Sunda-arc seismicity: continuing increase of high- magnitude earthquakes since 2004

Nishtha Srivastava1, Omar El Sayed1,2, Megha Chakraborty1,3, Jonas Köhler1, Jan Steinheimer1,2,

Johannes Faber1,2, Alexander Kies1, Kiran Kumar Thingbaijam5, Kai Zhou1,2, Georg Rümpker1,3, and Horst Stoecker1,2,4*

1Frankfurt Institute for Advanced Studies, 60438 Frankfurt am Main, Germany

2Institut für Theoretische Physik, Goethe- Universität Frankfurt, 60438 Frankfurt am Main, Germany

3Institute of Geosciences, Goethe- Universität Frankfurt, 60438 Frankfurt am Main, Germany

4GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany

5GNS Science New Zealand

*[email protected]

Abstract: Earthquakes with magnitude M ≥ 6.5 are potentially destructive events which may cause tremendous devastation, huge economic loss and large numbers of casualties. Models with predictive or forecasting power are still lacking. Nevertheless, the spatial and temporal information of these seismic events can provide important information about the seismic history and the potential future of a region. This paper analyzes the recently updated

International Seismological Centre earthquake catalog of body-wave magnitudes, mb, reported for ~313,500 events in the Sunda-arc region during the last 56 years, i.e., from 1964 to 2020. Based on the data, we report a hitherto unreported strong increase in seismicity during the last two decades associated with strong earthquakes with mb ≥ 6.5. A Gaussian Process Regression Analysis of these ISC-data suggests a continuation of this strong rise in number and strength of events with mb ≥ 6.5, in the region. These yearly maxima in the magnitude of the earthquakes also show another unexpected pattern: about every two-to-three years there is a new maximum in the magnitude and also in the number of earthquakes.

Furthermore, a noticeable increase is also observed in the yearly number of the events with mb ≥ 6.5. The trend line generated by Auto-Regressive Integrated Moving Average (ARIMA) method suggests continuing increase of such large-magnitude events in the Sunda-arc region during the next decade.

Introduction Earthquakes are considered as a major menace among all the natural hazards, affecting many countries worldwide and resulting in huge human losses each year. Single extremely strong earthquake events take up to several hundred thousand lives, the 2004 Mw 9.1 Sumatra earthquake, the 2010 Mw 7.0 Haiti earthquake and the 2011 Mw 9.0 Tohoku earthquake are horrific such examples. Large earthquakes can trigger ecological disasters if they occur close to a dam or a nuclear power plant, e.g., the 2011 Tohoku earthquake, whose subsequent tsunami drowned ~20,000 humans (as reported by the National Police Agency of Japan) and destroyed the Fukushima Dai-ichi nuclear power plant. These catastrophic events are not only collectively responsible for over 500,000 fatalities but also responsible for the destruction of social infrastructure and heritage sites, leading to economic damages exceeding US $200 billion (Kato and Ben-Zion, 2020). In spite of numerous theoretical modeling, observational studies and laboratory simulations, potential patterns underlying strong earthquakes are yet to be deciphered (Kato and Ben-Zion, 2020). Nonetheless, an improved understanding of earthquake occurrences would be beneficial for Early Warning, rapid response and mitigation plans, especially important for sustainable human habitats in earthquake-prone regions. This study focuses on identification of a temporal pattern associated with the earthquakes triggered in Indonesia over the last ~60 years and its surrounding regions. The region is influenced by the Eurasian, Indo-Australian, Philippine and Pacific plates making seismicity, volcanism and orogeny intensely active in the region (see Daly et al., 1991; Hamilton, 1970). The velocities of underflow along Benioff zones reach at least 10 cm/yr along Sumatra and Java forming the zone of subduction, the magmatic zone and the foreland basin (Hamilton, 1970). The southwest Sumatra subduction is part of a long convergent belt extending from the Himalayan front southward through Myanmar, continuing south past the Andaman and Nicobar Islands and Sumatra, south of Java and the Sunda Islands (Sumba, Timor), and then wrapping around towards north (McCaffrey, 2009). For the present analysis, we use the earthquake catalogue reported by the International Seismological Centre, to apply data mining and pattern deciphering of the seismicity. We adopt a classical Machine Learning approach, to quantify the trend associated with both the maximum magnitude of the seismic events, reported each year from 1964 to 2020, as well as a statistical analysis and forecasting of the trendline of the frequency of strong M>6.5 events as function of time.

