Article of the Month - June 2018

Non-Linear Crustal Deformation Modeling for Dynamic Reference Frame: A Case Study in Peninsular Malaysia

Wan Anom WAN ARIS, Tajul Ariffin MUSA, Kamaludin MOHD OMAR, Abdullah Hisam OMAR

This Peer Review paper is the navXperience AWARD WINNER and was presented at the FIG Congress 2018 in Istanbul, Turkey.

The best FIG Commission 5 Paper at a FIG Working Week or a FIG Congress  is awarded with the NavXperience Award. The award covers among others free participation at next Working Week/Congress. The first time the price was awarded at the Working Week in Helsinki, 2017. It is sponsored by the Berlin based company NavXperience and granted by FIG Commission 5. In 2018 the price was awarded  for the 2nd time. The paper  “Non-Linear Crustal Deformation Modeling for Dynamic Reference Frame: A Case Study in Peninsular Malaysia” by Wan Anom Wan Aris and others developed innovative methods to model non-linear crustal movements and consider these models for non-static reference frames. Besides the paper was structured in a very good and scientific way, impressing results were presented too. The academic merit is combined with the spirit of a young surveyor.

This article in .pdf-format (14 pages)

 

 

Key words: Crustal Deformation, Peninsular Malaysia, Non-linear,  Dynamic Reference Frame

SUMMARY

Series of major to great earthquakes struck the Sundaland platelet since December 2004 due to convergence between Indian and Australian plates along its western and southern boundaries. Since then the plate has been undergoing significant co-seismic and post-seismic afterslip deformation that is continuously distorting geocentric reference frame within affected countries such as Malaysia. The deformation produced coordinate shift in geodetic network thus, causing errors in Global Positioning System (GPS) / Global Navigation Satellite System (GNSS) satellite measurements which limits its accuracy for high precision positioning applications. In addition, the afterslip deformation exhibits on-going non-linear motion that needs to be modelled for maintaining accuracy of the geocentric reference frame in Peninsular Malaysia. This paper reports the work of crustal deformation modeling  the spatio-temporal crustal deformation due to Mw >7.9 earthquakes that is affecting geocentric reference frame and geospatial accuracy in Peninsular Malaysia. The fundamental works involved determination of co-seismic and post-seismic deformation to account for the non-linear effect of the crustal deformation. The study has found that afterslip deformation model enabled to minimize the effect of non-linear motion on geodetic network less than 2cm of accuracy. The work is crucial in order to improve the stability of reference frame due to great earthquakes especially in Peninsular Malaysia.

1. INTRODUCTION

Critical positioning activities such as national boundary determination, oil and gas field exploration, and high precision surveying applications need the utilization of geodetic reference frame. Since improvement of space geodesy and positioning, additional linear and non-linear crustal deformation signals such as plate rotation, co-seismic offsets and long-term post-seismic deformation have also become observable and must be taken into account to produce very stable reference frame (Bevis and Brown, 2014; Gomez et al., 2016). In particular, Peninsular Malaysia has experienced heterogeneous crustal deformations both in spatial and temporal due to four (4) earthquakes (>7.8Mw); 2004 Sumatra Andaman at 9.2Mw, 2005 Nias Simeulue (8.5Mw), 2007 Bengkulu (7.9Mw) and 2012 Indian Ocean (8.6Mw). Since then the region has experienced significant co-seismic displacement and yet undergoing long post-seismic deformation up to 39cm/year (Aris et al., 2016). In fact, this problem is worsening as this crustal deformation also exhibits non-linear motion until now due to significant crustal relaxation process. Currently, the realization of ITRF2014 has shown the inclusion of co-seismic and post-seismic deformation model by following logarithmic functional model (Altamimi et al., 2016) that will be used for a better stability of reference frame definition in Peninsular Malaysia. Even if these crustal deformation effects are conventionally modeled by piecewise linear fitting, one has to keep in mind that model uncertainties, model inconsistencies and possible model errors could falsify the corrections of the instantaneous station position (Altamimi et al., 2016). This paper discusses crustal deformation model in Peninsular Malaysia that cater for distribution of non-linear co- and post-seismic signals due to great earthquakes (>8Mw). The paper is organized into five (5) sections. Conceptual linear and non-linear crustal deformation in the present-day reference frame is provided in Section 2. Crustal Deformation  deformation model is discussed in Section 3. Assessment of the model is provided in Section 4. Finally, conclusion is drawn in Section 5.

