PUBLICATIONS. Geophysical Research Letters

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1 PUBLICATIONS Geophysical Research Letters RESEARCH LETTER Key Points: Empirical orthogonal functions (EOFs) are used to identify effective locations of offshore tsunami measurements An optimization method based on a mesh adaptive direct search (MADS) is used to reduce the measurement points Smaller number (23 points) of better distributed locations than the existing network would produce slip distributions with smaller errors Supporting Information: Supporting Information S1 Data Set S1 Correspondence to: I. E. Mulia, iyan@eri.u-tokyo.ac.jp; iyan.e.m@gmail.com Citation: Mulia, I. E., Gusman, A. R., & Satake, K. (2017). Optimal design for placements of tsunami observing systems to accurately characterize the inducing earthquake. Geophysical Research Letters, 44, 12,106 12, org/ Received 22 SEP 2017 Accepted 29 NOV 2017 Accepted article online 4 DEC 2017 Published online 17 DEC American Geophysical Union. All Rights Reserved. Optimal Design for Placements of Tsunami Observing Systems to Accurately Characterize the Inducing Earthquake Iyan E. Mulia 1, Aditya Riadi Gusman 1, and Kenji Satake 1 1 Earthquake Research Institute, University of Tokyo, Tokyo, Japan Abstract Recently, there are numerous tsunami observation networks deployed in several major tsunamigenic regions. However, guidance on where to optimally place the measurement devices is limited. This study presents a methodological approach to select strategic observation locations for the purpose of tsunami source characterizations, particularly in terms of the fault slip distribution. Initially, we identify favorable locations and determine the initial number of observations. These locations are selected based on extrema of empirical orthogonal function (EOF) spatial modes. To further improve the accuracy, we apply an optimization algorithm called a mesh adaptive direct search to remove redundant measurement locations from the EOF-generated points. We test the proposed approach using multiple hypothetical tsunami sources around the Nankai Trough, Japan. The results suggest that the optimized observation points can produce more accurate fault slip estimates with considerably less number of observations compared to the existing tsunami observation networks. 1. Introduction In response to several unanticipated large tsunami occurrences in the last decades, developments of an effective tsunami observing system have become a major concern among researchers as well as funding agencies. A number of tsunami observation networks are currently in operation throughout the world, and most of them are in Japan. One of the most remarkable network for tsunami observations is probably the S-net systems, where 150 seafloor observatories including both seismometers and ocean bottom pressure (OBP) gauges, also known as bottom pressure recorder, are connected by fiber optic cables of 5,800 km length with km spacing along the Japan Trench (Kanazawa, 2013). Another dense array of cabled OBP gauges called the Dense Oceanfloor Network System for Earthquakes and Tsunamis (DONET) systems consists of DONET1 (20 stations) and DONET2 (29 stations) and is available around the Nankai Trough (Kaneda et al., 2015). In addition, a few OBP-based systems are operating and managed by multiple agencies in Japan (see Tsushima & Ohta, 2014). Furthermore, tsunami measurements based on Global Positioning System (GPS) buoys have been deployed along the coast of Japan as well (Kawai et al., 2013). Outside Japan, a cabled observation network similar to the DONET and S-net for a more comprehensive measurement of other oceanic parameters was installed in Canada called the North-East Pacific Time-series Undersea Networked Experiments system (Barnes et al., 2008). Another large-scale ocean observing system is the National Science Foundation s Ocean Observatories Initiatives ( last accessed on 4 November 2017). Across the world oceans, global tsunami observation networks named the Deep-ocean Assessment and Reporting of Tsunamis (DART) systems developed mainly for transoceanic tsunami forecasting purposes were installed (Pacific = 47 stations, Atlantic = 7 stations, and Indian = 6 stations) (Bernard & Titov, 2015; González et al., 2005; Mungov et al., 2013; Titov, 2009). Descriptions on the data transmission, processing, and usage of the aforementioned tsunami observing systems have been well documented together with specifications of the associated instruments, as reviewed and summarized in Rabinovich and Eblé (2015). However, details on the selection of locations for placing the measurement devices are limited. Particularly for tsunami observations, the placement is often associated with historical records at the area of interest supported by expert judgments with various deciding factors, e.g., technical and financial limitations (Araki et al., 2008). Legal aspects such as public fishing rights can also be taken into consideration (Abe & Imamura, 2013). An attempt to incorporate useful information with emphasis on the tsunami warning efficacy to design tsunami observation networks has previously been proposed (Omira et al., 2009; Schindelé et al., 2008). They thoroughly analyzed and identified the locations MULIA ET AL. 