Development of Spectral Hazard Map for Indonesia with a Return Period of 2500 Years using Probabilistic Method

This study is performed to develop spectral hazard map for Indonesia with a Return Period of 2500 years earthquake. It will be proposed for revision of the Indonesian hazard map in SNI-03-1726-2002 as response to the meeting organized by the Department of Public Works on 27October-2008 in Jakarta. The meeting has decided to revise the Indonesia hazard map by referring to IBC-2006 where spectral acceleration values at Peak Ground Acceleration/PGA, 0.2 and 1.0 second with a return period of 2500 year will be applied for general buildings. The spectral hazard map was analyzed using total probability method and three dimensional (3-D) source models with recent seismotectonic parameters. Four source models were used in this analysis, namely: shallow background, deep background, fault, and subduction source models. Generally, the results of analysis show the values of PGA with a return period of 2500 years relatively higher 1.2-3.0 times than in SNI-03-1726-2002.


Introduction
Currently, Indonesia has three earthquake hazard maps issued by the Department of Public Works. The first map is Peak Ground Acceleration (PGA) map at bedrock for 500 years return period in the Indonesian Earthquake Code, SNI 03-1726-2002 [1]. This hazard map is used for designing general buildings. The second is the hazard maps for designing waterworks (dam). This map was developed by Najoan and published by the Research centre for Waterworks, Department of Public Works [2]. The third map is used for designing bridge and road construction published by the Research Centre for Roads and Bridgeworks [3]. This map is referred to the map developed by Najoan with 50 and 100 years life time of structure or 500 and 1000 years return period of earthquake.
The map for PGA at bedrock in the SNI 03-1726-2002 ( Figure 1e) was developed by averaging values from four seismic hazard maps developed by four different research groups in Indonesia (Figure 1a to 1d). These seismic hazard map were developed using total probability theorem [4] and by applying area sources model (2-dimension model). 1) Faculty of Civil and Environmental Engineering, ITB, Bandung, Indonesia Email: m_asrurifak@yahoo.com 2) Faculty of Mining and Petroleum Engineering, ITB, Bandung, Indonesia Note: Discussion is expected before June, 1st 2010, and will be published in the "Civil Engineering Dimension" volume 12, number 2, September 2010. This 2-dimension (2-D) model has some limitations in modeling the fault source geometries. Moreover, several great earthquake occurrences in Indonesia in the last two years inquire revision of seismic hazard parameters in SNI 03-1726-2002. These earthquake events must be considered in determining seismic hazard parameters especially maximum credible earthquake magnitude (MCE).

Mayor Tectonic of Indonesia Region.
Indonesia Region, famous as "supermarket of disaster", is located in a tectonically very complex and very active area. According to Bird et al. [5], this region consists of three large tectonic plates and nine small ones ( Figure 2). The plates with different types of movement have created subduction and fault zones which are continuously active [6].
The Australia plate subducts beneath the Eurasian plate along the Java trench. The direction of convergence is normal to the trench South of Java, but oblique to the trench Southwest of Sumatra. It is widely accepted that the oblique subduction of Sumatra is partitioned into normal subduction along the trench and strike-slip along the trench-parallel Sumatran Fault [7] . Further East, the continental part of the Australian plate collides with the Banda arc, resulting in widespread deformation throughout the Banda island-arc. Further complicating the tectonics of East Indonesia, Australian continent also collides with the Pacific oceanic plate, resulting in uplift and extensive faulting on the island of New Guinea. Australia-Pacific convergence is highly oblique and appears to be partitioned into components perpendicular and parallel to the margin. The magnitude produced by fault movement of this mechanism depends on the area of the fault coupling. There are some potential active faults distributions around Indonesia Islands. The active fault features and parameters used in study based on published reports proposed by several researchers [3, [8][9][10][11][12][13][14][15][16][17][18][19][20]. General condition of the mayor tectonic features was shown in Figure 3.