2. Linear and Non-Linear Trend in Spatial Crustal Deformation Model

In order to account for co-seismic and post-seismic of each site which is subject to major earthquakes, pragmatic approach by fitting logarithmic and/or exponential functions to the site-specific coordinate time series is necessary. Figure 1 demonstrates temporal change of coordinate over time t due to linear and nonlinear trend of crustal deformation. From the figure, coordinate point P at time tn is the displaced position from initial coordinate at t0 after occurrence of earthquake e1. In traditional way, the displacement of coordinate topocentric (north or east)  is computed by assuming that the crustal deformation depicts linear trend after the occurrence of earthquake as in Equation 1;

Figure 1: Demonstration of crustal deformation model for Peninsular Malaysia as applied by ITRF (Altamimi et al., 2016).

where; t  time; is co-seismic displacement at point P after earthquake e1, is total velocity displacement at point P from time te1 to tn, and is plate rotation deformation at point P from time te1 to tn.

Meanwhile, in the current practice of high precision ITRF, the  is computed by assuming that the crustal deformation refers to plate rotation and post-seismic trend after the occurrence of earthquake as in Equation 2 which depicts a non-linear trend.

                             (2)

where, ae1 and  is post-seismic amplitude and logarithmic decay rate, respectively for earthquake e1 at point P. For the case of multiple earthquake events, variable terms of deformation model (co-seismic, amplitude and logarithmic decay rates) can be imposed in Equation 1 or 2.  It is noted that, the application of high precision ITRF will be more practical when the  can be predicted at non-GPS CORS sites (i.e., passive network). This is possible when the terms , ae1, and are spatially modeled for north and east components separately. In this study, Co-seismic Spatial Deformation Model (CSDM) refers to spatial co-seismic displacement, for each major earthquake. Meanwhile, Spatio-Temporal Deformation Model (STDM) can be divided into three (3); Sunda Linear (SuLin-STDM), Velocity Linear (VeLin-STDM) and Post-seismic Non-Linear (PosNoLin-STDM) referring to the distribution of , and ae1 respectively. For the case of CSDM and STDM, this study has generated national grid namely Quasi Network (Q1- Q144) with spatial resolution 0.3°×0.3° (as shown in Figure 2-(a)). The information of , ae1, and at Quasi Network point were predicted from the knowledge of actual , ae1, and signals as quantified by MyRTKnet stations that records the 9 years ofcrustal deformation trend since 2004 Sumatra Andaman earthquake  (as shown in Figure 2-(b)).

 

Figure 2: (a) Quasi-Network grid (Q1-Q144) with spatial resolution 0.3°×0.3° ; and (b) distribution of MyRTKnet in Peninsular Malaysia.

The prediction of crustal deformation signals can be made through least square collocation which can be expressed by Moritz, (1962) and Moritz, (1980). The predicted signal S (i.e., intra-plate grid velocity to be predicted) at the nearest point is given as;

                                                                   (3)

where is empirical covariance functional matrix between signal L (i.e., co-seismic deformation, velocity fields and post-seismic amplitudes) at the observation points (i.e., GPS sites). While, is the covariance matrix of signal L between observation points. The curstal deformation signals at Quasi-Network is assumed to be a random field which comprises only one random function with a number of independent variables. Therefore, one can define a covariance function that depends only on the distance between the points. The empirical value is used to compose the covariance function CSL in order to estimate the signal S. The derivation of local empirical covariance function is extracted from a local data set. The computation of the variance and covariance from the given local data set is demonstrated in Equation 4 and 5, respectively (El-Fiky et al. 1997; Mikhail and Ackermann, 1976);

                                                      (4)

                                                    (5)

where distance between location of MyRTKnet stations (i and j) are divided into finite discrete intervals P.  The models were applied to predict both linear and non-linear motion for both north and east components to allow for determination of coordinate at specific epoch.