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2 for the placement of tsunami observing systems based on several criteria, but without actually applying an optimization algorithm. Spillane et al. (2008) introduced an optimization approach for placements of a few DART systems off Aleutians and Alaska. They enforced certain constraints in the optimization to determine the optimal tsunami detection time for tsunami early warning purposes. In this study, we use the same optimization algorithm as in Spillane et al. (2008) based on the mesh adaptive direct search (MADS) algorithm, but for a slightly different purpose and different optimization settings. Furthermore, we utilize a dimensionality reduction approach to efficiently initiate the optimization. Here we stress our design for the purpose of an accurate estimation of the fault slip distribution of tsunamigenic earthquakes within a targeted area, which may in turn lead to improved tsunami forecasts. We apply our method to the Nankai Trough region that has generated several major submarine earthquakes in the past: the 1946 Nankai (M8.0), 1944 Tonankai (M7.9), 1854 Ansei Nankai (M8.4), 1854 Ansei Tokai (M8.4), and 1707 Hoei (M8.4) earthquakes. A summary of historical tsunami events in Japan including the Nankai Trough can be found in Satake (2015). As a region that has frequently hosted large earthquakes and tsunamis, the Nankai Trough attracts the Japanese authorities to conduct extensive researches in order to mitigate future disasters in the region. Part of the research products advocated by the Central Disaster Management Council (CDMC) of Japan are hypothetical tsunami sources that can be considered as a reference for the future tsunamis originating from the Nankai subduction zone. Here we develop a design of a future tsunami observation network that is optimal with respect to the CDMC sources. Once the reference sources are selected, the first stage is to locate the best initial observation points. Similar to other oceanic or atmospheric field of quantities, these locations correspond to the extrema of the empirical orthogonal function (EOF) spatial modes derived from parameters of interest as described in section 3. To appraise the benefit of utilizing the EOF, we compare inverted slips from tsunami waveforms retrieved at the EOF-generated points against predefined and random points with the same number of observations. In the subsequence stage, we then use the EOF-generated points as an initial condition for further optimization by the MADS algorithm. The optimization works by systematically removing unnecessary points while reducing a specified cost function, which is the error of inverted slips relative to the references. The final result is a distribution of observation points that can produce better slip estimations compared to both the initial points and the existing observation networks in the region. 2. Hypothetical Scenarios The use of hypothetical experiments is required in designing future observations. In 2003, the CDMC introduced a hypothetical tsunami source model generated by an M8.7 earthquake (Central Disaster Management Council, 2003). The source has been widely used as a reference for a possible future tsunami in the region (Inazu et al., 2016; Mulia et al., 2017; Yasuda & Mase, 2012). More recently, the CDMC has updated the source model by including 11 different scenarios representing various slip distributions along the Nankai subduction zone (Central Disaster Management Council, 2012). Each source is characterized by the same magnitude of M9.1, but with different locations of asperities. Detailed descriptions of the sources (in English) were clearly explained in Goda et al. (2017). In our study, the updated sources provide more variations that we can take into account to develop an optimal observation network. The original source models developed by the CDMC each consist of 5,773 subfaults including plate interface subfaults and 104 subfaults that cover the Kumano splay fault (Central Disaster Management Council, 2012). The size of each subfault is 5 5 km, and the total source area is approximately km 2. The average slip values for all scenarios varies between approximately 8.8 to 11.2 m, and the large slip regions are confined at depths of less than 10 km. The moment magnitude is the same for each scenario (M9.1) with seismic moments range between and N m. The hypothetical sources also consider