Cakupan: 25/10/2013. Overview Seismicity of Indonesia. Konferensi Nasional Teknik Sipil 7, UNS Solo, 25 Oktober 2013

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1 Peran Akademisi dan Praktisi dalam Pembangunan Gedung dan Infrastruktur Tahan Gempa di Indonesia, Lessons Learned dari Pembuatan Peta Gempa Indonesia 2010 Masyhur Irsyam* dkk. *Ketua - Tim Revisi Peta Gempa Indonesia *Ketua - Pusat Penelitian Mitigasi Bencana ITB *Ketua - Himpunan Ahli Teknik Tanah Indonesia *Koordinator - Tim Mikrozonasi Gempa kota-kota Besar Indonesia *Anggota - Tim Penasehat Konstruksi Bangunan DKI Jakarta Cakupan: Alasan Mengapa Perlu Melakukan Revisi Peta Gempa Kondisi Tektonik dan Kegempaan Indonesia Peta Hazard dan Peta Resiko Gempa Pemakaian untuk Standard Perencanaan di Indonesia Konferensi Nasional Teknik Sipil 7, UNS Solo, 25 Oktober 2013 PENDAHULUAN Indonesia menempati zona tektonik yang sangat aktif karena tiga lempeng besar dunia dan beberapa lempeng kecil lainnya saling bertemu di Indonesia Overview Seismicity of Indonesia EURASIA PLATE PHILIPINE PLATE PASIFIC PLATE 12 cm/year 6 cm/year Main shocks INDO AUSTRALIA PLATE Peta tektonik kepulauan Indonesia dan sekitarnya (Bock et al., 2003) 1

2 Bidang Keilmuan yang terlibat Mitigasi Bencana Gempabumi: Geologi Seismologi Geofisika Teknik Sipil Arsitektur Urban Planning Sosiologi Psikologi Ekonomi dll Bidang kajian ilmu-ilmu dasar/sains Bidang-bidang aplikasi, rekayasa, dan analisis resiko Bidang-bidang sosial Earthquakes don t kill people. buildings kill people (Prof. Chris Scholz Columbia University) Strategi Mitigasi Gempa Fenomena Alam Gempa Sangat potensial mengakibatkan kerugian besar Kejadian alam yang belum dapat diperkirakan secara akurat: kapan, dimana, magnituda Gempa tidak dapat dicegah (FEMA 451b, 2007) Efek Gempa Strategi Fault rupture Tsunami Kelongsoran (besar) Likuifaksi Bangunan Tahan Gempa Manusia memiliki kebutuhan dasar untuk terlindungi dari implikasi buruk adanya gempa Goncangan/ Gerakan Tanah Hindari Hindari Hindari Hindari/ Ditanggulangi Ditanggulangi Infrastruktur perlu didisain tahan gempa Contoh kesiapan menghadapi gempa: Chile Februari 2010 Haiti Januari 2010 Kekuatan Gempa Energi yang dilepaskan Jumlah Getaran Perbandingan Efek Gempa Chile dan Gempa Haiti 500 kali-nya 512 kali-nya Korban Meninggal Ratusan jiwa Ratusan Ribu jiwa Kehilangan Rumah Sedikit Banyak Pemulihan Jaringan Komunikasi Cepat Lama H Newton s 2 nd Law: H = m x a Chile relatif sangat siap dalam menghadapi gempa. Undang-undang di Chile mengharuskan setiap bangunan untuk memiliki konstruksi tahan gempa. Pembangunan gedung dan infrastruktur tahan gempa: Peran penting Akademisi Praktisi yang didukung oleh Pemerintah/Lembaga Spectral Acceleration at Bedrock 2

