This study examines a relationship between earthquake size and maximum tsunami amplitude using large earthquakes of M_w> 7.5 that led to trans-Pacific and Indonesian tsunamis. The data were sampled from tide gauges or DART surface buoys for seven Pacific tsunamis (the 2006 Kuril, Russia, 2009 New Zealand, 2011 Tohoku-oki, Japan, 2013 Solomon Island, 2010 Maule, 2014 Iquique, and 2015 Illapel) and six Indonesian tsunamis (the 2004 Indian Ocean, 2006 Pangandaran, 2007 Bengkulu, 2010 Mentawai, 2010 Simeulue, and 2012 Northern Sumatera). We found that the size better scales with M_w instead of other measures when relating to the mean maximum amplitude η. The main finding for the trans-Pacific cases was that the M_w scale is a logarithmic function of the mean amplitude, M_w = 0.77 log η + 8.84, consistent with previous work. For the Indonesian events, it was found that M_w = 1.92 log η + 10.36, reflecting different tsunami dynamics in the Pacific and Indian Oceans. The apparent difference is thus attributable to differences in both the topographical complexity and tsunami directivity in the two oceans. This is vital as the results provide insight into the nature of tsunami propagation approaching shorelines hence useful for improved tsunami early warning.

Abstrak Gempa tektonik dan tsunami merupakan bencana kebumian paling berbahaya bila dilihat dari dampak kerusakan dan cakupan wilayah terdampak. Meskipun termasuk penting namun sampai saat ini belum banyak penelitian yang menganalisis relasi antara magnitudo momen gempa dan amplitudo maksimum tsunami. Oleh karena itu, penelitian ini bertujuan untuk menemukan dan menganalisis persamaan empiris yang mendiskripsikan hubungan antara magnitudo momen gempa  dan amplitudo maksimum tsunami  dengan bantuan 7 kasus tsunami lintas Samudera Pasifik (Kuril, Rusia 2006, Selandia Baru 2009, Maule, Chili 2010, Tohoku, Jepang 2011, Solomon 2013, Iquique, Chili 2014, dan Illapel, Chili 2015) dan 6 kasus tsunami di Indonesia, (Aceh 2004, Sumatera 2007, Sumatera 2010, Mentawai 2010, Sumatera 2012, dan Sumatera 2016). Data penelitian merupakan data sekunder yang diperoleh dari instrumen ukur pemantau tsunami DART buoys dan tide gauges yang dapat diakses di https://nctr.pmel.noaa.gov/database_devel.html dan http://ngdc.noaa.gov yang dikelola dan dikontrol oleh National Oceanic and Atmospheric Administration (NOAA) dan http://ptwc.weather.gov/ yang dikelola oleh Pacific Tsunami Warning Centre (PTWC). Hasil-hasil penelitian dalam bentuk persamaan empiris relasi antara  dan  untuk 7 kasus tsunami trans-Pasifik (far-field observations) adalah  sedangkan untuk kasus 6 tsunami di Indonesia (both near-field and far-field observations), . Perbedaan faktor pengali fungsi logaritmik  pada kedua persamaam empiris tersebut karena perbedaan kompleksitas topografi dan batimetri lautan dan variasi perilaku perambatan gelombang tsunami pada tsunami directivity yang berbeda antara Samudera Pasifik dan Samudera Hindia. Temuan penting penelitian ini adalah kedua persamaan empiris tersebut menunjukkan bahwa magnitudo momen  gempa pemicu tsunami merupakan fungsi logaritmik dari amplitudo maksimum tsunami  yang sesuai dengan temuan penelitian terdahulu.   Kata Kunci: magnitudo momen gempa, amplitudo maksimum tsunami, tsunami trans-Pasifik Abstract Tectonic earthquakes and tsunamis are the most dangerous geological hazards considering damaging impacts on living things, human properties, and affected areas. Despite its importance, little is known about a relationship between earthquake moment magnitude and tsunami maximum amplitude. Hence, this study aims to find and analyse empirical equations relating earthquake sizes measured as moment magnitudes  to tsunami maximum amplitudes  for cases of 7 trans-Pacific occurrences (the 2006 Kuril, Russian, 2009 New Zealand, 2010 Maule, Chili, 2011 Tohoku, Japan, 2013 Solomon, 2014 Iquique, Chili, and 2015 Illapel, Chili events) and 6 Indonesian tsunamis (the 2004 Indian Ocean, 2007 Sumatera, 2010 Sumatera, 2010 Mentawai, 2012 Sumatera, and 2016 Sumatera events). Data in this study were acquired from field measurements by tsunami monitoring instrument (DART surface buoys and tide gauges) available at https://nctr.pmel.noaa.gov/database_devel.html and http://ngdc.noaa.gov officially operated by the National Oceanic and Atmospheric Administration (NOAA) and http://ptwc.weather.gov/ officialy managed by the Pacific Tsunami Warning Centre (PTWC). The research results in terms of empirical relations between the moment magnitude  and the tsunami maximum amplitude  for 7 trans-Pacific tsunami events at distant observations are then provided by  whereas for the Indonesian tsunamis monitored at both near-field and far-field observations, . The difference in the multiplying factor of the logarithmic function in each equation is due to differences in complexity in the ocean topography and bathymetri between the Pacific and Indian Oceans as well as the nature of tsunami wave propagation for different tsunami directivities in the two Oceans. The findings are such that the moment magnitude scaled with  is found to be a logarithmic function of the tsunami maximum amplitude  for both regions of interest, consistent with that of previous work.   Keywords: earthquake moment magnitude, tsunami maximum amplitude, trans-Pacific tsunamis.