a kinematic source process with the assumed rupture propagation velocity of 2.5 km/s and the risetime of individual subfaults is set to 60 s. Overall, in addition to the present seismotectonic setting in the region, the hypothetical sources were also developed based on the past M8-class events. Such large earthquakes can be considered as worst-case scenarios, which is of importance for designing future observations. In this study, we develop a simplified version of the CDMC sources using a larger subfault size of km with the total number of 60 subfaults. All the fault parameters from the CDMC sources are interpolated with slight modifications to the rake and dip angle in order to generate realistic displacement patterns. Figure 1 MULIA ET AL. OPTIMAL TSUNAMI OBSERVATION NETWORK 12,107

3 Geophysical Research Letters Figure 1. Hypothetical fault slip distributions interpolated from the CDMC scenarios overlaid by the associated displacements. The continuous and broken light green contour lines indicate uplift (2 m interval) and subsidence (1 m interval), respectively. shows the interpolated slips for all scenarios together with the corresponding displacements computed using the analytical formula for elastic dislocations (Okada, 1985). Note that the interpolated slips exhibit smaller maximum slip amount than the original sources due to the larger subfault size. We also neglect the transient deformations caused by the kinematic source, assuming the instantaneous rupture, to minimize the computational cost. These simplifications are needed because our proposed method requires a long iterative process during the optimization to find the expected solution. Other than that, in our case, such a high-resolution model is not necessarily required due to the dimensionality reductions by the EOF. A few first leading modes considered in the EOF analysis extract only the main features or the most energetic parts of the source that can also be contained in a relatively low-resolution form. 3. Initialization by the EOF The observation points should be placed at the locations where the most energetic dynamics occur. Such locations can be easier to identify by reducing the complexity of a model. To that end, we use the EOF technique, also known as a proper orthogonal decomposition, which is a common approach to reduce the order of the model. Using the EOF, we can decompose any set of state variables into spatial and temporal modes. However, in our study, we focus only on the calculation of the EOF spatial modes. These modes provide information concerning the areas where modal activity is at its highest, which correspond to the main energy distribution of a system (Cohen et al., 2003). Here we derive the EOF spatial modes of tsunami amplitudes resulted from a numerical model based on the linear shallow water equation (e.g., Imamura et al., 2006) using real bathymetry data, i.e., GEBCO (Weatherall et al., 2015) resampled to 1 arc min grid size. The model domain covers an area of E and N, MULIA ET AL. OPTIMAL TSUNAMI OBSERVATION NETWORK 12,108

4 Figure 2. EOF analysis for the scenario 1 (results of the scenario 2 to 11 are shown in the supporting information). (a) Percentage of variance explained by the EOF modes for tsunami amplitudes. (b) The upper and lower figures show contour of the first and second EOF spatial modes (dimensionless), respectively, overlaid with their respective extrema locations. the simulation time is set to 60 min, and the time step is 1 s. We impose a closed reflective boundary condition along the minimum water depth of 10 m and an absorptive boundary at the open ocean. For the EOF computation, tsunami amplitudes at a specified area inside the model domain are stored every 10 s, resulting in 361 snapshots. The EOF area is limited at minimum water depth of 300 m to avoid generating points near the coast, because tsunami waveforms recorded at such locations are usually inadequate to infer the tsunami source due to the coastal morphology effects. As for the offshore limit, we extend the area toward part of the outer rise regions following the S-net configuration (see Figure 2). For the EOF decomposition, tsunami amplitudes at locations x i (i =1, p) and time or snapshots t j (j =1, n) are arranged to form a matrix F with the size of n p. Without limiting the EOF area, p is equal to the number of grids of the numerical model (216,961 grid points), which is very large. The specified EOF area only consists of 57,303 grid points; thus, the F matrix size is 361 5,7303. After removing the mean of each time series p in F, we then form the covariance matrix of F by calculating R = F T F. From here, we solve the eigenvalue problem, RC ¼ CΛ; (1) Λ is a diagonal matrix containing the eigenvalues λ i of R with the corresponding eigenvectors c i, which are column vectors of C. These eigenvectors are the EOF spatial