3 The 1 st Seismic Hazard Map in Indonesian Standard for Earthquake Resistance Building Design 1983 The 2 nd Seismic Hazard Map Indonesian Standard for Earthquake Resistance Building Design (SNI ) Horizontal Peak Ground Acceleration at bedrock S B for 10% in 50 years (+500 years) Rata-rata hasil perhitungan dari: -Praktisi (Konsultan) -Akademisi (ITB) -Kementerian (PU) -Lembaga (PSG) Earthquake Zone - 1 Earthquake Zone - 2 Earthquake Zone - 3 Earthquake Zone - 4 Earthquake Zone - 5 Earthquake Zone - 6 Earthquake events since the release of SNI-2002 Aceh Earthquake Mw=9.2 (December, 2004) Simeuleu Earthquake Mw=8.5 (11 April, 2012) Simeuleu Earthquake Mw=8.1 (11 April, 2012) Nias Earthquake Mw=8.6 (March, 2005) Padang Earthquake Mw=7.6 Why does the current code require Jambi improvements Earthquake Mw=6.6? (Sept, 2009) (Oct, 2009) 1. Mentawai To considers Earthquake recent Mw=7.2 great earthquakes in Indonesia (Oct, 2010) Lhok Nga after Aceh Earthquake 2004 Lam Paseh Tasik Earthquake Mw=7.4 (Sept, 2009) Yogya Earthquake Mw=6.3 (May, 2006) USGS 3

4 Mall Pantee Pirak, Banda Aceh 2004 Rapat di PU Pusat tgl 30 November Rapat dihadiri oleh 70 undangan mewakili: Akademisi, Asosiasi Profesi, Kementerian/ Lembaga - Keputusan rapat: Menteri PU perlu membentuk Tim Revisi Peta Gempa SNI Diharapkan Revisi Peta sudah dapat dihasilkan dalam 3 bulan (akhir Februari 2010) Team for Revision of Seismic Hazard Map of Indonesia 2010 Ketua: Prof. Masyhur Irsyam (Rekayasa Geoteknik Kegempaam Akademisi ITB + HATTI) Wakil: Dr. Wayan Sengara (Rekayasa Geoteknik Kegempaam Akademisi ITB) Sekertaris: Fahmi Almadiar, MT (Seismic Hazard Praktisi PU) Anggota: M Asrurifak, MT (Seismic Hazard Mahasiswa S3 ITB) Dr. Danny Hilman Ir. Engkon Kertapati (Geologi - Praktisi LIPI) (Geologi Praktisi Pusat Penelitian Geologi) M. Ridwan, MT (Geologi Praktisi PU) Dr. Irwan Meilano Prof. Sri Widiantoro Dr. Wahyu Trioso Drs. Suhardjono (Geodesi, Crustal Deformation Akademisi ITB) (Geofisika Akademisi ITB) (Geofisika Akademisi ITB) (Geofisika Praktisi BMKG) Peta Hazard: Prof. Phil Cummins - Akademisi Geo Science Australia Dr. Mark Petersen - Praktisi USGS Peta Resiko: Dr. Indra Djati Sidi Akademisi ITB Dr. Nicholas Luco Praktisi USGS Prof. Widiadnyana Merati Akademisi ITB Daniel Hutabarat, MT Mahasiswa S2 ITB Ministry of Energy+ Mineral Resources National Disaster Management Agency Supported by: Didukung oleh: Ministry of Public Works Bureau of Meteorology, Climatology, Geophysics ITB Indonesia Research Institute Ministry of Research and Technology 4

5 Reasons for Updating Estimated maximum magnitude of seismic sources for development of seismic hazard map 2002 Sumatra Subduction 8.5 Semangko 7.6 Sukabumi 7.6 Baribis 7.0 Palawan Tarakan Walanae Kutai Sulu Lasem 6.8 Palu-Koro 7.6 North Sulawesi 8.0 Sangihe 8.5 Sorong 7.6 Halmahera 8.4 Ransiki 6.5 Mamberamo 7.6 Aru g Previous Estimation Mw= Actual Mw=9.0 Jawa Subduction 8.2 Bumiayu 6.1 Flores Back-arc 6.1 Banda 8.5 Seram 8.4 Tarera-Aiduna 6.5 To update earthquake records and earthquake source data including active faults that have not been considered in the 2002 map Other Reasons for Updating: To account for New Data and Technology Development Eartquake Data up to1999 SNI

