 Research Letter
 Open access
 Published:
The waveform inversion of mainshock and aftershock data of the 2006 M6.3 Yogyakarta earthquake
Geoscience Letters volumeÂ 8, ArticleÂ number:Â 9 (2021)
Abstract
This study comprehensively investigates the source mechanisms associated with the mainshock and aftershocks of the Mwâ€‰=â€‰6.3 Yogyakarta earthquake which occurred on May 27, 2006. The process involved using moment tensor inversion to determine the fault plane parameters and joint inversion which were further applied to understand the spatial and temporal slip distributions during the earthquake. Moreover, coseismal slip distribution was overlaid with the relocated aftershock distribution to determine the stress field variations around the tectonic area. Meanwhile, the moment tensor inversion made use of nearfield data and its Greenâ€™s function was calculated using the extended reflectivity method while the joint inversion used nearfield and teleseismic body wave data which were computed using the Kikuchi and Kanamori methods. These data were filtered through a trialanderror method using a bandpass filter with frequency pairs and velocity models from several previous studies. Furthermore, the Akaike Bayesian Information Criterion (ABIC) method was applied to obtain more stable inversion results and different fault types were discovered. Strikeâ€“slip and dipnormal were recorded for the mainshock and similar types were recorded for the 8th aftershock while the 9th and 16th June were strike slips. However, the fault slip distribution from the joint inversion showed two asperities. The maximum slip was 0.78Â m with the first asperity observed at 10Â km south/north of the mainshock hypocenter. The source parameters discovered include total seismic moment M_{0}â€‰=â€‰0.4311Eâ€‰+â€‰19 (Nm) or Mwâ€‰=â€‰6.4 with a depth of 12Â km and a duration of 28Â s. The slip distribution overlaid with the aftershock distribution showed the tendency of the aftershock to occur around the asperities zone while a normal oblique focus mechanism was found using the joint inversion.
Introduction
In the early hours of May 27, 2006, at approximately 05.54 local times, an earthquake struck the city of Yogyakarta. The information from the Agency for Meteorology, Climatology, and Geophysics of Indonesia (BMKG) showed it had a magnitude of Mwâ€‰=â€‰6.3, centered at 8.003E and 110.320 S with a depth of 11.87Â km at the southeast of the city as shown in Fig.Â 1. The event was declared the deadliest shallow earthquake in the country (BMKG 2006) and destroyed most of the infrastructures in the region of Yogyakarta and Klaten, Central Java Province. The reports by the National Development Planning Agency (BAPPENAS) in cooperation with the Yogyakarta Special Region Government (DIY), Central Java Provincial Government, and international partners in 2006 showed the earthquake killed more than 5000 people, with 38.000 injured, 423.000 evacuated, and 156.000 buildings destroyed (Bappenas 2006).
The mechanism used to obtain valuable information on the earthquake source parameters such as magnitude, fault orientation, stress drop, and source process varied with different agencies such as Indonesia Meteorology, Climatology, and Geophysics (BMKG), United States Geological Survey (USGS), National Earthquake Information Center (NEIC), Kandilli Observatory and Earthquake Research Institute (KOERI), European Mediterranean Seismological Center (EMSC), and Institute de Physique du Globe de Paris (IPGP).
Several debates on the source are also in progress with most researchers reported to have believed the earthquake did not originate from the geological fault along the Opak River due to the distribution of the aftershock towards 10â€“15Â km on the east side (Fukuoka et al. 2006; Walter et al. 2007; Wulandari et al. 2018). Some others also believe some minor faults were reactivated by the earthquake on the east side of the Opak fault (Diambama et al. 2019; Budiman et al. 2019; Irham et al. 2014). According to Saputra et al. (2018), the Opak River consists of 56 faults with a maximum displacement of 2.93 while Nakano et al. (2006) found a different focal mechanism as shown in Fig.Â 1. Moreover, several factors have been indicated by researchers to be influencing this difference, such as the lack of seismometer networks of BMKG which has been existing before 2006, thereby, causing variations in the level of location accuracy, source depth, and fault orientation (Ma and Eaton 2011; Saunders et al. 2016).
The parameters discovered by several institutions to indicate the source of the earthquake are presented in Table 1. The majority were observed to have concluded the epicenter is on the east side of the Opak fault and this also indicates consistency based on the aftershock distribution (Walter et al. 2008).
Kawazoe and Koketsu (2010) determined the focal mechanism using the waveform inversion method and compared the findings with the data observed using the CRUST 2.0 velocity model (Bassin et al. 2000) as well as the leftlateral strikeâ€“slip and reverses dipâ€“slip. Meanwhile, Nakano et al. (2006) examined the focal mechanism dominated by strikeâ€“slip and horizontal coseismal displacement was discovered to have occurred around Bantul and Yogyakarta in the south and southwest direction with the focal mechanism found to be in the form of leftlateral strike. Similar results were also obtained by Abidin et al. (2009) through the Global Positioning System (GPS) data. Moreover, Tsuji et al. (2009) stated that coseismal displacement and strikeâ€“slip along the fault plane also reversed on the east side, thereby, experiencing an upward displacement. This indicates there are different opinions on the source mechanism of the Yogyakarta earthquake based on different studies.
This present study was, therefore, conducted for two reasons. The first involved using moment tensor inversion to determine the type of expansion experienced based on the mainshock and three aftershocks Mwâ€‰>â€‰4. The second was to determine the earthquake source model by understanding the distribution of cosmic slips in space and time using the joint inversion method. It is important to note that the moment tensor and joint inversions were calculated based on the fit between the observed and synthetic waveforms with the smallest variance.
