## A Case Study for the Great 1852 Banda Arc Mega-Thrust Earthquake and Tsunami

#### Introduction

Indonesia is one of the most tectonically active and densely populated places on Earth. It is surrounded by subduction zones that accommodate the convergence of three of Earth's largest plates. Some of the largest earthquakes, tsunamis, and volcanic eruptions known in world history happened in Indonesia (Harris & Major, 2016; McCue, 1999). Since these events, population and urbanization has increased exponentially in areas formerly destroyed by past geophysical hazards. Recurrence of some of these large events during the past two decades have claimed a quarter million lives (Tsunami Sources 1610 B.C. to A.D. 2017 from Earthquakes, Volcanic Eruptions, Landslides, and Other Causes, 2017).

Most casualties from natural disasters in Indonesia are caused by tsunamis (the Indian Ocean earthquake and tsunami of 2004 is a prime example of this), which, over the past 400 years, occur on average every 3 years (e.g., [Hamzah et al., 2000]). Many potential tsunami source areas, such as the eastern Sunda (Newcomb & McCann, 1987) and Banda (Harris, 2011) subduction zones have no recorded mega-thrust earthquakes (Okal & Reymond, 2003). However, some historical accounts of earthquakes and tsunamis in Indonesia provide enough detail about wave arrival times and wave heights from multiple locations to verify if mega-thrust events have happened in apparently quiescent regions, and assess the potential consequence of a similar event occurring in the future. Indeed, reliance on modern instrumental records of earthquake events to determine seismic risk severely biases hazard assessments, as the relevant temporal scales are hundreds or thousands of years on a given fault zone. To improve risk estimates, it is imperative to draw from historical records of damaging earthquakes, which reach beyond the 50–70 years horizon provided by modern instrumentation.

To this end, there has been substantial effort invested in the quantification of the characteristics of pre-instrumental earthquakes and tsunamis; see for example (Barkan & Ten Brink, 2010; Bondevik, 2008; Bryant et al., 2007; Fisher & Harris, 2016; Griffin et al., 2018; Grimes, 2006; Harris & Major, 2016; Jankaew et al., 2008; Z. Y. C.; Liu & Harris, 2014; Martin et al., 2019; Meltzner et al., 2010, 2012, 2015; Monecke et al., 2008; Nanayama et al., 2003; Newcomb & McCann, 1987; Reid, 2016; Sieh et al., 2008; Tanioka & Sataka, 1996). As noted in these references, the historical and prehistorical data sources are sparse in details and laced with high levels of uncertainty. To improve the usage of these imprecise accounts, we develop a systematic framework to estimate earthquake parameters along with quantitative bounds on the uncertainty of these parameter estimates. We do this using a Bayesian statistical inversion approach already leveraged in a variety of disciplines in the physical, social and engineering sciences, (see Dashti & Stuart (2017); Kaipio & Somersalo (2005); Tarantola (2005); as well as Fukuda & Johnson (2008); Malinverno (2002); Sraj et al. (2014, 2017)), to reconstruct large seismic events from historical accounts of the resulting tsunamis. These efforts are related to a slew of recent and currently active work that seeks to determine the seismic source of modern tsunamis by inverting the available instrumental observations (see [Fujii & Satake, 2007; Giraldi et al., 2017; Kubota et al., 2018; Mulia et al., 2018; Percival et al., 2011; Saito et al., 2011] for example).

Our focus here is on an initial case study concerning the reconstruction of the 1852 Banda arc earthquake and tsunami in Indonesia detailed in the recently translated Wichmann catalog of earthquakes (Harris & Major, 2016; Wichmann, 1922) and from contemporary newspaper accounts (Swart, 1853). To proceed with the Bayesian description of this inverse problem, we describe uncertainties in the noisy anecdotal observations of the 1852 tsunami via probability distributions. We next supplement this historical data with a prior probability distribution for the seismic parameters calibrated using modern instrumental seismic data. Finally, we develop a forward model mapping seismic parameters to shoreline observations using the Geoclaw software package (M. J. Berger et al., 2011; González et al., 2011; LeVeque et al., 2011; LeVeque & George, 2008) to numerically integrate the nonlinear shallow water equations, predicting the evolution of the tsunami initiated by seafloor deformation due to the earthquake itself. These three elements are then combined with Bayes theorem to produce a posterior distribution on the location, magnitude, and geometry of the most likely mega-thrust source for the 1852 tsunami.

Detailed information concerning the Bayesian posterior distribution, the output of our framework, is drawn from large scale computational simulations using Markov chain Monte Carlo (MCMC) sampling techniques (J. S. Liu, 2008). The solution of the inverse problem detailed here is reproducible from the described assumptions. Any of the assumptions can be modified by changing a few lines of code using a Python based software package available to the public upon request, and accessible via GitHub: https://github

The rest of this article is organized as follows. The next section includes a review of previous efforts related to this specific historical event, and a discussion of the source of the 1852 tsunami (mega-thrust earthquake or submarine slump). Section 3 describes the tectonic setting of the region in consideration. Section 4 gives a very brief overview of the Bayesian methodology, a description of the different assumptions and parameterizations used for this particular event as well as an overview of the relevant historical observations and the forward tsunami model used here. Section 5 discusses the results of the inference and describes in some detail the posterior distribution that yields information on the possible earthquakes that may have resulted in the observed tsunami. Finally Section 6 discusses the implications that can be derived from the posterior distribution, and a discussion of future work.