6 Semarang Fault South 25/10/ Procedure for Developing Probabilistic Hazard Map Seismic Hazard Analysis Probabilistic analysis Probability Density Deterministic Function analysis PENGEMBANGAN PROGRAM Total Probability Theorem Expert judgement 4. Perhitungan Seismic hazard gempa Calculation 1. Identification of Earthquake Sources Seismic design criteria Calculating Menghitung seismic hazard hazard dengan based input on dari Tahap (1) + (2) + (3) dengan Lokasi Location : koord. sumber : gempa coord of sources input in memperhitungkan the Step (1) + ketidakpastian (2) + (3) by Geometri Geometry : arah strike, sudut : direction dip, 0f strike, dip angle, considering epistemic. epistemic uncertainties kedalaman maksimum Mekanisme : subduksi, patahan maximum depth Mechanism normal, reverse : subduction, normal fault, reverse 3. Selection Pemilihan of Data strong Available motion strong motion fungsi atenuasi accelerogram accelerogram yang ada data Atenuation Function 1. Identifikasi sumber gempa Karakterisasi Characterization sumber gempa of Sources seimologi Frekuensi Frequency kejadian distribution Slip rate Slip rate Magnitude maksimum Maximum Magnitude Informasi Geologi, Information on geologi, seimology Katalog data gempa Earthquake cataloque Development of Maps of PGA & Response Spectra 2. Procedure for Developing Deterministic Seismic Hazard Map M=7.3 Site location Tectonic Setting and Earthquake Sources for Indonesia Semarang 0.11 g M=7.3 Identification of subduction and active faults surrounding the site location Selecting the worst scenario with maximum magnitude (M max ) and closest distance (R min ) for each source Determining the ground motions based on M max and R min with 84 percentile 6

7 Megarthrust Andaman-Sumatera Mw=9.2, a=4.70, b=0.83 Tectonic Setting for Indonesia Source Type I: Subduction Megathrust Megarthrust Middle1 Sumatera Mw=8.6, a=4.71, b=0.88 Eurasian Plate Megarthrust Middle 2 Sumatera Mw=8.5, a=5.35, b=0.97 Sulu Thrust Mw=8.5 Megarthrust North Sulawesi Mw=8.2, a=4.28 b=0.91 Philipine Plate Megarthrust Philipine Mw=8.2, a=4.64 b=0.87 West Molucca Sea Mw=7.9 East Molucca Sea Mw=8.1 Pasific Plate North Papua Thrust Mw=8.2 Seismic tomography to obtain the geometry for subduction zones Megarthrust S Sumatera Mw=8.2, a=5.76, b=1.05 Megarthrust North Banda Sea Mw=7.9, a=6.86 b=1.20 Megarthrust Jawa Mw=8.1, a=6.14, b=1.10 Indian-Australian Plate Megarthrust Sumba Mw=7.8, a=6.81, b=1.20 Megarthrust South Banda Sea Mw=7.4, a=7.56 b=1.34 Megarthrust Timor Mw=7.9, a=9.09 b=1.60 Seismic tomography to obtain the geometry for subduction zones (Widiyantoro, 2009 and Tim Revisi Peta Gempa Indonesia, 2010) Compilation of historical earthquake events due to megathrust 1941 (7.9) 2004 (M9.15) 1881 (7.9) Sumatran fault Zone EURASIAN PLATE (M 8.7) 1907 (~M7.8) 1861 (M~8.5) 1935 (M7.7) 1797 (M8.4) 1833 (8.9) 2007 (M 8.4) 2000 (M7.8) Currently locked, end of typical cycle Jakarta Unknown section, no large eartquakes in historical records INDIAN-AUSTRALIANPLATE Natawidjaja,

8 Perlu merekonstruksi kejadian-kejadian masa lalu Dikerjakan oleh Dr. Danny Hilman (Praktisdi LIPI) Beginning of the new earthquake cycle Inter-seismic period (slow strain accumulation) Slow uplift Slow Submergence (Natawidjaja, 2005) During recent giant earthquakes the islands RISE suddenly! The Sumatran Coasts SINK! New coast line Old beach Rising island creating new land in Simelue during Aceh-Andaman earthquake (Natawidjaja, 2005) (Natawidjaja, 2005) 8

9 Banda Aceh and East part of the islands SINKS Haloban in Banyak Island Sinked about 30 cm (Natawidjaja, 2005) (Natawidjaja, 2005) 9

10 Desa HALOBAN, P. Tuanku, Kep. Banyak (Natawidjaja, 2005) (Natawijaya, 2004) Corals tell about how the islands move up and down Penelitian Coral untuk studi Kejadian Gempa dan Deformasi (Natawijaya, 2005) (Natawijaya, 2004) (Natawijaya, 2004) 10