Data and methods
Moment tensor inversion mainshock and aftershocks
Data
The data used for the mainshock moment tensor inversion were obtained from the Incorporated Research Agency for Seismology (IRIS) while those for the aftershocks were retrieved from the Geofon and European Integrated Data Archive (EIDA) with the focus on the 8th, 9th, and 16th of June 2006 through (http://ds.iris.edu) and (http://eida.gfzpotsdam.de/webdc3), respectively. The distribution of the IRIS and BMKG networks for all stations is, however, presented in Fig.Â 2. The waveform data used to distribute the aftershocks were from the nonpermanent seismometer installed one week after the mainshock around the Opak fault from 3 to 7 June 2006 by the Universitas Gadjah Mada in cooperation with the GFZ, Potsdam, Germany (Wulandari et al. 2018). It consists of ten stations with threecomponent sensors and the experiment found approximately 524 aftershocks events which were relocated and plotted to visualize the spatial distribution as shown in Fig.Â 2. Meanwhile, the aftershocks data plotted were retrieved from Wulandari et al. (2018). It is important to note that the mainshock data were relocated using the SeisComP3 program while the aftershocks distribution data were through the NonLinLoc method (Wulandari et al. 2018).
Method
The waveform was corrected from its instrument response using the Fortran code developed by Yagi (2006) and the mainshock waveform was windowed with a data length of 100Â s which started 5Â s before the Pwave arrival time. Meanwhile, the aftershock waveform was windowed with a length of 50Â s starting 5Â s before the Pwave arrival time. The filters used during the process were in accordance with those applied in previous research as presented in Tables 2 and 3. Moreover, the filter and velocity model were both selected based on the smallest variance value. The variance is, however, the comparison between the observed and calculated synthetic waveform using Eq.Â (1) (Yamanaka and Ishida 1996; Ito et al. 2004).
where \({u}_{j}^{\text{obs}}\) is the observed waveform at each \(j\) station and \({u}_{j}^{\text{cal}}\) is the calculated waveform at each \(j\) station at time \(t\).
The optimal inversion model was obtained by computing the moment tensor inversion, which iterates at appropriate resampling time values from 0.1 to 10Â s.
A grid search method ranging from 1 to 25Â km was applied in this study to determine the depth of the hypocenter for both the mainshock and aftershock in each frequency range with a bandpass filter. The waveform was converted from velocity to displacement using a sampling time of 0.2Â sâ€“10Â s and the Green function calculated using five velocity models which are AK135 (Kennett et al. 1995), CRUST2.0 (Bassin et al. 2000), PREM (Dziewonski and Anderson 1981), JB (Jeffreys and Bullen 1940), and Koulakov (Koulakov et al. 2007). Some of them are presented in Table 4. The calculation of the Green's function tends to produce a good estimate for the subsurface velocity model.
The main equation for the calculation is Eq.Â 2, which describes the vertical component of the observation waveform at each j station:
where \({G}_{\text{jq}}\) is the Greenâ€™s function of time \(t\) and Ï„ is a unit step from the source positions of \(\text{x, y,}\) and \(z\). \({M}_{q}\) is the moment tensor element, \(V\) is the volume of the earthquake source space, \(q\) is the number of free components for the second pair selected, and \({e}_{0}\) is the observation error. Meanwhile, the focal mechanism represents a point source model. Therefore, Eq.Â (2) can be simplified into a vector shape to form Eq.Â (3) as follows:
It is possible to rewrite this in vector form as follows:
where \(T\left(t\right)\) is the source time function in the source centroid, \({x}_{c}{\text{,y}}_{c}{\text{,z}}_{c}\), \(\mathbf{d},\) and \({\mathbf{e}}_{\mathbf{j}}\) are data vector errors with Ndimensions, \(\mathbf{m}\) represents the five dimensions of the model vector parameter, and \(G\) is the Nâ€‰Ã—â€‰5 coefficient matrix. In Eq.Â 4, \({u}_{ud}\) and \({u}_{ns}\) are the observation waveform data for vertical and horizontal components while \(\left({t}_{1}\right), \left({t}_{2}\right)\dots .({t}_{n})\) are the arrival times of the observed waveforms at a station.
The solution to the matrix equation was determined using the least square method when the observed waveform and the convolution of the Green's function with the time function of the source are known. Meanwhile, Green functions for the nearfield data were calculated using the extended reflectivity method developed by Kohketsu (1995),Â Kuge (2003) and Yagi (2006). The source time function was also used to determine the moment tensor solution while the sliprate function was applied to the waveform data with a simple triangular function.
Joint inversion
Data
The wave data for P and S were downloaded in the form of 16 teleseismic waveform body with the vertical components recorded on the IRISDMC station which was downloaded via http://ds.iris.edu. Moreover, the teleseismic data for the mainshock event on 27 May 2006 were downloaded from The International Federation of Digital Seismograph Networks (FDSN) on January 2, 2019. The selected data have a high signaltonoise ratio and covers a good azimuth range with the source and station distances used observed to be within the range of 30Â°â€“90Â°. The teleseismic station configuration is, however, indicated in Fig.Â 3a. Meanwhile, the nearfield data which used the BMKG station network were downloaded from http://eida.gfzpotsdam.de/webdc3 on January 21 2006 and the configuration is shown in Fig.Â 3b.