3. CSDM & STDM

Nine (9) years of high precision daily GPS-derived coordinate time series (CTS) in north as east components has been generated by using GPS  data as recoreded by MyRTKnet stations since December 2004. The GPS-derived CTS at these CORS were utilised to estimate information of , ae1, and . Meanhwile, were extrapolated from the knowledge of Sunda plate motion model by Mustafar et al., 2016. These estimated values were then utilised to generate CSDM and STDM at Quasi Network points using least-square collocation as in Equation (3-5). Figure 3 presents CSDM vectors at Peninsular Malaysia during the occurance of four (4) great earthquakes. The vector of CSDM2004 was predicted from the knowledge of  (north and east) during 2004 Sumatra Andaman earthquake (9.2Mw) which was detected by fourteen (14) MyRTKnet stations. These vectors were headed to earthquake’s epicenter (northern part of Sunda trench) at azimuth N256o (southwestward) in northern part and decreased to N264o (northwestward) in southern part of the region. Large predicted co-seismic displacements (north and east) was found with the highest magnitude of 185 mm at point Q1 (northwestern part of the region) and decreased to 24 mm at Q144 (southeastern part of the region). Similar to CSDM2004, the vector of CSDM2005 was predicted from the knowledge of of 2005 Nias Simeulue earthquake (8.5Mw) by using fourteen (14) detected MyRTKnet stations. It can be inspected that, the pattern of CSDM2005 vectors varies over Quasi Network points. The predicted vectors were found to be headed to the earthquake’s epicenter with azimuth varying from ~N216o to ~N238o. Large predicted co-seismic displacements were found at Quasi Network points near to site PUPK at predicted displacement of 67 mm. Meanhwhile, CSDM2007 vectors was predicted from the knowledge of co-seismic deformation of 2007 Bengkulu earthquake (7.9Mw) as observed by twenty-eight (28) MyRTKnet sites. As seen from the figure, the magnitude and direction of CSDM2007 significantly vary over latitudinal direction. Heterogeneous co-seismic displacement can be seen from east to southeast direction and headed to the earthquake’s epicenter (in Mentawai trench, Indonesia) with azimuth that varies from ~N145o to ~N246o. Large predicted were found with highest magnitude of 31 mm at Quasi Network points near to site KUKP (southern part).

 

Figure 3: CSDM vectors, in Peninsular Malaysia during great earthquakes occurances.

Figure 4: SuLin-STDM, VeLin-STDM and PosNoLin-STDM at Quasi Network points.

Finally, vectors of CSDM2012 represents spatial distribution of during the 2012 Indian Ocean earthquake (8.6Mw). The model was determined from the knowledge of estimated from thirty-four (34) MyRTKnet sites. One can inspect that the vector of CSDM2012 headed to northeastward (azimuth from ~N145o to ~N246o) and depicted different co-seismic pattern as compare to the other CSDMs. This can be explained due to the internal deformation of the diffused plate boundary between India and Australia plates that caused the Peninsular Malaysia to be co-seismically displaced away from the earthquake’s epicenter.

