1 Introduction

The subduction process of Indo-Australian plate toward Sundaland block in the southern Java, Indonesia, suggests that this is a tectonically active region and prone to earthquake occurrences (Richards et al. 2007). One of the events is the 2006 M7.8 Java earthquake, which occurred on July 17, 2006 at 08:19 UTC (Fig. 1). This earthquake produced a devastating tsunami up to 7 m that caused casualties of more than 600 people and more than 50,000 people lost their houses (Kato et al. 2007).

Fig. 1
figure 1

Overview of tectonics condition in the study area. Dashed black lines indicate inland faults. Red triangles imply GPS stations used in this study. Beachball shows the epicenter location of the 2006 Java earthquake and the coseismic fault rupture is denoted by blue box, based on Bilek and Engdahl (2007). JT Java trench, CF Cimandiri fault, LF Lembang fault, BF Baribis fault. Seabed contours derived from ETOPO 1 (Amante and Eakins 2009)

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Soon after the mainshock, campaign Global Positioning System (GPS) measurements were taken near the source region by Geodesy Research Division of Bandung Institute of Technology (ITB) along the southern coast of western Java (Abidin et al. 2009). The campaign observation from 2006 to 2008 showed a significant signal of postseismic deformation after the earthquake. Using continuous GPS data from Geospatial Information Agency of Indonesia (BIG) during the time period of 2008–2010, Hanifa et al. (2014) analyzed postseismic deformation associated to afterslip using these continuous GPS datasets. Other study suggested that postseismic deformation associated to viscoelastic relaxation should also take into account for the 2006 Java earthquake (Gunawan et al. 2016).

This study analyzed postseismic deformation parameters of the 2006 Java earthquake using all available GPS datasets obtained from campaign observation from 2006 to 2008 and continuous observation from 2007 to 2014. Table 1 shows the description of GPS stations of this study. The early campaign GPS data are very important because they captured early postseismic deformation signal (Ito et al. 2012). Unfortunately, previous studies have never analyzed these early campaign data. The newly available continuous GPS data used in our analysis have never been used by previous study, which only analyzed continuous GPS data until 2010. Using these newly available GPS datasets, we analyzed the characteristics of postseismic deformation after the 2006 Java using analytical approach of logarithmic and exponential functions.

Table 1 Description of GPS stations of this study
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2 Data and method

In this study, we use two types of GPS datasets obtained from campaign and continuous observations, respectively. Abidin et al. (2009) reported campaign GPS observations during the time period of 2006–2008. In total, there are 30 GPS stations located along the southern coast of western Java. Unfortunately, among these 30 stations, only 6 stations were revisited continuously every year from 2006 to 2008. Most of these stations were only revisited two times during 2006–2007, or during 2007–2008. In this study, we use these 6 stations for further postseismic deformation analysis.

In addition to these campaign GPS data, we also use continuous GPS data installed and maintained by BIG in western Java. In this study, we use 3 GPS stations with continuous data available from 2007 to 2014. Figure 2 shows the distribution of GPS stations used in this study.

Fig. 2
figure 2

GPS displacements with reference to Sundaland block at continuous and campaign GPS stations indicated by green circles and red circles

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We analyzed these GPS data and obtained daily solutions using scientific software GAMIT/GLOBK (Herring et al. 2010a, b). During the analysis, we fix the preliminary coordinate results of ten International GNSS Service (IGS) stations to obtain daily solutions in International Terrestrial Reference Frame (ITRF) 2008. These IGS stations include COCO, CNMR, DARW, DGAR, HYDE, IISC, KARR, PIMO, TOW2, and TNML. The daily solutions were then transformed into ITRF2000 reference frame (Altamimi et al. 2011) and recalculated relative to Sundaland block reference frame using transformation parameters of rotation pole as follows: 49.0°N, −94.2°E, 0.336°/Ma (Simons et al. 2007). Figure 3 shows the time series of GPS data used in this study.

Fig. 3
figure 3

Time series of GPS data used in this study. Red line indicates the best fit of logarithmic function, while blue line implies the best fit of exponential function

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In the next analysis procedure, we modeled GPS time series displacements using the logarithmic function of Marone et al. (1991) and the exponential function of Savage and Prescott (1978). In these equations, t corresponds to time since earthquake, u(t) is the displacement in north and east components, c is the data offset, τ log and τ exp are the decay times in logarithmic and exponential functions, respectively, and a is the amplitude associated with the decay.