The teleseismic data used for the wave inversion calculation consist of 12 stations, windowed with a data length of 90Â s, 5Â s before the P wave, filtered with a bandpass filter in the frequency range of 0.008â€“0.1Â Hz, and converted to displacement with a sampling time of 0.5Â s. Meanwhile, the nearfield data used 14 components from 5 broadband seismometer stations including four which are TNG, BJI, KMMI, and DNP from the BMKG network and one which is XMIS from the IRISDMC network. The data were windowed with a data length of 180Â s, 5Â s before the P wave, filtered using a bandpass filter with a frequency range of 0.05â€“0.15Â Hz, and converted to displacement with a sampling time of 0.5Â s. The first P wave was, however, manually picked with the help of the Seismic Analysis Code (SAC) program when it arrived at each seismogram (Helffrich et al. 2013).
Method
The rupture process of the Yogyakarta earthquake source was determined using the equation from Yagi et al. (2004) which was developed by Yoshida and Koketsu (1992). The equation represents the rupture process as a temporal and spatial slip distribution in the fault plane and the wave received by the station is the observed waveform at each station j given as indicated in Eq.Â 5:
where \({W}_{j}^{{\text{obs}}}\) is the observed waveform at station \(j\), \({X}_{mnkl}\) is the slip component at each \(mn\) sub faults and each \({l}^{th}\) time change, \({g}_{mnkj}(t)\) is the basic seismic wave Green function of the point source with slip units on each \(mn\) sub faults, \(\tau\) is the instantaneous time at the subfault points, \({T}_{mn}\) is the basic function of the start time for each sub faults, and \({\mathrm{e}}_{j}\) is the gaussian error with the variance \({\upsigma }_{j}\). Meanwhile, the Green function used for teleseismic data was calculated using the Kikuchi and Kanamori (1991) method while the seismic velocity model applied to calculate Green data nearfield and teleseismic functions was Koulakov and Jeffreys Bullen (JB), respectively, as indicated in Table 3.
A numerical method was applied to the standard waveform inversion scheme to obtain a more objective source model (Harzell and Heaton 1983; Yoshida 1992). Moreover, the inversion code developed by Yagi et al. (2004) was also adopted to calculate inversion due to its ability to represent rupture as a slip distribution over time and space in a fault plane. The initial model of the fault plane was determined from the area distribution while Papazachos et al. (2004) was also applied to calculate the slip lengths and areas. Furthermore, the fault plane was divided into MxN sub faults with the length and width represented by \({d}_{x}\) and \({d}_{y}\), respectively. The sliprate function on each subdefault was determined using a simple triangular series of functions for the length of the dislocation or rise time, \(\tau\). Therefore, Eq.Â (5) was simplified into a vector form as follows:
where \({\mathbf{A}}_{{\varvec{j}}}\) is a matrix having dimensions in the form of some data points at each station \(j\times\) the number of model parameters \({N}_{j}\).
Changing the number of model parameters leads to an unstable solution due to the ability of a small change in data to cause a big difference. Therefore, smooth limits were applied to the slip distribution over time and space to produce a stable inversion.
There are two constraints, spatial and temporal, discovered in the seismic wave analysis conducted using observational data. This method was, however, used to obtain the best model parameters calculation by minimizing the number of residual squared, S, which was determined using the following equation:
where \(\mathbf{T}\) is the matrix of \({N}_{1}x {N}_{a}({N}_{1}=MNLK)\), \(\mathbf{D}\) is the matrix of \({N}_{2}x {N}_{a}({N}_{2}=MNK)\), \(MNK\) is slip component \({K}^{th}\) on the sub faults \({MN}^{th}\) and timestep \({L}^{th}\), while \({N}_{a}\) is the model parameter.
The relationship of Eq.Â 5 coded by Yagi et al. (2004) showed the smoothing constraints of space and time as provided in the following equation:
where \({a}_{klmn}\) is the model parameter determined from the observed data, \({X}_{kmn}(\xi )\) is the basic slip function of slip \({k}^{th}\), and \({T}_{lmn}(t)\) is the time base function of the \({l}^{th}\) slip time. Meanwhile, the smoothing constraint with respect to time was obtained by simplifying Eq.Â 8 into Eq.Â 9:
where \({X}_{mnk0}={X}_{mnkl}=0\). This was further converted into a vector form:
where \(\mathbf{T}\) is the matrix of \({N}_{1}\times {N}_{a}({N}_{1}=MNLK)\). Meanwhile, the distribution of slip to space for the smoothing constraint is presented in the following vector form:
where \(\mathbf{D}\) is the matrix of \({N}_{2}\times {N}_{a}\left({N}_{2}=MNK\right).\)
The leastsquare method was applied to determine the best estimate for the model parameters by providing the covariance value Ïƒ (Cheng et al. 1985). Meanwhile, it is impossible to directly determine the values of \({\upsigma }_{t}\) and \({\upsigma }_{d}\) while \({\upsigma }_{\mathrm{j}}\) can be selected from the data quality. Therefore, \({\sigma }_{t}\) and \({\sigma }_{d}\) were selected objectively using Akaike's Bayesian Information Criterion (ABIC) method (Akaike 1980) to obtain the optimal values with the grid search method. The same equation was also used in Fukahata et al. (2003, 2004) and it is usually represented as follows:
where N is the total number of observed equations and C is a constant. The grid search method was applied in this study to obtain the optimal values of \({\sigma }_{t}\) and \({\sigma }_{d}\) while the nonnegative leastsquares (NNLS) method was used to solve the leastsquares problem with a positive constraint on the model parameters.
Results
Moment tensor inversion of mainshock event
The mainshock source mechanism was determined by the grid search method using different frequency ranges and velocity models as shown in Tables 2 and 4 and the results are presented in Fig.Â 4. Meanwhile, the velocity waveform was converted to displacement using a sampling time of 0.1â€“10Â s in order to select the appropriate stable result.
