Estimation of Strain Rate in the Opak Fault with

Postseismic Correction After the 2006 Yogyakarta

Earthquake

1st Nurul Ninatin

Geodetic Engineering Student

Universitas Gadjah Mada

Yogyakarta, Indonesia nurul.ninatin@mail.ugm.ac.id

2nd Nurrohmat Widjajanti

Department of Geodetic Engineering

Universitas Gadjah Mada

Yogyakarta, Indonesia nwidjajanti@ugm.ac.id

3rd Cecep Pratama

Departement of Geodetic Engineering

Universitas Gadjah Mada

Yogykarta, Indonesia cecep.pratama@ugm.ac.id

Abstract—The 2006 Yogyakarta earthquake was indicated

as a result of the Opak fault which is still active today. Global Navigation Satellite System (GNSS) measurements as soon as possible after an earthquake are very important because it is an early indication of postseismic deformation. The characteristics of postseismic deformation can be modeled by logarithmic equations with the assumption that the deformations that occur due to the influence of afterslip. In this study, fifteen periodic GNSS data provided by Geodetic Laboratory Universitas Gadjah Mada (UGM) and four continuous GNSS data provided by Geospatial Information Agency of Indonesia (BIG) were used to determine the velocity and strain rate around the Opak fault. The result showed that the Yogyakarta region especially in the Opak fault area has been deformed with the variying horizontal velocity rate. The stations move to the southeast direction as an effect of the movement of the Eurasian and Indo-Australian plates. Based on the computation of the principal strain using modified least square method, strain rate value in the Opak fault area are less than 1 micro strain/yr with extensional strain is dominated. Some stations especially on continuous stations have decreased of strain values and their standard deviasion after corrected by postseismic parameters in logarithmic functions. It shows that to captured the postseismic deformation would be better to use continuous data.

Keywords - Opak Fault, GNSS, Postseismic Deformation,

Logarithmic Function, Strain Rate

I. INTRODUCTION

The earthquake on May 27, 2006 with a magnitude of 6.3 Mw had shaken the Yogyakarta and surrounding areas which included the regions of Bantul, Kulonprogo, Gunung Kidul, Sleman, Prambanan, Klaten, Solo, and Karanganyar. Nearly 7,000 people lost their lives; thousands of people were injured, and lost their families and property. This earthquake is a tectonic earthquake that has a shallow hypocenter about 17 km below the ground surface. According to previous study, the hypocenter is estimated to be just below Bantul Regency [1].

The 2006 Yogyakarta earthquake was indicated as a result of the Opak fault which is still active today. The Opak fault is classified as a sinistral fault (left-lateral) with a strike angle of about 48˚ and a deep angle of about 89˚. This fault is located around 5 to 10 km east of the Opak fault area, commonly depicted along the Opak river [2]. Tectonic activity in Yogyakarta which is relatively high can result in the emergence of movement and deformation of the soil layer both horizontally and vertically, so that regular monitoring is needed. Measurement of Global Navigation Satellite System (GNSS) is one method that can be used to estimate the value of movement and deformation in the monitoring [3]. The Geodetic Engineering Laboratory of

Universitas Gadjah Mada (UGM) since 2013 has examined the existence of the Opak fault by establishing a GNSS observation station in the Opak fault area that is periodically carried out [4].

In an earthquake cycle, the deformation process is divided into four stages, namely interseismic, preseismic, coseismic, and postseismic [5], [6], [7]. Previous study [2] explained that the postseismic stage is defined as the stage when the remnants of earthquake energy are released slowly and over a long period of time until the condition returns to a new equilibrium stage. GNSS measurements as soon as possible after an earthquake are very important because it is an early indication of postseismic deformation [8], [9]. In this study an analysis of the strain of the Opak fault was carried out at the postseismic stage with periodic GNSS observations data from 2013 to 2018 provided by Geodetic Laboratory UGM and from 2007 to 2019 for Continuously Operating Reference Station (CORS) around Yogyakarta provided by Geospatial Information Agency of Indonesia (BIG) named InaCORS BIG.