3 Modeling results

During the time period of 2006–2008, GPS stations along the southern coast of western Java moved toward the rupture area of the 2006 Java earthquake, consistent with the motion of the coseismic rupture suggesting the occurrence of postseismic deformation during this time period (Ito et al. 2016). Further analysis using continuous GPS data from 2008 to 2010 also suggested the ongoing postseismic deformation in this region (Gunawan et al. 2016). Using different datasets to Gunawan et al. (2016) and include data in a longer time period until 2014, we show that postseismic deformation of the 2006 Java earthquake area is still continuing (Fig. 2).

We applied the logarithmic and exponential mathematical functions to model the GPS time series, the unknown parameters a, c, τ log, and τ exp are calculated using least square approach. In the first step, we vary τ log and τ exp in the range of 480–500 and 860–880 days for every 0.1-day step. For each τ log and τ exp, we calculated a and c. During the search of best-fit parameters, we found that the decay time obtained for logarithmic function, τ log, is 488.0 ± 0.1 days, while that for exponential function, τ exp, is 871.0 ± 0.1 days (Fig. 4). Our analysis was performed using the data interval of 0.1 days, and each GPS station has different values of a and c, both in logarithmic and exponential functions. Table 2 shows the best-fit postseismic deformation parameters with minimum standard deviations for logarithmic function at each GPS station, while the best-fit parameters for exponential function are listed in Table 3.

Fig. 4
figure 4

Best-fit calculated decay time for (left) logarithmic function and (right) exponential function

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Table 2 Best-fit postseismic deformation parameters calculated in logarithmic function
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Table 3 Best-fit postseismic deformation parameters calculated in exponential function
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4 Discussion

Our results suggest that the fits to the data using logarithmic and exponential functions are similar. As shown in Tables 2 and 3, there were only small differences between RMS results, as a result of the sensitivity of the availability of early GPS data just after earthquake occurrences to the logarithmic and exponential functions. As reported for other earthquake cases, such as the 2004 M9.2 Sumatra-Andaman earthquake (Anugrah et al. 2015), the 2005 M8.7 Nias earthquake (Kreemer et al. 2006), the 2007 M8.5 Bengkulu earthquake (Alif et al. 2016), and the 2010 M7.8 Mentawai earthquake (Ardika et al. 2015), they obtained a better data fit using logarithmic function for the early postseismic GPS data.

In the case of the 2006 Java earthquake, such early continuous GPS data are not available. The continuous GPS data in western Java are only available 2 years after the earthquake. On the other hand, the campaign GPS data were only measured once per year from 2006 to 2008. With this type of campaign GPS data, we cannot capture early postseismic deformation after the 2006 Java earthquake comprehensively. Hence, continuous GPS data soon after earthquake are very important for crustal deformation studies.

The decay time of postseismic deformation result suggests that the afterslip decay time of the 2006 Java earthquake is in the order of hundreds of days. This is much longer than that for a general megathrust earthquake (Bürgmann et al. 2001; Freed 2007; Anugrah et al. 2015). Those analyses showed that for an M6–8 class earthquake, the decay time value is ~10 days. Our decay time of 488 days suggests that the 2006 Java earthquake is much longer than those earthquake cases, even for the M9 class earthquake (Fig. 5).

Fig. 5
figure 5

Correlation between decay time after earthquake occurrences and earthquake magnitude for various earthquake cases

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As suggested in a previous study (Ammon et al. 2006), the 2006 Java earthquake was considered as “tsunami earthquake” based on the characteristics of its long rupture duration (Bilek and Engdahl 2007), low rupture velocity (Kato et al. 2007), and the coseismic slip that occurred on shallow parts of the fault (Fujii and Satake 2006). In addition to those studies, our result of long decay postseismic deformation time supports the characteristic of a “tsunami earthquake.” Our results of long decay time after the 2006 Java earthquake strongly suggest that the southwestern Java regions have lower rigidity than general megathrust earthquake cases and tend to continuously slip during long-term periods as a result of stress transfer from the mainshock (Polet and Kanamori 2000).

Our results regarding decay time in the order of hundreds of days as observed by 8 years’ data after the event suggest that other physical mechanisms of postseismic deformations should be taken into account (Gunawan et al. 2014). In a much longer time period, the contribution of viscoelastic relaxation in the asthenosphere becomes compulsory as afterslip tends to decrease with time. Using an analytical approach of logarithmic and exponential functions, we showed that postseismic deformation parameters can be analyzed comprehensively.

5 Conclusions

In this study, we showed that we can fit campaign and continuous GPS data in western Java, Indonesia, using logarithmic and exponential functions. Similarities of misfit from two different functions suggest the importance of GPS data availability just after earthquake occurrences for crustal deformation analysis. Our results on postseismic deformation decay time indicate that it is in the order of 100 days after the mainshock. These findings suggest the 2006 Java earthquake be considered as a “tsunami earthquake” where the regions have low rigidity and tend to continuously slip for long time periods.