11 Java Megathrust Earthquakes Natawijaya, 2010 Kegempaanhasilrelokasi Kegempaanhasilrelokasi (Engdahl, 2009) <50km (Engdahl, 2009) July 2006 (Mw 7.8) 1994 (Mw 7.8) Irwan Meilano, Aceh 3. Tripa 4. Renun Tectonic Setting for Indonesia Source Type II: Active faults have been well identified 8. Sumpur 1.Seulimeum 5. Toru 9. Sianok 77. Manokwari trench 57. Gorontalo 12. Siulak 74. Sorong 75. Ransiki 54. Batui thrust Dikit 72. Sula-Sorong 70. Yapen 50. Palu-Koro Angkola 7. Barumun 14. Ketaun 53. Poso 10. Sumani 18.Semangko 11. Suliti 15. Musi 51. Matano 31. Baribis 73. Sorong-Maluku 58. Lawanopo 34. Wetar back arc 78. Lowland 33. Semarang 16. Manna 52. Walanae 55. Tolo thrust 71. Tarera-Aidun 17. Kumering 30. Bumiayu 19.Sunda 34. Jogja 76. Membrano thrust tbelt 36. Flores back arc 32. Cimandiri 79 Highland thrust belt Historical Earthquakes along The Sumatran Fault Zone (Natawijaya, 2010) Seismic Gap? March 2007 (M6.3 & 6.1) Oct 2009 (M 6.7) (7.7) (7.6) ( >7) 1926 (~7) 1933 (7.5) 1936 (7.2) 1942 (7.3) Compilation of Historical Earthquake Events due to Faults 23 destructive events in the past 200 years or 1-2 large earthquakes occur every decade 1943 (7.3) 1952 (6.8) 1964 (6.5) 1967 (6.8) 1979 (6.6) 1984 (6.4) 1987 (6.6) 1990 (6.5) 1994 (6.9) 1995 (7.0) 1997 (6.5) 11

12 Tracing Coordinates of Faults, Subduction, and Relocated Epicenters on SRTM Collect GPS data Velocity Movement Based Slip Rate Velocity Movement and Slip-rateBased on GPS Seismic Sources: Source Type III: Shallow and Deep Background It is very suitable for unmapped faults, but have historical earthquake records It is used o account for epicenters that do not belong to well identified active faults Spatially smoothed-gridded seismicity 12

13 All shocks Main Shocks Selection of Attenuation Functions Classification of Main Shocks Based on Type of Source (conducted by S3 Student) Shallow backgound Megatrust Subduksi Megathrust Fault Fault Background Subduction Megathrust Fault/ Shallow Crustal Background Benioff 1 Benioff 2 Subduksi Benioff Benioff Zone/ Deep BG Subduction Benioff Benioff 3 Benioff 4 13

14 SEAOC Vision 2000 Committee dan FEMA 273 Content: Reasons for Revision of Seismic Hazard Map Design Live 50 tahun Probability of Exceedance 20% 10% Earthquake Level Immediate Occupancy ccccccc Live Safety (Rare Earthquake) 225 years 500 years SNI 1983 SNI 2002 Tectonic Setting and Seismic Sources New Seismic Hazard and Risk Maps Applications for the Indonesian codes Deterministic maps 84%: Subductions Faults Probabilistic maps: ,000 years 2,500 5,000 10,000 Peak Ground Acceleration (PGA) at Bedrock S B (for 50 years Earthquake) Peak Ground Acceleration (PGA) at Bedrock S B (for 100 years Earthquake) Didukung oleh: Didukung oleh: 14

15 Peak Ground Acceleration (PGA) at Bedrock S B (for 200 years Earthquake) Peak Ground Acceleration (PGA) at Bedrock S B Probability of exceedence 10% in 50 years (500 years EQ) Didukung oleh: Didukung oleh: Peak Ground Acceleration (PGA) at Bedrock S B Probability of exceedence 10% in 100 years (1,000 years EQ) Peak Ground Acceleration (PGA) at Bedrock S B Probability of exceedence 2% in 50 years (2500 years EQ) Didukung oleh: 15