There are several models of mathematical functions approaches to get the value of postseismic correction, namely linear and non-linear functions (logarithmic functions, exponential functions, etc.). This research focuses on the use of logarithmic functions models. Logarithmic functions are functions with independent variables in the form of logarithms. The characteristics of postseismic deformation can be modeled by logarithmic equations with the assumption that the deformations that occur due to the influence of velocity of afterslip [10]. Previous study [11] explained that based on several earthquake cases such as the Andaman earthquake (2004), Nias (2005), Bengkulu (2007), and Mentawai (2010) produced better fit values if used logarithmic functions for GNSS data in the early postseismic phase. The pattern of these models is influenced by several parameters, namely coseismic offset (c), decay amplitude (a)

and the parameter value of the fitting model (τlog) [10]. Third,

this parameter is assessed to have an insufficient effect on the Opak fault and according to the Opak fault characteristics.

II. DATA AND OBSERVATION

This study analyzed the deformation pattern surrounding

the Opak fault based on fifteen periodic data GNSS

measurement from 2013 to 2018 and four continuous data

from 2007 to 2019. As shown in Fig. 1 there are nineteen

stations of observation in this study. The fifteen periodic

stations are TGD1, TGD2, TGD3, TGD4, TGD5, TGD6,

SGY1, SGY2, SGY3, SGY5, SGY6, OPK3, OPK6, OPK7,

and OPK8. The continuous stations are JOG2, JOGS, CBTL

and CPTS. Data is processed using GAMIT/GLOBK,

Velocity Interpolation for Strain Rate (VISR) algorithm, and

Generic Mapping Tool (GMT) softwares which refer to the

International Terrestrial Reference Frame 2008 (ITRF 2008).

The result from GAMIT is time series of coordinate and

displacement value. Then used VISR to estimate the 2D

strain rate, and the last is plotting using GMT.

III. METHODS

There are some geodesy methods which can be used to estimate the post-seismic earthquake, such as InSAR and GNSS methods [10]. This study used GNSS methods. Postseismic means the measurement is carried out after the earthquake. There are two kinds of data which are continuous and periodic data. The result of the measurements in the field is RINEX data, then processed using GAMIT [11], which resulting the time series coordinates data and the value of its displacement. The displacement data and its standard deviation are processed to generate the linear and non-linear velocity values. TABLE I shows the linear velocity value annually for each observation station.

TABLE I. VELOCITY RATE USING LINEAR FUNCTION

Sta.

code

Secular velocity using linear function

VE

(mm/yr)

σE

(mm/yr)

VN

(mm/yr)

σN

(mm/yr)

CBTL 27.17 0.06 -8.45 0.02

CPTS 28.00 0.10 -11.32 0.08

JOGS 26.95 0.03 -8.66 0.02

JOG2 24.56 0.09 -8.08 0.06

TGD1 22.99 2.19 -9.32 1.19

TGD2 29.89 2.31 -8.87 1.39

TGD3 28.98 1.29 -10.87 1.41

TGD4 26.01 1.59 -9.27 0.91

TGD5 23.63 3.84 -6.91 1.06

Sta.

code

Secular velocity using linear function

VE

(mm/yr)

σE

(mm/yr)

VN

(mm/yr)

σN

(mm/yr)

TGD6 31.52 1.64 -10.03 0.95

SGY1 31.67 1.33 -9.17 2.30

SGY2 31.50 2.65 -8.70 2.78

SGY3 19.05 6.37 -9.81 0.55

SGY5 24.00 1.31 -9.08 1.37

SGY6 22.66 6.41 2.57 11.21

OPK3 29.58 1.97 -6.99 2.16

OPK6 28.86 2.24 -9.44 1.19

OPK7 25.35 5.66 -14.11 2.91

OPK8 27.21 1.51 -7.97 2.55

In the next analysis procedure are modelled GS time

series displacements using the logarithmic functions [10]. This is a function with a free variable as the correction in the form of logarithm, which can be used to determine postseismic parameters. The formula can be shown in equation (1) and the result shown in TABLE II.

u(t) = c + a ln (1 + t/τlog)

In this case,

u(t) : position (north and east)

t : observation time

c : offset

a : amplitude

τlog : decay time

TABLE II. VELOCITY RATE USING LOGARITHMIC FUNCTION

Sta.

code

Secular velocity using logarithmic function

VE

(mm/yr)

σE

(mm/yr)

VN

(mm/yr)

σN

(mm/yr)

CBTL 24.71 0.06 -10.91 0.02

CPTS 25.84 0.10 -13.49 0.08

JOGS 24.37 0.03 -11.24 0.02

Fig. 1. Location of Opak Fault monitoring stations Fig. 1. Location of Opak Fault monitoring stations

Sta.

code

Secular velocity using logarithmic function

VE

(mm/yr)

σE

(mm/yr)

VN

(mm/yr)

σN

(mm/yr)