FigureÂ 4 shows the beachball variations and the time sampling with the smallest variance value for each velocity model was found to be 0.5Â s while the frequency was 0.01 â€“ 0.05Â Hz. This sampling time was observed to be very stable with the five velocity models while those above 1 were precarious. Moreover, the frequencies with low variance were found at low values between 0.01 to 0.05Â Hz. This means the appropriate velocity model to describe the subsurface structure of the study area is Koulakov with a sampling time of 0.5Â s and a frequency of 0.01 to 0.05Â Hz. The minimum variance value for the grid search method was 0.234 based on the comparison between the observed and synthetic waveforms as shown in Fig.Â 5. Furthermore, the parameters of the Yogyakarta seismic source on May 27, 2006, include the moment 0.2808 Eâ€‰+â€‰19 (Nm) which is equivalent to the moment magnitude M_{w}â€‰=â€‰6.2. Meanwhile, the fault parameters obtained for Nodal 1 were strike 353.7Â°, dip 43.4Â°, and slip âˆ’ 126Â° while Nodal 2 had 218.7Â°, 56.2Â°, and âˆ’ 61Â°, respectively, and the hypocenter was 12Â km.
The results of the moment tensor inversion from nearfield data for the mainshock are shown by Nodal 2 with the type of faulting found to be strikeâ€“slip and dipnormal. The selection of Nodal 2 was, therefore, based on the Opak fault lithology and geological maps with a southern direction. This, therefore, made strike 218.7Â° the most suitable strike direction. The faulting type is, however, depicted as a beachball as shown in Fig.Â 6.
Moment tensor inversion of aftershocks event
The aftershock mechanism was determined in the same way as the mainshock by using the grid search method as observed in previous studies at different velocity models and frequency ranges as indicated in Tables 3 and 4, respectively. The aftershock reversal results for June 8, 9, and 16 are presented in Figs.Â 7, 8, and 9, respectively. Meanwhile, the waveform velocity was converted to displacement using a sampling time of 0.2 to 10Â s.
The graphs in the figures are presented as a function of time sampling and variance for each model while the speed and range of the bandpass filter are indicated in Table 2. The sampling time of 1Â s and above for the aftershock on June 8, 9, and 16 in the five velocity models have the same trend which is the focal ball and unstable variance values. Meanwhile, the 0.5s sampling time for all the aftershocks was very stable, therefore, the Koulakov velocity model was applied because it is very representative of the subsurface structure of the study area. The lowest dispersion frequency recorded for the five velocity models and aftershocks was 0.1â€“0.3Â Hz while the smallest variance values for 8, 9, and 16 were 0.2178, 0.1949, and 0.2432, respectively. The parameters of the inversion result for the aftershock source are presented in Table 5.
FigureÂ 10 shows the fitting shape of the observed waveform and the synthetic waveform displacement for the aftershocks and the waveform fitting produced is the best result from the grid search process.
The variation of the fault plane types for the aftershocks is presented in Table 5 and the typical dipnormal was found to have been used on June 8 while strikeâ€“slip dominated June 9 and 16. Moreover, the magnitude has a similar result with the catalog from International Seismological Center (ISC) which was 4.4, 4.1, and 4.0 for 8, 9, and 16, respectively, as shown in Fig.Â 11. Meanwhile, the variance value obtained from the inversion is also presented in Table 5.
The aftershock moment tensor inversion shown in Table 5 serves as the basis to examine the consistency of the fault plane caused by the mainshock. The beachball solution from this inversion is, however, indicated in Fig.Â 11.
FigureÂ 11 shows the inversion result for the mainshock and aftershocks moment tensor and the mainshock focal mechanism was found to be a dipnormal strikeâ€“slip type of fault and the same was observed for June 8 while June 9 and 16 had a strikeâ€“slip. There is, therefore, a strong suspicion that June 9 and 16 aftershocks originated from a different fault plane than the mainshock with the report presented by USGS showing strikeâ€“slip was predominant.
Joint inversion
Akaike's Bayesian Information Criterion (ABIC) was adopted to obtain more objective parameters (Akaike 1980). The Green function for teleseismic body waves was calculated using the Kikuchi and Kanamori (1991) method while the technique developed by Kohketsu (1985) was used for the nearfield data.
Fault model
The fault model used in this study was the Hazkel finite model, which assumes there is no change in the slip angle along the rupture and that faulting occurs in a single fault plane. This means fault dimensions are essential to determine the detailed global features of the fault plane and coseismic rupture of an earthquake. The seismic traces in the fault plane can, however, be used to estimate its extent. Therefore, mapping the distribution of the Yogyakarta earthquake aftershock from several previous studies shows the area of the Opak fault plane is 28Â km long and 15Â km wide (Walter et al. 2008; Anggraini 2013). Meanwhile, Papazachos et al.'s (2004) equation showed the length is 30Â km and the width is 20Â km. The initial model of the fracture area used in this study was divided into stage 1 and stage 2 to obtain the area of the fault plane which corresponds to the actual area of the Opak Fault. Stage 1 was based on the aftershocks distribution while Stage 2 was based on the equations of Wells and Coppersmith (Wells and Coppersmith 1999). The fault plane on stage 1 with a strike length of 32.5Â km and a dip width of 15Â km was divided into 15â€‰Ã—â€‰6 sub faults with each having a length of 2.5Â km. The dimensions of the fault plane on stage 2 are smaller than stage 1 with a long strike of 17.5Â km and a dip width of 15Â km, which was further divided into 7â€‰Ã—â€‰6 subfaults. Moreover, the hypocenter position used was the result of the relocation from the mainshock released by USGS using the software sesicomp3. The fault plane model is presented in Fig.Â 12. Moreover, the velocity model used to calculate the teleseismic body wave data was Jeffreys Bullen (JB) while five velocity models were used to calculate the nearfield data as shown in Table 4. Meanwhile, the JB velocity model for the teleseismic data was changed into four nearfield data rate models to obtain the smallest variation.
