Modeling of Crustal Deformation Due To Sumatra Tectonic Earthquakes Based On GNSS Remote Sensing Data

Indonesia is at the confluence of three large plates, so it often experiences earthquakes. Therefore, earthquake disaster mitigation efforts must be increased. One of the efforts that can help the government prepare a disaster mitigation system for earthquakes and their associated disasters is research on fault deformation. This research utilizes continuous data from the Global Navigation Satellite System (GNSS), especially the Global Positioning System (GPS), which is processed into surface deformation. The crustal deformation was modeled based on the Okada formulation with estimated earthquake parameters and then verified with surface deformation to obtain optimal parameter values. Automation is carried out with a computerized system to speed up the estimation process, and more optimal results are obtained using the Hooke-Jeeves numerical method. We do modeling for tectonic earthquakes in Sumatra during 2005 and 2007 with magnitudes > 8 Mw. The modeling results were validated with seismic data and seismological theory of the seismic moment. The success of this modeling can be taken into consideration in earthquake prediction as part of an earthquake disaster mitigation system.


Introduction
The three most important plates affecting the Indonesian region are the Eurasia Plate, the Indo-Australian Plate, and the Pacific Plate [1].Sumatra is one of the regions in Indonesia that sits atop the Eurasian Plate which is in the subduction zone of two large plates, where the Indo-Australian oceanic Plate is obliquely subducting the Eurasian Plate, striking N140E at the rate of 50 -70 mm/yr [2].The subduction zone commonly known as Sunda Megathrust makes Sumatra prone to numerous earthquakes with a high potential for large earthquakes.
Several major earthquakes have been recorded due to tectonic activity in the Sunda megathrust starting in 2004 with a series of Mw > 8 earthquakes such as the 26 December 2004 Mw 9.2 Sumatra-Andaman event, the 28 March 2005 Mw 8.6 Nias-Simeulue event, and the 12 September 2007 Mw 8. 4 Bengkulu event.Large earthquake events always have an impact on life and material losses so mitigation efforts are needed to increase readiness and knowledge in reducing the risk of worse losses.One way to improve the ability to knowledge about earthquake disasters is research on crustal deformation.Information on long-term patterns of crustal deformation is very useful for earthquake hazard assessments.
Many studies have researched and modeled the crustal deformation in the 2005 Nias-Simeulue earthquake and the 2007 Bengkulu earthquake.[3][4][5][6][7][8].Most of the previous studies used Global positioning system (GPS) data as observed data from the Sumatran GPS Array (SuGAr) station and inversion techniques as modeling methods but had different estimation and modeling approaches thus resulting in a difference in the approximate fault geometry even if it is not significant.The information obtained from the results of previous research modeling still has parameters that have not been achieved in describing crustal deformation events in the coseismic phase.In this study, we used the Okada model with parameter estimation: coordinates of the fault observed, fault geometry (depth, dip, strike), an area of crustal deformation (length and width), and fault dislocation (size and direction of deformation).The observation data to be used is taken from The SuGAr data and the modeling technique used is an inversion technique as has been done in previous studies.The inversion technique to the okada model is not simple because there are four interrelated estimation parameters so computerization assistance is needed to use numerical methods to achieve optimal results.The corresponding numerical method for multivariable with nonlinear functions is the Hooke-Jeeves numerical method.

GNSS Data Processing
GNSS is an abbreviation of Global Navigation Satellite System.The GNSS is a technology used to determine position or location (latitude, longitude, and altitude) and time in scientific units on Earth.Satellites transmit high-frequency radio signals containing time and position data that can be received by a receiver, allowing users to determine their exact location anywhere on the surface of the Earth.So far, four types of GNSS have been and will be fully operational in the coming years, namely: GPS -Global Positioning System (USA), GLONASS -Global Navigation Satellite System (Russia), Beidou (Compass -China) and Galileo (European Union) [9].GNSS surveys, especially GPS, have been widely used for deformation monitoring.GPS has a high level of accuracy in point-based monitoring.GPS provides vector values for points in three dimensions and a single coordinate system.The resulting vector values of movement have precision levels of up to millimeters, spatially and temporally [10].
One widely used GPS observation network for deformation monitoring is the Sumatran GPS Array (SuGAr).SuGAr is a Continuously Operating Reference Station (CORS) station managed by the Earth Observatory of Singapore in collaboration with the Indonesian Institute of Sciences (LIPI), currently named BRIN.SuGAr is spread over 1300 km on the west coast of Sumatra Island.SuGAr records GPS data with high accuracy every day, and the data can be accessed after three months and utilized for deformation studies.
The GPS data is in RINEX (Receiver Independent Exchange) format.The data is processed using GAMIT and GLOBK software.The final output of GAMIT is the Q-file which contains processing results, and the H-file, which contains the processing results in the form of covariance matrices as input for further processing with GLOBK.Then, the results of the GLOBK processing include time series of observation points, topocentric and 3D cartesian coordinates along with standard deviations for each station, baseline length along with its precision, and the magnitude and direction of the observation point displacement.[11].