Seismic Hazard Analysis
The goal of most seismic hazard modeling is to apply the basic understanding of regional seismic sources in the development of models that capture geologic and seismic event [21]. The process begins with the identification and description of possible earthquake sources, such as active faults or seismic zones. An analysis of past seismic event in the area is conducted to identify patterns, outliers and trends. There are two general approaches for seismic hazard analyses: deterministic seismic hazard analysis (DSHA) and probabilistic seismic hazard analysis (PSHA) [22]. In traditional earthquake engineering, seismic hazard analysis is performed deterministically, considering only a single maximum credible earthquake event. The probabilistic approach is more rational than this worst-case scenario, since it accounts for all possible events (including, of course, the worst expected) that would seismically effects a site.
The method of PSHA was developed by McGuire [23] based on the probability concept developed by Cornell [4], which assumed the earthquake magnitude M and the hypocenter distance R as a continuous independent random variable. Although the basic steps of the method remain the same up to today, the models and the computational techniques of the analysis keep being improved as the earth scientists and engineers collect and process more information about earthquakes. The total probability theorem can be represented in the most basic form as follows, (1) Where, fM = density function of magnitude fR = density function of hypocenter distance P [I ≥ i⎮M and R] = conditional probability of (random) intensity I exceeding value i at the site for a given earthquake magnitude M and hypocenter distance R.
The analysis is done using the software from the USGS [24]. Site space for analysis used 0.1 degrees of latitude and longitude, so that the calculations of seismic hazard for the Indonesia region are over than 96,600 sites. Results obtain from this form are acceleration at each site, can be used for the development of mapping spectra response on the bedrock. The selected period is PGA, T = 0.2 sec and T = 1.0 sec, where this period is as in the IBC-2006 [25].

Seismic Source Models
A seismic source model is defined as a seismically homogenous area, in which every point within the source zone is assumed to have the same probability of being the epicenter of a future earthquake [26]. The Models were developed using earthquake catalogs, tectonic boundaries, and fault information, where composed of background seismicity, fault and subduction sources (Fig. 4) as recently developed by USGS for U.S. hazard map [27]. Background seismicity in the model accounts for random earthquakes on unmapped faults and smaller earthquakes on mapped faults. A type of background seismicity is gridded models that are based on spatially smoothed earthquake rates [28]. Background sources are based on the declustered (dependent event removed) earthquake catalog. This model accounts for the observation that larger earthquakes (M ≥ 5) occur near smaller (M≥ 4 or 5) earthquakes. Gridded seismicity included in the model is based on earthquakes at five depth intervals: 0-50 km as shallow source, 50-100 km, 100-150 km, 150-200 km and 200-300 km as deep source model. A truncated-exponential or Gutenberg-Richter (GR) [29] magnitude-frequency distribution between M 5.0 and M 6.5 is used to model rates for different sizes of earthquakes in each grid cell or zone.

Surface
Fault source model is used for well-mapped as geographically and seismologically faults. The length of the mapped fault and downdip width estimated from seismicity may be used to calculate maximum magnitudes of earthquakes expected to occur on these faults [30]. For determining magnitude from fault area or surface length on different segments or multi-segment ruptures the relations of Wells and Coppersmith [30] are used. The major tectonic feature ( Figure 3) and sense of faulting, slip-rate, dip, width and maximum magnitude are estimated based on published data.
Subduction source model is the model of the seismic source, which represents the earthquake occurrence when plates are being subducted under an island arc or continent. Information used as input parameters of this model include the location of subduction in the latitude and longitude coordinates, rate and b-value of the subduction area that can be obtained from the historical earthquake data with least square (GR) method [29]. This model was Limited to 50 km depth of the source rupture or Megathrust zones, deeper zones or Benioff zones are represented by deep background source models.

Recurrence relations
Recurrence relations are the means of defining the relative distribution of large and small magnitude and incorporating the seismic history into the hazard analysis. On the basis of worldwide seismicity catalog, Gutenberg-Richter [29] established the loglinear relation given by Equation (2). This relation has been assumed to apply to individual areal and fault sources as well. One of the steps in characterizing seismic sources is the assignment of a maximum magnitude to each source. This requires the GR line to taper into the maximum value as shown in Figure 5.a. This distribution is called the truncated exponential and is given in exponential form in Equation (3).