The rupture velocity was set to be equal with the maximum shear wave velocity of 4.6Â km/s used in Koulakov et al. in order to save computation time. The waveform data applied to implement the sliprate function was a simple triangular function sequence with a rise time of 1Â s while the dislocation time and rupture propagation for each sub faults were used to determine the sliprate function duration. Moreover, the hypocenter depth was determined by calculating the mainshock moment tensor inversion using the grid search method. The fault plane parameter and hypocenter depth were further used as the initial input parameters to calculate the joint inversion.
Source rupture process
The rupture of the Yogyakarta earthquake source on May 27, 2006, was due to a joint inversion as indicated in Fig.Â 13, which shows the source mechanism, moment rate function, and the coseismic slip distribution. The focal mechanism from the joint inversion is similar to the initial input with the fault parameters recorded to be strike 217.6Â°, dip 56Â°, and slipâ€‰âˆ’â€‰53Â° as shown in Fig.Â 13a while the source duration of moment rate function length was 28.5Â s as indicated in Fig.Â 13b. Bilek and Lay (2002) have previously stated that shallow earthquakes close to subduction zones have weak geological material because they are composed of young sedimentary rocks (Pribadi et al. 2014). Moreover, Saputra et al. (2018) also reported geological conditions in the eastern and western parts of the Opak fault to have different structures. The east has a more slightly fragile structure, which makes it susceptible to landslides while the west has a young Merapi sedimentary formation structure and this difference leads to a variation in the P and S wave velocity, thereby, making the rupture duration of the source reach 28.5Â s. It is important to note that the total seismic moment produced was M0â€‰=â€‰0.4311Eâ€‰+â€‰19 (Nm) or Mwâ€‰=â€‰6.4 as shown in Fig.Â 13b and this is similar to the M0â€‰=â€‰0.422Eâ€‰+â€‰25 (Nm) or M0â€‰=â€‰6.3 released by USGS. Meanwhile, the energy moment was released at the 6th second after the first initial break and the total slip vector produced was 0.78Â m as shown in Fig.Â 13d. The slip moved in an NS direction from the hypocenter point, later to the SW direction towards the surface, and moved in a dip direction at the 15th second to the end. This shows the Yogyakarta earthquake fault type is more dominant dipnormal than strikeâ€“slip as shown in Fig.Â 13c.
FigureÂ 14a shows a series of snapshots showing the Yogyakarta earthquake dislocation distribution to the surface area from 0 to 28Â s. The change in dislocation was observed not to have occurred at the initial break but at the third second by moving southward as far as 10Â km up to the eighth second after which it moved northward for 20Â km up to the twelfth second and the slip movement was seen moving in the direction of 15Â km from the fifteenth up to the last second. The maximum slip recorded was 0.72Â m at the 10Â km north of the hypocenter. This means the first and second asperity zones are both 10Â km south of the hypocenter as shown in Fig.Â 13c. Meanwhile, the slip rate of snapshots per second is illustrated in Fig.Â 14b and the average rupture speed was found to be 4Â m/s.
FigureÂ 15 compares the observed waveform in blue with the synthetic waveform in red displacement for the nearfield data in (a) and body wave teleseismic data in (b). The variance value was recorded to be 0.3412 and this is quite large, even from the waveform fitting perspective, and observed to be quite good at the beginning of the P wave arrival. The limited quality of the signal recorded by the teleseismic station is also a factor in the variance value. This is due to the fact that earthquakes with 6.3 magnitudes are less well recorded at longrange stations and also affected by layer inhomogeneity. Moreover, limited azimuthal coverage of nearfield data also has effects on the quality of inversion calculation. It is important to note that the nearfield and teleseismic data do not have very good quality, but showed a fairly good resolution quality and this is one of the advantages of simultaneous inversion using ABIC optimization (Akaike 1980). Therefore, the variance values obtained are the best results from the joint inversion.

1.
FigureÂ 16 illustrates the Yogyakarta earthquake coseismic slip overlaid with the distribution of the relocated aftershock. It also explains the aftershock distribution pattern with the coseismic slip distribution. FigureÂ 17 shows the depth profile of the aftershock is divided into a few slices which are Aâ€“AÊ¹, Bâ€“BÊ¹, and Câ€“CÊ¹, and the most dominant aftershocks were observed to have occurred at a depth of 10Â km as indicated in Fig.Â 17b. Meanwhile, the Câ€“CÊ¹ section shows an empty space with no energy released as shown in the slip distribution of Fig.Â 16 and the aftershock was discovered to have lain on a high enough slip. This pattern shows the faults are in the same plane, but those located on the west are different. Moreover, the aftershock moment tensor inversion previously produced on June 9 also indicated different types of faults and this further shows the complexity of the faults in the study area.
Discussion
The moment tensor inversion obtained using nearfield data showed the mainshock fault source parameters of the Yogyakarta earthquake which occurred on May 27, 2006 were strike 218.7Â°, dip 56.2Â°, and slipâ€‰âˆ’â€‰61Â° and discovered to be caused by an oblique fault. This is in line with the findings of previous studies that the Yogyakarta mainshock was not caused by pure strikeâ€“slip but has a dipnormal component. Moreover, Kawazoe and Koketsu (2010) divided earthquake source mechanism into two types which are the leftlateral strikeâ€“slip faulting and reverse dipâ€“slip faulting and this further indicates the possibilities of two different fault segments for the source mechanism.