Spatial Distribution and Magnitudes of the Earthquakes The present study region is located between 13° South to 11° North and near the equator between 92° to 166° East. The seismic events triggered in Sunda-Arc region have been continuously recorded since the year 1964 onwards and are reported by the International Seismological Centre (ISC, http://www.isc.ac.uk, accessed in January 2021). The dataset comprises ~313,500 events with the information of latitude, longitude, origin time, focal depth and magnitude of the events.

Saturation effects associated with the body wave magnitudes (mb) are certainly relevant for mb ≥ 6 and may lead to an underestimation of earthquake strength as measured by energy release or rupture area (Geller, 1976; Howell Jr, 1981; Kanamori, 1983; Giardini, 1988). Additionally, there are some potential limitations due to the quality of the recorded data, methods and guidelines followed in the estimation of mb, as well as distribution of reporting stations (Giardini, 1988). Previous researchers have investigated the reliability and consistency of the ISC catalogue reporting with time since 1963 and concluded that the consideration of the events with reported body wave magnitude greater than 4.5 to be safe (Giardini, 1988; Habermann, 1982). As the ISC-catalogue has predominantly reported body-wave magnitudes for this region, we base the temporal analysis on this type of magnitude. Events reported without information on mb, spatial coordinates and temporal information are excluded from the analysis.

The spatial distribution of the seismic events with mb ≥ 4.5 reported is shown in Figure 1 along with the pie-charts of focal depth distribution. The distribution of the focal depth of the seismic events for each magnitude range is shown with different colors in addition to a pie- chart for better understanding of focal depth distribution in the region. On the western side, the seismicity is observed along the collision of the Eurasian and the Indian plates which form a subduction zone, the so-called Sunda Trench. Parallel to this Sunda Trench is the ~1900 km long Sumatran Fault which has a long history of many damaging earthquakes (McCaffrey, 2009). Towards the eastern side, active deformation takes place within a complex Suture Zone (linear belt of intense deformation) which includes several relatively small fault lines and subduction zones (Hall, 2009).

Figure 1: Spatial distribution of seismic events reported between 1964-2020 by the International Seismological Centre for magnitudes in the range of mb ≥ 6.5, 6.5 > mb ≥ 6.0, 6.0 > mb ≥ 5.5 and 5.5 > mb ≥ 4.5. At least 70% of the earthquakes reported in these magnitude ranges are shallow in nature with their corresponding focal depth in the range of 0-70 km Figure 1 exhibits a dominance of shallow seismic events reported with focal depths in the range of 0-70 km. This is observed for all magnitude ranges and is likely related to the more brittle nature of the crust in shallow regions. This dominance depletes due to the changes in rheology with increasing depths. Although the events look more or less uniformly distributed for focal depth below ~250 km, two separate clusters with deep focal depths are observed beyond this depth. One of the two clusters represent the tectonic activity of the plates of the Java region while other deep earthquakes are observed due to the complex tectonics along the line of collision of Sunda plate with Philippine Sea plate and Caroline plate (McCaffrey, 2009). Two narrow clusters of high magnitude events with mb > 6 are also observed below 500 km depth. Temporal Observation, Analysis and Discussion Due to generally improved availability of seismic data, establishment of new seismographic stations, and better global coverage, ISC has an enhanced reporting of seismic events (Storchak et al., 2015). Timelines showing the steep growth in the numbers of reporting for the present study region is shown in Figure 2. The number of events reported with mb ≥ 3.5 are shown in a stacked bar graph.

