## Article of the Month - June 2018 |

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.

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* t _{n}* is the displaced position
from initial coordinate at

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 *e ^{1}*,
is total velocity displacement at point

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, *a ^{e1}* and
is post-seismic amplitude and logarithmic decay
rate, respectively for earthquake