Tsuji et al. (2009), however, found a movement in the direction of the fault line on the east side along the Opak fault line. These results confirmed the joint inversion findings indicated in the slip distribution of Fig.Â 11c which showed a slip shift towards the dip at the 15th second. The most significant slip also occurred at the second asperity at 0.72Â m.
The moment tensor inversion for June 8, 9, and 16 aftershocks were calculated using temporary nearfield data and the fault source parameters also showed the complexity of the Opak fault (Budiman et al. 2019; Saputra et al. 2018; Anggraini 2013). The aftershock of June 8 was observed to have dipnormal faults while 9 and 16 had strikeâ€“slip as shown in Table 5. This means the Yogyakarta earthquake mainshock activated several active faults on the eastern side of the Opak fault (Anggraini 2013; Budiman et al. 2019; Irham et al. 2014).
The rupture process of the earthquake source was also determined using joint inversion and the earthquake source mechanism, moment rate function, and the coseismic slip distribution were discovered. The focal mechanism from the inversion was observed to be similar to mainshock moment tensor inversion with the fault parameters recorded to be strike 217.6Â°, dip 56Â°, and slipâ€‰âˆ’â€‰53Â°. This, therefore, shows the consistency between the moment tensor and joint inversions. Moreover, a dipnormal fault type was recorded in the joint inversion with a smaller slip than the moment tensor inversion. Yagi (2006) in Ohsumi and Baba (2007) showed the rupture due to the Yogyakarta earthquake was in two stages with the first stage observed to have the first subevent in the southwest to northeast directions while the second stage had the second subevent. The findings of this study also indicated two weak zones which were located 10Â km south of the hypocenter as the first Asperity and 10Â km to the north as the second Asperity. Kawazoe and Koketsu (2010) also identified two zones of violence near the hypocenter and in the southwest and this raised the suspicion that the rupture was from two different events. These results are also confirmed by the aftershock moment tensor inversion with the type fault recorded for June 9 and 16 aftershocks different from June 8. This means the reactivation of several minor faults possibly occurred on the east side of the Opak fault (Anggraini 2013; Walter et al. 2008; Saputra et al. 2018; Budiman et al. 2018).
The coseismic slip distribution overlaid with the aftershock relocation distribution as indicated in Fig.Â 15 showed the aftershock spread out parallel to the Opak fault. Meanwhile, another pattern was discovered to the west of the Opak fault distribution and believed to have originated from different fault segments. This, therefore, confirms the findings from the moment tensor inversion for June 9 and 16 aftershocks.
Conclusions
The moment tensor inversion of the mainshocks and aftershocks as well as the joint inversions were calculated to obtain a more comprehensive source model for the Yogyakarta May 27, 2006 earthquake. The exact source mechanism was determined using the mainshock waveform inversion after which the source parameters which include dipnormal and strikeâ€“slip were used as the input to calculate the joint inversion. Moreover, the ABIC method was adopted to obtain a stable result in the joint inversion (Akaike 1980) and determine the coseismic slip distribution in the rupture area which was found to be bilateral. The slip distribution direction was generally discovered to have propagated along the fault plane in the strike direction and later moved and stopped at the dip direction. It spread from the hypocenter point to the south for 10Â km and later moved north for 20Â km after which it moved towards the dipnormal. The earthquake was found to have originated from the Opak fault and also reactivated a minor fault on the east side. It was also strongly suspected to be from two different sources as observed from the mainshock and aftershock moment tensor inversion and the results of joint inversion.
Availability of data and materials
The data were maintained by the Agency of Meteorology, Climatology, and Geophysics of Indonesia and available upon request.
Change history
27 May 2021
The author name spell error has been corrected in the reference Kasemsak 2017
References
Abidin HZ, Andreas H, Kato T, Ito T, Meilano I, Kimata F, Natawidjaya DH, Harjono H (2009) Crustal deformation studies in Java (Indonesia) using GPS. J Earthq Tsunami 3(2):77â€“88
Akaike H (1980) Likelihood and Bayes Procedure in Bayesian Statistic. University Press, New York, pp 143â€“166
Anggraini A (2013) The 26 May 2006 Yogyakarta earthquake, aftershocks and interactions, Doctoral Thesis, Universitaet Potsdam
Bappenas (2006) Preliminary Damage and Loss Assessment, Yogyakarta and Central Java Natural Disaster, Report of the Ministry of National Development Planning, Republic of Indonesia (Bappenas) with Provincial Government of Yogyakarta Special Region (DIY)
Bassin C, Laske G, Masters G (2000) The Current Limits of Resolution for Surface Wave Tomography in North America. EOS Trans AGU 81:F897