Figure 2: Number of earthquakes reported between 1964-2020 in the study region. Data were obtained from the International Seismological Centre website (http://www.isc.ac.uk)

As expected, a strong increase in the number of low magnitude events is observed over time in the reported data. This is not surprising, as it is probably due to the significant increase of both the quality and number of sensors employed over the last five decades. In contrast to this, the sudden increases in the number of events with mb ≥ 6.5 detected in the dataset, after 1982 and after 2000, are surprising. In order to analyse the time dependence of the number and the strength of the seismic events in the region, a non-parametric, generic supervised machine learning method, the Gaussian Processes Regression (GPR) is used, based on the Bayesian approach. GPR not only works well with small datasets, but also provides uncertainty measurements. The motivation to use GPR here, instead of a linear or an exponential regression, is to avoid assuming an underlying functional form that might influence the identifying the predominant trend. The Gaussian Process Regressor implements Gaussian processes which is a stochastic approach such that every finite collection of those random variables has a multivariate normal distribution for regression purposes. Here, the prior mean is assumed to be constant and is either zero or is the training data’s mean. The prior’s covariance is specified by passing a kernel object. The hyperparameters of the kernel are optimized during fitting of Gaussian Process Regressor by maximizing the log-marginal-likelihood (LML) based on the passed optimizer. As the LML may have multiple local optima, the optimizer can be started repeatedly. The first run is conducted by starting from the initial hyperparameter values of the kernel; subsequent runs are conducted from hyperparameter values that have been chosen randomly from the range of allowed values (cf. Pedregosa et al., 2011; Rasmussen and Williams, 2016). For the analysis, Gaussian Processing implementation in the Scikit-Learn Python library is used. In detail, a Matern Kernel is used that represents a generalization of the Radial-basis function Kernel k.

For the points xi , xj it is given by: 휈 1 √2휈 √2휈 푘(푥 , 푥 ) = ( 푑(푥 , 푥 )) 퐾 ( 푑(푥 , 푥 )) 푖 푗 훤(휈)2휈−1 푙 푖 푗 휈 푙 푖 푗 with d(.,.) defined as the Euclidean distance, l as the length scale of the kernel, 흂 as an additional smoothness factor, K흂 (.) as a modified Bessel function and 횪(.) as the Gamma function (Pedregosa et al., 2011). For the regression, the parameters are found to be l = 35 and 흂 = 1.5 by fitting to the given dataset.

Figure 3: (a) The yearly maximum body-wave magnitude from 1964-2020 plotted against the corresponding years to perform a Gaussian Process Regression (GPR). (b) Number of earthquakes of body-wave magnitude greater than equal to 6.5 reported between 1964-2020 in Indonesia is plotted. A clear increase is observed in the average number of events in recent years. The grey area in the bottom figure shows the 95% confidence band associated with the forecasting. (c) Chi-square plots for both trendlines, blue line is for Yearly peaks in the reported magnitude and orange line is for number of high magnitude events reported annually.

The yearly maximum mb values for all earthquakes in the region is plotted against the corresponding years, and a Gaussian regression, as shown in Figure 3(a), is performed. The GPR analysis confirms quantitatively a continuous increasing magnitude of the earthquakes. Another inspection into the temporal evolution of the statistics of these rare strong earthquakes is obtained by the measured yearly number of events with mb ≥ 6.5. The number of strong earthquake events of mb ≥ 6.5 when plotted against the corresponding year, seems to double after ~ 1984, and increase substantially in a further step beginning in 2004. To analyse the time series qualitatively, we apply the Auto Regressive Integrated Moving Average (ARIMA) model. ARIMA is a widely used powerful machine learning method to capture temporal structures and time series forecasting. This model is governed by three distinct parameters which account for seasonality, trend and noise in the datasets: p (the autoregressive part), d (the integrated part), and q (the moving average part), respectively. In short, p incorporates the effects of previous values, d embodies the amount of difference (the number of times the difference with the past values is considered), and q gives the error in the model as a linear combination of the error observed for previous values (Hyndman and Athanasopoulos, 2018). The first step of the computation is to optimize the p, d and q values. Here, a grid search is performed to explore various combinations of parameters. The optimum set of parameters then yields the best performance for the selected criteria. The performance of the set of p, d, q is based on the respective model’s ability to accurately predict future data points. For this purpose, the Akaike Information Criterion (AIC) value is used. AIC is a measure, which tests how well a model fits the data while respecting the overall complexity of the model (Bozdogan, 1987). A model that fits the data using a lot of features has a larger AIC score than a model which uses fewer features to achieve the same fit quality. The best set of parameters, i.e. those which produced the best fitting model with lowest AIC score, was selected by grid search.