Okada Model and Hooke-Jeeves Numerical Method for optimation
The horizontal displacement vectors obtained from GPS survey can be used to estimate the geometry of the fault that caused the earthquake.The fault geometry is estimated assuming a homogeneous, linear, and elastic dislocation model of the Earth's crust.The model used is the Okada model [12,13], which describes the relationship between the fault system displacement and the surface displacement by assuming an isotropic and elastic Earth's crust.After obtaining the deformation source parameters including position, size, direction, dip, and slip vector, the surface displacement, dilation, and Coulomb stress change are calculated.Figure 2   The Okada model is written in FORTRAN language with the name DC3D.f.DC3D0 and DC3D are derived from papers in 1985 [12] and 1992 [13], respectively.The code DC3D0 is used to calculate the deformation field on the surface and DC3D is used for inside of the earth.
The Okada model is commonly used in inversions of geodetic data to estimate fault slip.Optimal estimation can be achieved with the support of the Hooke-Jeeves numerical method.Hooke-Jeeves numerical method is known as a "direct search" to describe the sequential examination of the trial solutions that involve comparing each trial solution with the "best" obtained until then along with a strategy to determine [14].The basic form of the Hooke-Jeeves numerical method begins with determining the first estimation parameter is arbitrarily chosen to be the first "base point".Estimation of the second parameter and compared to the first "base point".If the second parameter is better than the first base point then the second parameter becomes the second base point.This process continues, each new point is compared with the current base point until it reaches the best value.The initial parameter estimate must be well defined in order to reduce the loop in the search for the optimal value.The optimal value is determined based on the root mean square (rms) from the comparison horizontal and vertical displacement of observational data with modeling.

Seismic moment
Seismic moment is a measure of the size of an earthquake based on the area of the fault surface, the average amount of slip, and the force required to overcome the frictional forces that bind the rock (1)

Result of GNSS Data Processing
The result GNSS data processing using GAMIT/GLOBK is surface deformation.The deformation are written in the direction of east, north, and Up.The eastward displacement is positive value as well as the northward.On the contrary, the westward and southward is characterized by negative values.Up displacement is positive value for surface rise and negative value when surface down.The surface deformation used in modeling crustal deformation due to the 2005 Nias-Simeulue earthquake (Table1) and modeling crustal deformation due to the 2007 Bengkulu earthquake (Table 2).The results of data processing obtained are not much different from the results of previous studies [3][4] [7].balanced by the fault.The seismic moment can also be calculated from the amplitude spectrum of seismic waves and is related to displacement as follows: where μ is the rigidity of the medium, D the average dislocation, and S is the area [15].The relation between seismic moment and magnitude is where Mw is magnitude. .with an almost perpendicular slope so that the deformed area face is not visible in figure 3. The visible area in modeling is only the width of the deformed area.The epicenter position be in the modeling area.The area of the modeling results is 319.84 x 39.11 km 2 .

Modeling Crustal Deformation due to
The 2007 Bengkulu earthquake event.The result of modeling process obtained the value of rms horizontal displacement is 44.635 mm and the value of rms vertical displacement is 90.6619 mm.The size of the raid was 7 meters at a depth of 18.05 km with a dip of 32.6º.The epicenter position be outside the modeling area but not far away (figure 3).The area of the modeling results is 160.79 x 254.4 km 2 .

Seismic Moment Analysis
The results of the seismic moment calculation by equation (1) in the 2005 Nias-Simeulue earthquake crustal modeling obtained a seismic moment value of 8.9 x 10 21 Nm with a rigidity estimated of 30 GPa.The magnitude value by equation ( 2) is obtained a value Mw 8.56.The magnitude value obtained from the model is 0.04 less than the measurement magnitude Mw 8.6 .The results of the seismic moment calculation by equation (1) in the 2007 Bengkulu earthquake crustal modeling obtained a seismic moment value of 8.73 x 10 21 Nm with a rigidity estimated of 30 GPa.The magnitude value by equation ( 2) is obtained a value Mw 8.56.The magnitude value obtained from the model is greater by 0.16 than the measurement magnitude Mw 8.4.

Conclusions
The okada model successfully modeled crustal defomation with verification of GNSS data and validation of seismic moment calculations.The rms values for horizontal displacement of two models are 79.9582mm and 44.635 mm, for vertical displacement is 92.7804 mm and 90.6619 mm.The magnitude value based on the calculation of the siesmic moment is Mw 8.56 for both models.

Figure 1 .
Figure 1.Location of SuGAr station and earthquake event epicenter.
shows the fault geometry parameters of the Okada model, which include Length, Width, Dip, Strike, Strike slip, and Dip slip.

Figure 2 .
Figure 2. The fault geometry parameters in Okada model

Figure 3 .
Figure 3. Deformation modeling (a) the 2005 Nias-Simeulue earthquake (b) the 2007 bengkulu earthquake.observation data is displayed on the white color arrow for horizontal displacement and the white bar for vertical displacement.Green arrows and red bars are the result of horizontaal and vertical modeling.Yellow arrow as direction and large fault dislocation.The area of the crustal deformation is depicted on a bright blue square.Yellow star as the earthquake epicenter point.

Table 2 .
Coseismic displacement due to the 2007 Bengkulu earthquake.Modeling Crustal Deformation due to The 2005 Nias-Simeulue earthquake event.The result of modeling process obtained the value of rms horizontal displacement is 79.9582 mm and the value of rms vertical displacement is 92.7804 mm.The size of the raid was 23.341 meters at a depth of 20.38 km with a dip of 88.28º