BMKG (2006) Katalog Gempa bumi Signifikan dan Merusak 1821â€“2017. Pusat Gempa bumi dan Tsunami Badan Meteorologi Klimatologi dan Geofisika, Jakarta
Bilek LS, Lay T (2002) Tsunami earthquake possibly widespread manifestation. Res Lett, Geophys. https://doi.org/10.1029/2002GL015215
Budiman R, Sahara DP, Nugraha AD (2019) Determining Source Model and Aftershocks of 2006 Yogyakarta Earthquake, Indonesia using Coulomb Stress Change, IOP Conference Series. Earth Environ Sci 318:88
Cheng A, Jackson DD, Matsuura M (1985) Dislocation model for aseismic fault slip in the transverse ranges of Southern California, Scientific and TechnicalÂ Aerospace Reports, vol 24, Issues 9â€“12
Diambama AD, Anggraini A, Nukman M, LÃ¼hr BG, Suryanto W (2019) Velocity structure of the earthquake zone of the M6.3 Yogyakarta earthquake 2006 from a seismic tomography study. Geophys J Int 216(1):439â€“452. https://doi.org/10.1093/gji/ggy430
Dziewonski AM, Anderson DL (1981) Preliminary reference Earth model. Phys Earth Planet Inter 25(4):297. https://doi.org/10.1016/00319201(81)900467
Elnashai AS, Jig Kim S, Jin Yun G, Sidarta D (2006) The Yogyakarta Earthquake of May 27, 2006, MAE Center Report No. 07â€“02, MidAmerica Earthquake Center, Newmark Civil Engineering Lab, University Illinois at UrbanaChampaign
EkstrÃ¶m G, Nettles M, DziewoÅ„ski AM (2012) The global CMT project 2004â€“2010: Centroidmoment tensors for 13,017 earthquakes. Phys Earth Planet Inter 200â€“201:1â€“9
Fukahata Y, Yagi Y, Matsuâ€™ura M (2003) Waveform Inversion for Seismic Source Processes using ABIC with Two Sorts of Prior Constraints: Comparison between Proper and Improper Formulations. Geophys Res Lett 30:95
Fukahata Y, Nishitani A, Matsuâ€™ura M (2004) Geodetic Data Inversion Using ABIC to Estimate Slip History During One Earthquake Cycle with Viscoelastic SlipResponse Functions. Geophys J Int 156:140â€“153
Fukuoka K, Ehara S, Fujimitsu Y, Harmoko U, Harmoko U, Setyawan A, Setiadji LD, Harijoko A, Pramumijoyo S, Wahyudi Y (2006) Interpretation of May 27 2006, Yogyakarta Earthquake Hypocenter and Subsurface Structure Deduced from the aftershock and Gravity Data, The Yogyakarta Earthquake of May 27 2006. Star Publishing Company Inc, New York
Hartzell S, Heaton T (1983) Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial ValleyCalifornia, earthquake. Bull Seism Soc Am 73:1553â€“1583
Helffrich G, Wookey J, Bostow I (2013) The Sesimic Analysis Code: A Primer and Userâ€™s Guide. Cambridge University Press, Cambridge
Irham NM, Kirbani SB, Sismanto W (2014) The subsurface modelling of Opak fault Yogyakarta Region with inversion method of Gravity Data. Int J Basic Appl Sci 14:06
Ito Y, Matsubayashi H, Kimura H, Matsumoto T, Asano Y, Sekiguchi S (2004) Spatial Distribution for moment Tensor Solutions of the TokachiOki earthquake (MJMA=8.0) and the aftershock. Earth Planets Space 56:301â€“306. https://doi.org/10.1186/BF03353055
Jeffreys H, Bullen KE (1940) Seismological Tables. British Association for the Advancement of Science, London
Kasemsak S (2017) Focal Mechanism of M_{w} 6.3 Aftershocks from Waveform Inversions. Int J Geophys, Phayao Fault Zone, Northern Thailand. https://doi.org/10.1155/2017/9059825
Kawazoe Y, Koketsu K (2010) Source Fault and Rupture Process of the 2006 Yogyakarta Earthquake, American Geophysical Union, Fall Meeting 2010. 2010AGUFM.S43A2030K.
Kennett B, Engdahl E, Buland R (1995) Constraints on seismic velocities in the Earth from traveltimes. Geophys J Int 122:108â€“124. https://doi.org/10.1111/j.1365246X.1995.tb03540.x
Kikuchi M, Kanamori H (1991) Inversion of complex body wavesâ€”III. Bull Seismol Soc Am 81(6):2335â€“2350
KOERI (2006) Moment tensors, European Mediterranean Seismological Centre (EMSC). https://www.emsccsem.org/Earthquake/tensors.php?view=649. Accessed 11 Nov 2018
Kohketsu K (1985) The Extended Reflectivity Method for Synthetic NearField Seismograms. J Phys Earth 33:121â€“131
Koulakov I, Bohm M, Asch H, Luhr BG, Manzanares A, Brotopuspito KS, Fauzi P (2007) P and S velocity structure of the crust and upper mantle beneath central Java from local tomography inversion. J Geophys Res 112:18. https://doi.org/10.1029/2006JB004712
Kuge K (2003) Source modeling using strongmotion waveforms: toward automated determination of earthquake fault planes and momentrelease distributions. Bull Seismol Soc Am 93:639â€“654. https://doi.org/10.1785/0120020076
Ma S, Eaton D (2011) Combining doubledifference relocation with regional depthphase modelling to improve hypocentre accuracy. Geophys J Int 185:871â€“889. https://doi.org/10.1111/j.1365246X.2011.04972.x
Mikumo T, Yagi Y (2003) Slipweakening distance in dynamic rupture of inslab normalfaulting earthquakes. Geophys J Int 155:443â€“455. https://doi.org/10.1046/j.1365246X.2003.02047.x
Miyatake T, Yagi Y, Yasuda T (2004) The Dynamic Rupture Process of the 2001 Geiyo Japan Earthquake. Geophys Res Lett. https://doi.org/10.1029/2004GL019721
Nakano M, Kumaga H, Miyazawa K (2006) Source Estimation of the May 2006 Java Earthquake, EOS. Trans Am Geophys Un 87:9
NEIC (2006) Focal Mechanism of the 2006 Yogyakarta Earthquake, National Earthquake Information Center (NEIC). http://neic.usgs.gov/neis/eqdepot/2006/eq060526neb6/neicneb6q.html. Accessed 14 Nov 2018