The increasing trend-lines in Figure 3 could be explained by lack of the reporting in the past but improved regional coverage in later years. However, the growing numbers of strong events from the year 2004 onwards can be clearly seen. As not only that magnitude has increased drastically but also the number of events with magnitude, mb > 6.5. It can be concluded that the seismic activity in the region has significantly increased since 2004. The 26 December 2004 Sumatra-Andaman earthquake is considered to be one of the largest seismic events followed by a devastating tsunami in recorded history which diminished the contribution from the vast number of lower magnitude events (Lay et al., 2005). This event occurred at a focal depth of approximately 30 kms and ruptured ~1300 km of the Indo- Australian subduction zone curved plate boundary from northwestern Sumatra to Andaman Island. One of the strongest aftershocks of this event, which triggered on 28 March 2005, ruptured the adjacent 300 kms (Lay et al., 2005). This highly active tectonic regime also appears to be host to some great historical earthquakes which are reported to be triggered to the southeast of the 2004 rupture zone in the years: 1797, 1833 and 1861. Additionally, two great earthquakes were also reported in the year 1881 and 1941 thus establishing the threat of great earthquakes for the region in the future as well (McCann et al., 1979; Newcomb and McCann, 1987; Zachariasen et al., 1999; Natawidjaja et al., 2004: Lay et al., 2005). Lay et al (2005) observed that 40 years prior to the 2004 event little seismicity occurred within 100 km of the trench between the epicenters of the large events triggered in the year 2004 and 1881 thus suggesting a long-term strain accumulation in the eventual rupture zone. The average increase of the number of events with mb ≥ 6.5 is also observed in the trendline of Figure 3(b). The noticeable increase from 2000 prior to 26 December 2004 earthquake could be an indicator of accelerating moment release (AMR) pattern in seismicity which has been an intriguing topic for various theoretical and observational studies (Bowman et al., 1998; Bowman and King, 2001; Brehm and Braile, 1998; Bufe and Varnes, 1993; Bufe et al.,1994; Jaume ́, 2000; Jaume ́ and Sykes, 1999; Jaume ́ and Bebbington, 2004; King and Bowman, 2003; Main, 1999; Papazachos et al., 2002; Papazachos and Papazachos, 2001; Robinson, 2000; Rundle et al., 2000; Saleur et al.,1996; Sammis and Smith, 1999; Varnes, 1989; Vere-Jones et al., 2001; Yang et al., 2001; Zöller and Hainzl, 2002). A study by Nishenko and McCann (1979) claims that the inner structure variations on the inner wall of trenches appear to reflect changes in both the lengths of rupture zones and in the source areas of tsunamis that are associated with large shallow earthquakes. Upper slope basins, deep sea terraces and other topographic features may act as an indicator of the tectonic reason and seismic-tsunami risk along convergent plate margins (McCann et al 1979). With this thought in mind, one potential reason for the increase of earthquakes with mb ≥ 6.5 after the 2004 earthquake could be an opening of a comparatively bigger lock between the subducting and overriding plate. This lock along the fault boundary could be the cause of huge stress accumulation later resulting in a great earthquake and tsunami. In light of this reporting, one may have further ask questions listed below: ● How does uncertainties in the reported magnitudes affect the analysis? ● Is the analysis impacted by the considered magnitude-type (mb, instead of Mw)? ● Can the findings be further consolidated using independent dataset(s) from different agencies? ● The events reported here are heterogeneous in terms of underlying tectonics. They would fall in different classifications: shallow crustal, subduction interface, and intraslab events. Different tectonic regimes have varying seismogenic potential owing to geology, fault geometry and material properties. How does this aspect affect the results? ● What is the behavior of interevent times for the large magnitude events i.e., peaks in the time series)? ● What are the spatial distances between the subsequent peaks and how do they correlate, in terms of magnitudes?

Owing to the underlying complex tectonic structure of this seismogenic regime, we envisaged further extension of this study by segregating the spatial and temporal clusters of the seismicity to understand the reported phenomenon. A follow up paper will address the above mentioned research concerns.

Summary and Conclusion: The average number of strong earthquakes per year in the Sunda Arc as reported by ISC are clearly increasing. The analysis shows that during the next decade more and stronger earthquakes may occur along the Indonesian segments of the Pacific Ring of Fire. A further extension of this study is being carried out, to incorporate the complexities in the underlying different seismotectonic regimes. Lastly, the observed trend of seismic activity on the rise is worrisome. It would be imperative that Indonesia must prepare: Earthquake-resistant buildings, improved warning systems and practical evacuation protocols must be prioritized. Machine Learning and

Deep Learning based methods may become the key to fostering these efforts.