The velocity vector of SuLin-STDM, VeLin-STDM and PosNoLin-STDM are presented in Figure 4. The SuLin-STDM vectors appeared to be consistent at all Quasi Network points. This indicate the tectonic motion depicted as rigid but follow rotation of Sunda plates. The region moves southeastward (in range of azimuth N95o – N101o) with slow variation of magnitude at 31.713 mm/yr in the southern part and 33.212 mm/yr in the northern part of the region. From the figure, one can inspect inhomogeneous direction of intra-plate velocities from sites in northern to southern part that moved horizontally southeastward (in range of azimuth N130o – N150o) with average magnitude of 15.389 mm/yr. The magnitude increased gradually over longitudinal and latitudinal with average magnitude of 22.989 mm/yr and moved southeastwardly (in range of azimuth N110o – N122o). Finally, the pattern of PosNoLin-STDM indicates that the region is being driven by a single afterslip mechanism since the day of the great 2004 Sumatra Andaman and subsequent earthquakes. The decay rate of post-seismic,  was found at 148.5 and 204.1 days for north and east components. From the analysis, these decay rates were also found to be consistent for all sites, however, the post-seismic amplitudes of the afterslip tends to varies over the region in spatial sense. Large post-seismic amplitudes can be noticed at Quasi Network points situated in the northwestern part of Peninsular Malaysia with magnitude ~121.5 mm. The post-seismic amplitudes, ae1  decreased over latitudinal of the region with minimum magnitude of 24.2 mm within southern part of the region.

4. ASSESSMENT OF CSDM AND STDM IN RESOLVING REFERENCE FRAME DISTORTION

For assessment of STDM and CSDM, experimental works has been conducted to test the efficiency of the model to predict crustal deformation trend by following three (3) assumptions; Assumption 1, Assumption 2 and Assumption 3 and its explanation as tabulated in Table 1. Crustal deformation trend prediction for each three assumptions was performed at four (4) different locations of testing point. These points were closed to MyRTKnet stations (i.e., SGPT, UPMS, TERI, and JHJY) whereby the 9 years of daily GPS-derived CTS in north as east components from these four MyRTKnet sites were independent from STDM and CSDM generations. Figure 5 shows locations of PN1 situated in the northern part of Peninsular Malaysia (assessed with MyRTKnet station SGPT).  The assessment result is potrayed in Figure 6.

  

Table 1: Three (3) assumptions of crustal deformation trends in Peninsular Malaysia to simulate the test based on the assumptions

Figure 5: Locations of PN1 situated in northern part of Peninsular Malaysia.

As seen in Figure 6, the simulated CTS at PN1 based on Assumption 1 led to large difference of RMSe about 59.238 mm and 181.425 mm in north and east components respectively. The simulated CTS from Assumption 2 were different from actual GPS-derived CTS in north component with RMSe at 22.889 mm. However large RMSe was depicted in easting components up to 77.227 mm. Simulated CTS from Assumption 3 shows good fit with the GPS-derived CTS in north and east components with averaged RMSe and averaged R2 at 9.984 mm and 0.918 mm respectively.

Figure 6: Misfit between the simulated CTS and observed GPS-derived CTS at four locations. Green, cyan and red represents residual simulated CTS based on Assumption 1, Assumption 2 and Assumption 3, respectively.

From Figure 6 (a), the simulated CTS from Assumption 1 and 2 were unable to predict the non-linear trend of post-seismic effect after the 2005 Nias Simeulue earthquake and thus resulting large coordinate dispute over the time with RMSe up to 114 mm. Nevertheless, simulated CTS from Assumption 3 provide good fit of coordinate change prediction in both north and east components with averaged RMSe of 11.538 mm. Nevertheless, simulated CTS from Assumption 3 provide good fit of coordinate change prediction in both northing and easting components with averaged RMSe 12.557mm and averaged R2 at 0.892. In overall, the use of CSDMs works-well to ‘mimic’ the co-seismic displacement during the day of major earthquake’s occurrences. However, large post-seismic amplitudes can be found in the northern and west-coast of Peninsular Malaysia which is responsible for the inability of VeLin-STDM to determine the actual trend of crustal deformation within the region. It is expected that the used of SunLin-STDM and PosNoLin-STDM are efficient to resolve such distorted geodetic network and adequately describe the non-linear trend of post-seismic deformation.Further analysis on residual coordinate was made between predicted CTS and GPS-derived CTS. The green, cyan and red nodes in scatter plot of Figure 6 (b) represent residual from simulated CTS based on Assumption 1, Assumption 2, and Assumption 3 respectively. It can be inspected that ~83% of simulated CTS from Assumption 1 fall inside the 2cm limit, and ~17% fall between 2 and 4 cm. Meanwhile, 22% of simulated CTS from Assumption 2 fall within 2 cm limit, and the other 78% were distributed from 2 to 10 cm. Nevertheless, simulated CTS from Assumption 1 signify the presence of systematic bias. The results from this assessment indicates that after the occurrence of major earthquakes in Sundaland, crustal deformation of Peninsular Malaysia is still induced by the similar rotation of Sunda plates as it was before, but undergoing significant afterslip deformation (i.e., co-seismic and post-seismic), that agree with Assumption 3 of the study.

