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


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.


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.


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