Acknowledgement Nishtha Srivastava appreciates the "KI-Nachwuchswissenschaftlerinnen" - grant SAI 01IS20059 by the Bundesministerium für Bildung und Forschung - BMBF. Calculations were performed at the Frankfurt Institute for Advanced Studies' new GPU cluster, funded by BMBF for the project Seismologie und Artifizielle Intelligenz (SAI). Kai Zhou and Jan Steinheimer are supported by the BMBF through ErUM-Data funding and the Samson AG AI grant. Kai Zhou also thanks the GPU grant provided by the NVIDIA Corporation. Horst Stöcker acknowledges the Judah M. Eisenberg Professur Laureatus - Chair of the Walter Greiner Gesellschaft and of the Fachbereich Physik at Goethe Universität Frankfurt. Authors also appreciate the feedback received from Dr Madhusree Mukerjee. References 1.Kato, A. & Ben-Zion, Y. The generation of large earthquakes.Nat. Rev. Earth Environ.1–14 (2020). 2.Daly, M. C., Cooper, M. A., Wilson, I. D. & Hooper, B. D. Cenozoic plate tectonics and basin evolution in indonesia.Mar.Petroleum Geol.8, 2–21 (1991). 3.Hamilton, W. Tectonic map of indonesia: A progress report (no. 70-150).US Geol. Surv.(1970). 4.McCaffrey, R. The tectonic framework of the sumatran subduction zone.Annu. Rev. Earth Planet. Sci.37, 345–366 (2009). 5.Giardini, D. Frequency distribution and quantification of deep earthquakes.J. Geophys. Res. Solid Earth93(B3),2095–2105 (1988). 6.Howell Jr, B. On the saturation of earthquake magnitudes.Bull. Seismol. Soc. Am.71(5), 1401–1422 (1981). 7.Geller, R. Scaling relations for earthquake source parameters and magnitudes.Bull. Seismol. Soc. Am.66(5), 1501–1523(1976). 8. Kanamori, H. Magnitude scale and quantification of earthquakes. Tectonophysics 93(3-4), 185–199 (1983). 9. Habermann, R. Consistency of teleseismic reporting since 1963. Bull. Seismol. Soc. Am. 72(1), 93–111 (1982). 10. Hall, R. Indonesia, geology. Encycl. Islands, Univ. California Press. Berkeley, California, 454–460 (2009). 11. Storchak, A., D. et al. The isc-gem global instrumental earthquake catalogue (1900–2009): introduction. Phys. Earth Planet. Interiors 239, 48–63 (2015). 12. Rasmussen, C. E. & Williams, C. K. I. Gaussian processes for machine learning. The MIT Press. (2016). 3. Pedregosa, F. et al. Scikit-learn: Machine learning in python. J. Mach. Learn. Res. 12, 2825– 2830 (2011). 14. Hyndman, R. & Athanasopoulos, G. Forecasting: principles and practice. OTexts, year = 2018, . 15. Bozdogan, H. Model selection and akaike’s information criterion (aic): The generaltheory and its analytical extensions. Psychometrika 52, 345–370 (1987). 16. Lay, T. et al. The great sumatra-andaman earthquake of 26 december 2004. science 308(5725), 1127–1133 (2005). 17. Newcomb, K. & McCann, W. Seismic history and seismotectonics of the sunda arc. J. Geophys. Res. Solid Earth 92(B1), 421–439 (1987). 18. Zachariasen, J., Sieh, K., Taylor, F., Edwards, R. & Hantoro, W. Submergence and uplift associated with the giant 1833 sumatran subduction earthquake: Evidence from coral microatolls. J. Geophys. Res. Solid Earth 104(B1), 895–919 (1999). 19. Natawidjaja, D. et al. Paleogeodetic records of seismic and aseismic subduction from central sumatran microatolls, indonesia. J. Geophys. Res. Solid Earth 109(B4) (2004). 20. McCann, W., Nishenko, S., Sykes, L. & Krause, J. Seismic gaps and plate tectonics: seismic potential for major boundaries. Earthq. prediction seismicity patterns 1082–1147 (1979). 21. Bowman, D. D., G. Ouillon, C. G. Sammis, A. Sornette, and D. Sornette, An observational test of the critical earthquake concept, J. Geophys. Res., 103, 24,359–24,372 (1998). 