5. CONCLUSION

This paper demonstrated on how to resolve reference frame distortion effects of Sundaland plate motion and recent major earthquake by utilization of linear and non-linear reference frame using CSDM and STDM concepts. As the focus of the study, Peninsular Malaysia is affected by four earthquakes (>7.8Mw) situated in Sumatra plate boundaries since December 2004. Therefore, site velocity, co-seismic and post-seismic logarithmic-based parameters from these four earthquakes has been estimated and the parameter of estimation was utilized to model the SuLin-STDM, VeLin-STDM, PosNoLin-STDM, and CSDMs at Quasi Network points using least-squares collocation approach. As a result, 144 Quasi Network points has been generated and each Quasi Network points comprised known STDMs and CSDMs magnitudes. This has enabled the determination of STDMs and CSDMs magnitudes at each any point in Peninsular Malaysia. Three (3) assumptions were made to check the ability of linear and non-linear STDMs in simulating crustal deformation trend at the selected point.  From the analysis, the CSDM is able to predict co-seismic displacement during the day of great earthquake’s occurrences. In addition, the utilization of SuLin-STDM and VeLin-STDMs were found imprecise for estimating the non-linearity of crustal deformation trend within the region. The assessment shows that ~83% of simulated CTS can achieve up to 20 mm of accuracy by inclusion of linear and non-linear STDMS. The results indicate after the occurrence of major earthquakes in Sundaland, crustal deformation of Peninsular Malaysia is still induced by the similar rotation of Sunda plates as it was before, but undergoing significant afterslip deformation that depicts non-linear crustal deformation over the region. Therefore, the utilization of SuLin-STDM, PosNoLin-STDM and CSDM is appropriate to cope with non-linear crustal deformation due to significant co- and post-seismic deformation thus support stability of reference frame realization in this region.

ACKNOWLEDGEMENT

The authors would like to thank to Department Surveying and Mapping Malaysia for providing the GPS/GNSS data of this study. The authors would also like to thanks to Ministry of Education, Malaysia and Universiti Teknology Malaysia, for their financial support in this study. This research was also partly funded by a grant Fundamental Research Grant Scheme (FRGS: 4F962)  (2017 – 2020): Modeling Afterslip Crustal Deformation Of Sundaland’s Earthquake for Malaysia.

REFERENCES

Altamimi, Z., P. Rebischung, L. Métivier, and Xavier, C. (2016). ITRF2014: A new release of the International Terrestrial Reference Frame modeling nonlinear station motions. J. Geophys. Res. Solid Earth, 121, 6109–6131, doi:10.1002/2016JB013098.

Aris, W. W.A., Musa, T.A.,and Omar, K., Estimation of Co- And Postseismic Deformation after the Mw 8.6 Nias-Semeulue and Mw 8.5 Bengkulu Earthquakes from Continuous GPS Data, The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-4/W1, 2016, International Conference on Geomatic and Geospatial Technology (GGT) 2016, 3–5 October 2016, Kuala Lumpur, Malaysia(SCOPUS).

Bevis, M., and Brown, A. (2014). Trajectory models and reference frames for crustal motion geodesy. J. Geod 88:283-311. doi:10.1007/s00190-013-0685-5.