LogN(M) = a -bM
Where N(M) is the number of earthquakes per year with a magnitude equal to or greater than M and a and b are constants for the seismic zone. N is associated with a given area and time period.
The truncated exponential model is used for shallow and deep background sources with weighting of 1.0. Fault segments tend to have occurrences of earthquakes of similar size or within a narrow range of magnitudes. These earthquakes are called characteristic earthquakes. Typically smaller earthquakes on the fault follow the GR line and the characteristic earthquakes occur at higher rates. So for fault and subduction sources both truncated exponential (GR) and characteristic models (char) are used with a weighting of 0.34 and 0.66, respectively A characteristic model is used following Youngs and Coppersmith [31] shown in Figure 5b.
Determining the maximum magnitude in seismic source model for the hazard analyses is important. There are two ways in determining the maximum magnitude. The first is determined from historical earthquake, and second is determined at the zones where only few historical earthquake data but the fault system that have potential for the occurance of big earthquake magnitude, so that the value of the maximum magnitude can be taken using the equation proposed Wells & Coppersmith [30].

Data Collection and Processing
The analysis of seismic hazard assessment at the site of interest needs all data that record the earthquake event occurred in that site for a specific Figure 5. a)Truncated exponential distribution of recurrence rates, b) Characteristic earthquake occurrence model after Schwartz and Coppersmith [31]  Period of data from 1900 to 2007, but the annual rate for the analysis uses data from 1964 to 2007. The catalogs from various sources generally have varied magnitude scale. The varied magnitude should be converted into one same scale before it is uses in PSHA. Magnitude scale like surface wave magnitude (Ms), local Richter magnitude (ML), and body wave magnitude (mb) is converted to the moment magnitude (Mw). The analysis of conversion in this study uses earthquake catalog of Indonesia region that is collected from various sources as mentioned above. Using regression analysis ( Figure  6) correlation formula for the conversion magnitude scale for Indonesia region, is obtained as seen in Table 1.
PSHA is based on independent earthquake (mainshock) event. Several empirical criteria to identify dependent event developed based on a range of time and a specified distance from a large earthquake occurrence have been made by some researchers as Arabasz & Robinson [34], Garner & Knopoff [35] and Uhrhammer [36]. Shorting dependency result using Garner & Knopoff [35] can be seen in Figure 7.

Attenuation
Attenuation relations tend to be regionally specific, unfortunately there is no attenuation specifically developed for Indonesia region. The only way is to adapt attenuation function derived in other region, which is similar to Indonesia region tectonically and geologically. It is of importance that the selection was based on earthquake mechanism, which is generally categorized into background, fault and subduction source zones. Some attenuation relationships have used Next Generation Attenuation (NGA) as listed: a) Attenuation for Shallow Background. 1) Boore-Atkinson NGA [37].
Logic-tree by Power et. al. [44]; Kulkarni et al. [45]; Coppersmith and Youngs [46] is used in this study in order to allow uncertainties in selection of models for recurrence model, maximum magnitude and attenuation function to be considered. The weighting of logic tree used in the analysis can be seen in Table  2a and 2b.

Result and Discussion
Spectral hazard analysis on this study uses shallow background, deep background, fault and subduction seismic source models as recently developed by USGS for U.S. hazard map [27].
Hazard maps of PGA at bedrock with 5% damping and spectral acceleration at 0.2, and 1.0 sec with 2% probability of exceedance in 50 years or equivalent to 2500 year return period are shown in Figures 8 to  10. respectively.

Recurrence Mmin Mmax Mechanism Attenuation
Shallow background (GR)  The spectral hazard map developed in this study will be proposed as a revision for the current seismic hazard map of Indonesia in Indonesian Seismic Building Code SNI-03-1726-2002 especially for maximum credible earthquake magnitude (MCE) design.