16 Peak Ground Acceleration (PGA) at Bedrock S B Probability of exceedence 0.5% in 50 years (10,000 years EQ) Deterministic Peak Ground Acceleration (PGA) for Faults at Bedrock S B with 84% percentile (150% Median) Deterministic Peak Ground Acceleration (PGA) for Subduction at Bedrock S B with 84% percentile (150% Median) PGA Spectral Acceleration at S s and S 1 for 50, 200, 500, 1000, 2500, years and Deterministic approach 0.2 sec 1.0 sec PGA S 0.2 S 1 16

17 Content: Reasons for Revision of Seismic Hazard Map Tectonic Setting and Seismic Sources New Seismic Hazard and Risk Maps Applications for the Indonesian codes Buildings Tim Revisi SNI Ketua: Prof. Gde Widiadnyana Merati (Akademisi ITB) Struktur Bangunan Atas: Struktur Bangunan Bawah: Dr. F.X. Toha (Ketua ITB) Prof.Bambang Budiono (Ketua - ITB) Dr. Wijoyo Prakoso (UI) Prof. Iswandi Imran (ITB) Prof. Paulus Rahardjo (Unpar) Dr. Muslinang M. (ITB) Dr. Wayan Sengara (ITB) Dr. Dyah Kusumastuti (ITB) Sindhu Rudianto, MSc (HAKI) Ir. Teddy Boen (HAKI) Dr. Sylvia Herina (Puskim) MaryokoHadi, DipI.E.Eng (Puskim) Dr. Bigman Hutapea (HATTI) Dr. Dradjad H. (HAKI) Prof. Masyhur Irsyam (ITB) Ir. Stefy Tumilar (HAKI) Process of Development of Hazard Map Continuous Updating: to account for New Data and Technology Process of Development of Hazard Map Continuous Updating: follows the concept to account of UBC for New Data IBC and 2009 Technology ASCE Eartquake Data up to1999 SNI (National Concencus March 2010): IBC 2009 is adopted for SNI-2010 July 2010: ProbabilisticHazard Maps signed by Ministry of PW Seismic Hazard: - Probablistic: 10% PE in 50 yrs (500 yrs eq.) Eartquake Data up to1999 SNI (March 2010): adopted for SNI MCE R (Risk-Adjusted Maximum Considered Eq.) Risk of Collapse 1% in 50 yrs: Seismic Hazard: - Probabilistic - Deterministic Approach Pleno meeting Fragility Pleno of meeting Buildings November 2010: January 2011: map adopted for Risk-Targeted SNI-2010 Ground Motion 17

18 Application of Hazard Maps: depends on the type of infrastructure Buildings National Consensus: Adapt ASCE 2010; combines Probabilistic + Deterministic + Building Fragility Coordinated by: Research Institute for Human Settlements Ministry of Public Works SEAOC Vision 2000 Committee dan FEMA 273 Design Live 50 tahun Deterministic maps Probability of Exceedance 20% 10% 2% Risk of Colapse: 1% MCE G map Earthquake Level Immediate Occupancy ccccccc Live Safety (Rare Earthquake) Near Collapse (Very Rare Earthquake) Near Collapse (Very Rare Earthquake) Probabilistic maps: 50 years ,000 2,500 years 10, years 500 years MCE*: - Prb 2,500 years + - Deterministic MCE G + MCE R **: - Probabilistic + - Deterministic + - Fragility Building Fragility SNI 1983 SNI 2002 IBC 2009 SNI 2013 ASCE 2010 *MCE: Maximum Considered Eq. (Gempa Maksimum Dipertimbangkan Rata-rata Geometric) **MCE R : Risk-Adjusted Maximum Considered Eq. (Gempa Maksimum Dipertimbangkan Resiko-Tersesuaikan) MCE R maps Seismic Base Shear S s Risk-Adjusted Maximum Considered Earthquake MCE R S 1 Maximum Considered Earthquake Geometric mean (MCE G ) PGA Upper Structure Jepit Sub Structure Liquefaction potential s active/passive PGA MCE G Maximum Considered Earthquake Geometric mean 18