JOG2 22.17 0.09 -10.46 0.06

TGD1 20.63 2.17 -11.68 1.20

TGD2 27.53 2.30 -11.21 1.37

TGD3 26.60 1.29 -13.22 1.42

TGD4 23.62 1.59 -11.62 0.91

TGD5 21.22 3.84 -9.31 1.06

TGD6 29.17 1.63 -12.37 0.95

SGY1 29.28 1.33 -11.51 2.29

SGY2 29.12 2.64 -11.04 2.79

SGY3 16.65 6.39 -12.19 0.54

SGY5 21.60 1.28 -11.46 1.39

SGY6 20.32 6.40 0.27 11.22

OPK3 27.18 1.96 -9.38 2.19

OPK6 26.47 2.26 -11.78 1.18

OPK7 22.97 5.66 -16.45 2.92

OPK8 24.82 1.50 -10.31 2.57

Further the velocity rate was used to determine the 2D strain rate using VISR algorithm. This algoritm was used to estimate principal strain using modified least square method [14]. The algorithm of modified least square can be written in equation (2).

μ is the vector for the unknowns parameters, A is the partial derivative matrix, X is the covariance matrix of velocity data, and δ is the velocity data. In the case of horizontal strain

only, μ = (Ux, Uy, ω, xx, xy yy)T which Ux and Uy are

the translation components in x and y directions, ω is the rotation, and τxx, τxy, and τyy are the horizontal strain components. The least square equation in this method is modified by using spatial weighting function in various form. The last is the visualization using GMT.

IV. RESULT AND DISCUSSION

A. Velocity Rate of GNSS Stations

The velocity rate using linear and logarithmic functions can be seen in Fig. 2. The result of velocity rate shows that there are not significant differences between linear and logarithmic functions. Based on Fig. 2. there are four stations with high standard deviation. The SGY6 and OPK3 have a north-south component that has high standard deviation, and then SGY3 and OPK7 have east-west compenent that has high standard deviation. We can see that the stations move to the southeast direction as an effect of the movement of the Eurasian and Indo-Australian plates [15].

The result in logarithmic functions shows the ranges of velocity are from 16.65 mm/yr to 29.28 mm/yr in the east component with the biggest value of SGY1. In the north component, the value ranges from -16.45 mm/yr to 0.27 mm/yr with the biggest value of OPK7. Their standard deviation of east and north components in continuous stations are less than 1 mm/yr while in the periodic stations ranges from 0.54 mm/yr to 11.22 mm/yr.

B. Principal Strain Rate

We estimated the two dimensional strain rate inferred by the horizontal velocity. The strain can be seen in Fig. 3. Strain rate value shows less than 1 micro strain/yr. The result indicates the Yogyakarta region experiences east-west extension and north-south compression. It is opposite with previous study [16] which use Sunda Block reduction and use moving average filter to corrected the velocities. The extensional strain rate models were dominated. It is corresponding to previous study [17]. It might be related with tectonic activities effects after the 2006 Earthquake in Yogyakarta [2]. The compression of north-west of Opak Fault was increased. This result might be related with volcano activities near Central Java and northern of Yogyakarta [18].

Fig. 2. Direction and magnitude of velocity using linear and logarithmic functions

There are no significant differences between linear and logarithmic functions. Even some stations, especially on continuous stations had decreased strain values and their standard deviasion after corrected by postseismic parameters in logarithmic functions. Java regions have lower rigidity than general mega thrust earthquake cases and tend to continuously slip during long-term periods as a result of stress transfer from the main shock [19]. We speculate that data measurements still need to be continued and that several new observation stations need to be built, especially for continuous stations.

V. CONCLUSION

The result showed that the Yogyakarta region especially in Opak Fault area has been deformed with variying horizontal velocity rate. The stations move to the southeast direction as an effect of the movement of the Eurasian and Indo-Australian plates. Strain rate value in the Opak Fault area are less than 1 micro strain/yr with extensional strain is dominate. Some stations especially on continuous stations have decreased of strain values and their standard deviasion after corrected by postseismic parameters in logarithmic functions. It shows that to capture the postseismic deformation would be better to use continuous data.

ACKNOWLEDGEMENT

The author thanks to Department of Geodetic

Engineering, Universitas Gadjah Mada, for maintaining and

providing the GNSS network and also to Geospatial

Information Agency of Indonesia (BIG) for providing the

continuous GNSS observation data. Most figures were

generated by Generic Mapping Tools version 6 [20].

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