El-Fiky G.S., Kato, T., Fujii, Y. (1997). Distribution of vertical crustal movement rates in the Tohoku district, Japan, predicted by least-squares collocation. Journal of Geodesy, 71: 432-442. doi: 10.1007/s001900050111; Print ISSN: 0949-771.

Gomez, D. D., Pinon, D.A., Smalley Jr, R., Bevis, M., Cimbaro, S. R., Lenzano, L. E., Baron, J. (2016). Reference frame access under the effects of great earthquakes: a least square collocation approach for non-secular post-seismic evolution. J. Geod. (2016). 90:263-273. Doi:10.1007/s00190-015-00871-8.

Mikhail E.M., Ackermann, F. (1976). Observation and least squares. Harper and Row, New York.

Mustafar A.M., Simons, W.J.F., Tongkul, F., Satirapod, C., Omar, K.M., Visser, P. (2016). Quantifying Deformations in North Borneo with GPS. Journal of Geodesy.

BIOGRAPHICAL NOTES

Wan Anom Wan ARIS holds a M.Sc. in Geomatics Engineering from Universiti Teknologi Malaysia. She is currently undertaking PhD studies at Faculty of Geoinformation & Real Estate, Universiti Teknologi Malaysia. Her research area is GNSS data processing techniques for crustal deformation studies in Southeast Asia.

Tajul Ariffin MUSA is a senior lecturer in the Faculty of Geoinformation & Real Estate, Universiti Teknologi Malaysia. He obtained his PhD (Satellite Navigation & Positioning) from University of New South Wales, Australia.  He specialises in surveying and mapping, satellite geodesy, atmospheric and space weather study. His research activities are focused on developing Global Positioning System (GPS) real-time surveying system and applications, GPS for meteorology, ionospheric measurements and its modelling for space weather monitoring.

Kamaludin MOHD OMAR holds a M.Sc. in Geodetic Science from Ohio State University. He is currently an associate professor and head of Geoinformation Department, Faculty of Geoinformation and Real Estate, Universiti Teknologi Malaysia. He specializes on geoid determination, high precision positioning and satellite altimetry.

Abdullah Hisam OMAR is a senior lecturer in the Faculty of Geoinformation & Real Estate, Universiti Teknologi Malaysia. He obtained his PhD from Universiti Teknolohi Malaysia. He specialises in surveying and mapping, satellite geodesy, atmospheric and space weather study. His research activities are focused on positioning, mapping and Marine Cadastre in Malaysia.

CONTACTS

Ms. Wan Anom Wan Aris
Geomatics and Innovation Research Group, Faculty of Geoinformation & Real Estate 81310 Universiti Teknologi Malaysia Johor Bahru, MALAYSIA.
Email: anomaris@gmail.com kamaludinomar@utm.my
Web site: http://www.geoinfo.utm.my/Research_Group/gng/aboutus.html

Dr. Tajul Ariffin Musa
Geomatics and Innovation Research Group, Faculty of Geoinformation & Real Estate 81310 Universiti Teknologi Malaysia Johor Bahru, MALAYSIA.
Email: tajulariffin@utm.my
Web site: http://www.geoinfo.utm.my/Research_Group/gng/aboutus.html

Assoc. Prof. Kamaludin Mohd Omar
Geomatics and Innovation Research Group, Faculty of Geoinformation & Real Estate 81310 Universiti Teknologi Malaysia Johor Bahru, MALAYSIA.
Email: kamaludinomar@utm.my
Web site: http://www.geoinfo.utm.my/Research_Group/gng/aboutus.html

Dr. Abdullah Hisam Omar
Geomatics and Innovation Research Group, Faculty of Geoinformation & Real Estate 81310 Universiti Teknologi Malaysia Johor Bahru, MALAYSIA.
Email: abdullahhisham@utm.my
Web site: http://www.geoinfo.utm.my/Research_Group/gng/aboutus.html

 


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