19 Spectral Acceleration Spectral Acceleration 25/10/2013 MCE R : Risk-Adjusted Maximum Considered Earthquake ASCE-2010: Risk of Collapse is 1% in 50 yrs Ss Risk-Adjusted Maximum Considered Earthquake (MCE R ) Ground Motion Parameter for Indonesia for 0.2 s Spectral Response Acceleration (5% of Critical Damping), Site Class B Risk-Targeted Ground Motion RTGM P f = ʃ 0 Risk/probability of collapse =1/5000 H(a) Hazard Fragility Curve (Conditional probability of failure) dp f (a) da Capacity da Luco, 2009 (Prepared by Team on Indonesian Risk-Targeted Ground Motions) Ss Risk-Adjusted Maximum Considered Earthquake (MCE R ) Ground Motion Parameter for Indonesia for 1.0 s Spectral Response Acceleration (5% of Critical Damping), Site Class B S MS = F a S S S DS = (2/3) S MS Site Effect and Amplifcation Factor Spectra at ground surface S M1 = F v S 1 S D1 = (2/3) S M1 0.4 S DS S MS = F a S S S M1 = F v S 1 Ground Surface 0.2 T 0 = 0.2 T s 1.0 T S S F a (Tabel 4) F v (Tabel 5) Spectra at BedrockS B Soil Type (Prepared by Team on Indonesian Risk-Targeted Ground Motions) S 1 T S S (Gambar 9) S 1 (Gambar 10) Bedrock S B 19

20 Spektral acceleration (g) 25/10/ Comparison SNI 2002 with SNI 2013 for Jakarta Soft Medium Puslitbang Jalan + Jembatan PU +Akademisi Design +Praktisi live= 70 years Probability of Exceedance=7% Highway Bridges Earthquake Level= 1,000 years earthqauke Medium SNI-2013 Medium SNI Perioda (sec) Soft SNI-2002 Soft SNI Guideline Seismic Load Design for Bridge Standar Nasional Indonesia 500 years earthquake Design Standard for Seismic Resistance Bridge Revisiin of SNI is on going by the Bureau of Bridge Internal consensus for RO has been agreed by the Research Center for Highway and Bridge Consept of RO refer to AASHTO, Hydraulic Puslitbang Structures Air PU +Akademisi +Praktisi Hydraulic Structures Refer to USBR: Probabilitic: 50, 100, 200, , 2.500, 5.000, yrs + Deterministic 84% For checking the safety of existing large dams: 5,000 and 10,000 years earthquake Ports and harbours Design Earthquake: 500 yrs? Railway bridges 20

21 National Electric Company Concrete Dam for Electricity? PENELITIAN-PENELITIAN KEDEPAN Mikrozonasi untuk kota-kota di indonesia (kota besar dan dekat sumber gempa) Concrete Dam in West Java, 2013 Aceh Recommendation from PRP (Project Review panel): -The Operating Basis Earthquake (OBE): 145 yr -The Maximum Credible Earthquake (MCE): Probabilistic return period of 2475-yr + Deterministic 84th percentile level Manado Padang Bengkulu Lampung Ambon Jakarta Semarang Kendari Makassar Bandung Surabaya Jogjakarta Denpasar Kupang Jayapura Example of Microzonation Study for Istanbul City (Ansal, 2010) Development of Micozonation Maps for: DKI Jakarta ( ) Denpasar, Manado, Jayapura, Padang ( ) Coordination Ministry of Public Walfare ITB Ministry of Public Works Berau of Meteorology, Climatology, Geophysics Government of Jakarta National Disaster Management Agency Ministry of Energy+ Mineral Resiurces Ministry of Research and Technology 21

22 Master Plan Penelitian Pengurangan Resiko Bencana Conclusions The role of academicians and practicions are very important in mitigating seismic hazard Perlunya: - Mata kuliah wajib Rekayasa Gempa di Prodi Teknik Sipil - Perlu mengantisipasi pasar bebas 2015 dng bebas masuknya konsultan asing Revision of seismic hazard maps for Indonesia has been developed based upon updated available seismotectonic data, new fault models, and recent groundmotion prediction equations. Probabilistic Seismic Hazard Analysis and Deterministic Analysis has been conducted. Seismic Hazard For buildings: Mpas of Maximum Considered Earthquakes (MCE G and MCE R ) have been developed based on Probabilistic +Determintic + Fragility. For highway bridge, dam, port, etc: Revisions for seismic resistance design (including the maps) are still on going. Non Engineering Building 22

23 Acknowledgements The authors gratefully acknowledge: - The Ministry of Public Works -The Ministry of Research and Technology -National Disaster Management Agency (BNPB) through AIFDR (Australia- Indonesia Facility for Disaster Reduction ) -USGS for their supports and assistances during this asigment 23