Ohsumi T, Baba K (2007) Field investigation on the damage of Prambanan temple, housing and infrastructure caused by earthquake in Central Java, Indonesia. Proc JSCE Earthq Eng Symp 29:50â€“59. https://doi.org/10.11532/proee2005a.29.50
Papazachos BC, Scordilis EM, Panagiotopoulos DG, Papazachos CB, Karakaisis GF (2004) Global relations between seismic faultparameters and moment magnitude of earthquakes. Bull Geol Soc Greece 36(3):1482
Pinar A, Kuge K, Honkura Y (2003) Moment tensor inversion of recent small to moderate sized earthquakes: implications for seismic hazard and active tectonics beneath the sea of Marmara. Geophys J Int. https://doi.org/10.1046/j.1365246X.2003.01897.x
Pribadi S, Puspita N, Yudistira T, Afnimar P, Ibrahim G, Laksono BI, Adnan Z (2014) Identification of earthquake that generate tsunamis in Java and Nusa Tenggara using rupture duration analysis. AIP Conf Proc 10(1061):4897118
Saunders I, Kijko A, Fourie CJS (2016) Statistical evaluation of seismic event location accuracy by the South African National Seismograph Network over four decades. South African J Geol. 119:291â€“304. https://doi.org/10.2113/gssajg.119.1.291
Saputra A, Gomez C, Delikostidis I, ZawarReza P, Hadmoko DS, Sartohadi J, Setiawan MA (2018) Determining Earthquake Susceptible Areas Southeast of Yogyakarta, Indonesiaâ€”Outcrop Analysis from Structure from Motion (SfM) and Geographic Information System (GIS). Geosciences. 8(4):2076â€“3263
Suardi I (2009) Analysis of Source Rupture Process of the September 2, 2009, Tasikmalaya Earthquake by Using the Joint Inversion Method of Near Field and Teleseismic Data, Dissertation, Study Program of Earth Sciences, Institut Teknologi Bandung, Bandung
Tsuji T, Yamamoto K, Matsuoka T, Yamada Y, Onishi K, Bahar A, Meilano I, Abidin HZ (2009) Earthquake fault of May 26 2006, Yogyakarta earthquake observed by SAR interferometry. Earth Planets Space 61:29â€“33
USGS (2006) Earthquake Hazards Program, Momen Tensor, United States Geological Survey (USGS). https://earthquake.usgs.gov/earthquakes/eventpage/usp000ej1c/momentensor. Accessed 21 Jan 2019.
Walter TR, Luhr B, Sobiesiak M, Grosser H, Wang R, Parolai S, Wetzel HU, Zschau J, Milkereit C, Gunther E (2007) Soft Volcanic Sediments Compound 2006 Java Earthquake Disaster, EOS, Trans. Am Geophys Un 88:486
Walter TR, Wang R, Luehr BG, Wasserman J, Behr Y, Parolai S, Anggreni A, Gunther E, Sobiesiak M, Grosser H, Wetzel HU, Milkereit C, Brotopuspito KS, Harjadi P, Zshau J (2008) The May 26, 2006, magnitude 64 Yogyakarta earthquake south of Mt. Merapi Volcano: Did lahar deposits amplify ground shaking and thus lead to the disaster. Electr J Earth Sci 9:5. https://doi.org/10.1029/2008GC001810
Wells LD, Coppersmith JK (1999) New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bull Seismol Soc Am 84(4):974â€“1002
Wulandari A, Anggraini A, Suryanto W (2018) Hypocenter analysis of aftershocks data of the Mw 6.3, May 27, 2006, Yogyakarta earthquake using octtree importance sampling method Appl. Mech Mater 881:89â€“97
Yagi Y (2004) Source rupture process of the 2003 TokachiOki earthquake determined by joint inversion of teleseismic body waves and strong ground motion data. Earth Planet Space 56:311â€“316. https://doi.org/10.1186/BF03353057
Yagi Y (2006) Earthquake focal mechanism, IISEE Lecture Note 2006â€“2007. IISEE, BRI, Tsukuba
Yamanaka H, Ishida H (1996) Application of Genetic Algorithms to an Inversion of Surface Wave Dispersion Data. Bull Seism Soc Am 80:436â€“444
Yoshida S, Koketsu K (1992) Simultaneous inversion of waveform and geodetic data for the rupture process of the 1984 NaganokenSeibu, Japan earthquake. Geophys J Int 103:355â€“362
Acknowledgements
HS appreciates Lembaga Pengelola Dana Pendidikan (LPDP) for funding his doctoral study program and also immensely grateful to BMKG, IRIS, and GFZ for providing the waveform data and earthquake source parameters used in this research. The authors also thank Prof. Yuji Yagi for developing the script for moment tensor and joint inversions used in this research as well as the Universitas Gadjah Mada for the support provided through the Doctoral Program of Physics at the Faculty of Mathematics and Natural Sciences.
Funding
This research was partly funded by the Lembaga Pengelola Dana Pendidikan (LPDP) funds, but had no role in the study design, data collection, and analysis, decision to publish, or preparation of the manuscript.
Author information
Authors and Affiliations
Contributions
HS initiated the research idea, prepared the initial draft article and the analysis while W corrected, weighed, and analyzed the results. Meanwhile, IS provided critical comments, performed data curation, acquisition, and examined the results. AA added supporting data and supervision and WS reviewed, edited, visualized, and analyzed the results. All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Saputra, H., Wahyudi, W., Suardi, I. et al. The waveform inversion of mainshock and aftershock data of the 2006 M6.3 Yogyakarta earthquake. Geosci. Lett. 8, 9 (2021). https://doi.org/10.1186/s4056202100176w
Received:
Accepted:
Published:
DOI: https://doi.org/10.1186/s4056202100176w