumental earthquakes (blue circles) occurred along the Dead Sea Fault system (red color line). Abbreviations of the active faults: AMF: Amanus fault; AVF: Araba Valley fault; EAFS: East Anatolian fault system; JVF: Jordan Valley fault; LAF: Latakia fault; SSF: Saint Simeon fault; SRF: Serghaya fault; YAF: Yammouneh fault. Topographic and bathymetric data are from the United States Geological Survey (USGS) and the European Marine Observation and Data Network (EMODnet), respectively. Black triangle is a location of GPS station named ad-Dahab (DHAB).
Table 1 A list of large historical earthquakes along with some selected instrumental earthquakes occurred along the DSFS. It includes the date of the earthquake, the locality of strongest effect, the references, the moment magnitude (Mw), the focal depth, and the estimated horizontal coseismic displacements (DGPS).
| Date | Earthquake | Reference(s) | Mw | Rhyp =h (km) |
DGPS (cm) |
|---|---|---|---|---|---|
| 18 Jan. 747 | Galilee | Sbeinati et al., 2005; Ambraseys et al., 1994 | 6.9 | 25 | 18.66 |
| 05 Dec. 1033 | Jordan Valley | Ambraseys et al., 1994 | 6.8 | 25 | 15.06 |
| 12 Aug. 1157 | Hama | Sbeinati et al., 2005 | 7.0 | 15 | 31.02 |
| 29 Jun. 1170 | Missyaf | Sbeinati et al., 2005 | 7.1 | 35 | 21.42 |
| 20 May 1202 | Baalbak | Ambraseys and Melville, 1988 | 7.0 | 30 | 20.02 |
| 01 May 1212 | Shaubak | Ambraseys et al., 1994 | 6.8 | 25 | 15.06 |
| 29 Dec. 1408 | Shughur | Sbeinati et al., 2005; Ambraseys & Melville, 1995 | 7.0 | 25 | 23.17 |
| 24 Nov. 1705 | Yabroud | Ambraseys & Finkel, 1993; Sbeinati et al., 2005 | 6.6 | 35 | 07.37 |
| 30 Oct. 1759 | Safad | Ambraseys and Barazangi, 1989 | 6.4 | 20 | 07.45 |
| 25 Nov. 1759 | Damascus | Ambraseys and Barazangi, 1989 | 7.0 | 30 | 20.02 |
| 26 Apr. 1796 | Latakia | Sbeinati et al., 2005 | 6.4 | 20 | 07.45 |
| 13 Aug. 1822 | Aleppo | Sbeinati et al., 2005; Darawcheh et al., 2019 | 7.0 | 18 | 28.42 |
| 01 Jan. 1837 | W. Bekaa | Sbeinati et al., 2005 | 7.0 | 20 | 26.81 |
| 03 Apr. 1872 | Umeq | Sbeinati et al., 2005 | 6.8 | 10 | 23.42 |
| 11 Jul. 1927 | Nablus | Zohar and Marco, 2012 | 6.3 | 15 | 06.96 |
| 16 Mar. 1956 | Chim | International Seismological Center | 5.5 | 15 | 01.26 |
| 22 Nov. 1995 | Nuweibaa | Al-Tarazi, 2000 | 7.0 | 12.5 | 33.36 |
Discussion
The current study presents a synthesis of a large number of GPS measurements of near-field coseismic displacements associated with worldwide earthquakes during the modern period of GPS observations. The derived relationship relates the GPS coseismic displacement (as a dependent variable) to the moment magnitude and the distance between the GPS stations and the earthquake hypocenter (as independent variables). However, other factors or independent variables such as local geology (site effect), faulting mechanisms, and directivity effect due to the slip on the fault could affect this relationship. Unfortunately, these factors have not been included in the relationship. In fact, most of GPS stations are installed on rocky sites or bedrocks. In this case, the relationship is likely not affected by the site effect. However, the effect of faulting mechanisms and directivity merit to be studied and investigated in further works. In this study, surveying a wide range of GPS seismology dataset could make the established relationship global, and not confined for specific conditions. Consequently, this relationship could be a worldwide applicable.
Going back to the late 1960s, the relationship between near-field displacements and fault slip were beginning to be explored using simple kinematic models involving a dislocation in an elastic half-space. One of the earlier studies is Savage and Burford (1973) which applied this concept to the San Andreas fault using trilateration measurements. Such study examines the strain accumulation phase of the earthquake cycle - thus, the system is modeled as a fault that is slipping from surface to the base of the locking depth. This model (and more complicated ones) can be used to fit geodetic observations (GPS, InSAR, and classic terrestrial measurements) to estimate, by using the inverse solution, the near-field displacement in function of the fault slip rate and the position in the survey site. As one can see from the simple mathematical models, there is a predictable relationship between distance and local displacement for a given amount of fault slip, which is directly related to earthquake moment and magnitude following well established relationships from instrumental data (e.g., Wells and Coppersmith, 1994). This relation also depends on the locking depth. Also, it is to mention that the locking depth can vary from one location to the next, even along the same fault (e.g., Smith-Konter et al., 2011) which discussed the case of San Andreas fault. Therefore, the locking depth is not an easy task to be taken into consideration in the derived relationship (4). As regard with the DSFS, a variation in locking depth along the southern DSFS (Figure 7) has been observed from GPS measurements (Al-Tarazi et al., 2011). It is important to realize that, in practice, there is considerable uncertainty and a range of values for locking depth estimates. Also, the locking depth for faults along the central DSFS (i.e., Yammuneh and Serghaya faults) are not well determined. Therefore, our globally estimated relationship could be preliminary and applicable with some caution.
Conclusion
In this study, an attempt was made to derive an empirical relationship for a preliminary assessment of coseismic horizontal displacement values in the near field. The dataset, compiled for this research, has served as a basis for empirically establishing a relationship of the GPS coseismic displacement as a function of the moment magnitude and the distance between the GPS stations and the earthquake hypocenter. The coseismic horizontal displacement values, recorded at 120 GPS stations from 120 different earthquakes around the world of moment magnitude greater than 4.8, have been used for the regression analysis. The regression coefficients in the target relationship were determined by using multi regression analysis. The established relationship has been preliminarily applied for a set of large historical and instrumental earthquakes occurred along the DSFS. The established relationship has been globally estimated considering only three affecting variables. Therefore, it could be preliminary and applicable with some caution. Further efforts should be carried out to develop such an approach once more GPS Seismology data are available and additional affecting variables are included.