22. Bowman, D. D., and G. C. P. King (2001), Accelerating seismicity and stress accumulation before large earthquakes, Geophys. Res. Lett., 28, 4039– 4042. 23. Brehm, D. J., and L. W. Braile (1998), Intermediate-term earthquake prediction using precursory events in the new Madrid seismic zone, Bull. Seismol. Soc. Am., 88, 564– 580. 24. Bufe, C. G., and D. J. Varnes (1993), Predictive modeling of the seismic cycle of the greater San Francisco Bay region, J. Geophys. Res., 98, 9871– 9883. 25. Bufe, C. G., S. P. Nishenko, and D. J. Varnes (1994), Seismicity trends and potential for large earthquakes in the Alaska-Aleutian region, Pure Appl. Geophys., 142, 83–99. 26. Jaume´, S. C. (2000), Changes in earthquake size-frequency distributions underlying accelerating seismic moment/energy release, in Geocomplexity and the Physics of Earthquakes, Geophys. Monogr. Ser., vol. 120, edited by J. B. Rundle, D. L. Turcotte, and W. Klein, pp. 199 – 210, AGU, Washington, D. C. 27. Jaume´, S., and M. Bebbington (2004), Accelerating seismic release from a self-correcting stochastic model, J. Geophys. Res., 109, B12301, doi:10.1029/2003JB002867. 28. Jaume´, S. C., and L. R. Sykes (1999), Evolving toward a critical point: A review of accelerating seismic moment/energy release prior to large and great earthquakes, Pure Appl. Geophys., 155, 279– 305. 29. King, G. C. P., and D. D. Bowman (2003), The evolution of regional seismicity between large earthquakes, J. Geophys. Res., 108(B2), 2096, doi:10.1029/2001JB000783. 30. Main, I. G. (1999), Applicability of time-to-failure analysis to accelerated strain before earthquakes and volcanic eruptions, Geophys. J. Int., 139, 1–6. 31. Papazachos, B. C., and C. B. Papazachos (2001), Precursory accelerated Benioff strain in the Aegean area, Ann. Geofis., 44, 461– 474. 32. Papazachos, B. C., A. S. Savvaidis, G. F. Karakaisis, and C. B. Papazachos (2002), Precursory accelerating seismic crustal deformation in the northwestern Anatolia fault zone, Tectonophysics, 347, 217– 230. 33. Robinson, R. (2000), A test of the precursory accelerating moment release model on some recent New Zealand earthquakes, Geophys. J. Int., 140, 568–576. 34. Rundle, J. B., W. Klein, D. L. Turcotte, and B. D. Malamud (2000), Precursory seismic activation and critical-point phenomena, Pure Appl. Geophys., 157, 2165–2182. 35. Saleur, H., C. G. Sammis, and D. Sornette (1996), Discrete scale invariance, complex fractal dimensions, and long-periodic fluctuations in seismicity, J. Geophys. Res., 101, 17,661– 17,677. 36. Sammis, C. G., and S. W. Smith (1999), Seismic cycles and the evolution of stress correlation in cellular automaton models of finite fault networks, Pure Appl. Geophys., 155, 307– 334. 37. Varnes, D. J. (1989), Predicting earthquakes by analyzing accelerating precursory seismic activity, Pure Appl. Geophys., 130, 661– 686. 38. Vere-Jones, D., R. Robinson, and W. Yang (2001), Remarks on the accelerated moment release model: Problems of model formulation, simulation and estimation, Geophys. J. Int., 144, 517– 531. 39. Yang,W., D. Vere-Jones, and M. Li (2001), A proposed method for locating the critical point of a future earthquake using the critical earthquake concept, J. Geophys. Res., 106, 4121– 4128. 40. Zöller, G., and S. Hainzl (2002), A systematic spatiotemporal test of the critical point hypothesis for large earthquakes, Geophys. Res. Lett., 29(11), 1558, doi:10.1029/2002GL014856.