modes, in which the first mode is associated with the largest eigenvalue. To obtain a more stable solution of the eigenvalue problem, a method based on a singular value decomposition is suggested (Björnsson & Venegas, 1997). When the modes are plotted as a map, the pattern represents a standing oscillation. Furthermore, the extrema (minima/maxima) of the first few leading EOF spatial modes are the good locations, if not optimum, to place the observation points (Yildirim et al., 2009). The explained variance on kth mode can be computed by λ k = X λ i. i In the oceanography and atmospheric sciences, the EOF analysis has been widely used to determine the best locations for placing observation points to measure parameters of interest such as tides, sea temperatures, or MULIA ET AL. OPTIMAL TSUNAMI OBSERVATION NETWORK 12,109

5 winds (e.g., Yang et al., 2010; Yildirim et al., 2009; Zhang et al., 2016). However, in their applications, the EOFbased approach was applied to oceanic and atmospheric state variables that possess a noticeable periodicity. Thus, computing the EOF from one instance at a certain period of time should relatively suffice the basic requirement, which is not the case for tsunamis. The use of multiple sources is required to account for the variability that determines the optimal configuration of the resulted tsunami observation network. We exploit the 11 source scenarios to generate the EOF spatial modes after considering the associated displacement from each source as an initial condition for the tsunami modeling. 4. Tsunami Waveform Inversion Satake (1987) proposed a method to estimate the fault slip distribution from tsunami waveforms recorded at observation stations by an inversion analysis. This is similar to the inversion of seismic waves to study earthquake sources, but the substantial advantage is that the ocean bathymetry, which controls the tsunami propagation velocity, is more accurately known than the seismic velocity structure. Many studies have successfully applied the tsunami waveform inversion to various events (e.g., Gusman et al., 2015; Percival et al., 2011; Satake et al., 2013; Tang et al., 2012; Tanioka & Satake, 2001). In our study, the method is used as one of the main components of the whole proposed algorithm. More specifically, we use the tsunami waveform inversion analysis to test the resulted observation points by comparing the inverted slips against the hypothetical sources. The errors of such a comparison are also considered as the cost function in the optimization stage. We assume that the observing system considered here is based on the OBP, where the noise level is expected to be lower than a typical surface observation such as the GPS buoy system. Therefore, a white Gaussian noise with signal-to-noise ratio estimated from maximum signal amplitude ratio to the standard noise deviation of 30:1 is added to recorded waveforms at every generated observation points. In the real case, however, the recorded tsunami waveforms at this type of measurement is subjected to several natural interferences: seismic noise (Saito et al., 2010; Satake et al., 2005), acoustic waves (Maeda et al., 2011; Nosov & Kolesov, 2007), and permanent seafloor displacements (Tsushima et al., 2012). In this synthetic experiment, we assume that all those effects have been removed or dealt as suggested by the corresponding studies. 5. Optimization to Improve the Accuracy The purpose of the optimization stage in this study is to remove initial observation points provided by the EOF that give an adverse effect to the accuracy of the tsunami waveform inversion. The optimization performs a combinatorial search of optimal observation sets that can produce the smallest error of inverted slips relative to the references. In brief, a typical formulation of an optimization is as follow, min f ðþ; i (2) i Ω where i is a vector of decision variables adjusted to minimize the cost function fsubjected to feasible set of constraints Ω. However, in this study, we adopt an unconstrained optimization. Here the number of decision variables is equal to the number of observation points generated by the EOF. We restrict the decision variable values to 0 and 1, in which i = 1 if we consider the observation points to be included in the inversion analysis, or i = 0 otherwise. The cost function is the sum of slip estimate errors with respect to the 11 hypothetical sources. During the optimization, the tsunami waveform inversion is computed iteratively until no more reduction of the cost function is observed. A schematic illustration of the proposed method is shown in Figure S1 in the supporting information. We use the MADS algorithm first developed by Audet and Dennis (2006) with a free software package called the nonlinear optimization by mesh adaptive algorithm (Le Digabel, 2011). 6. Results As shown in Figure 2 (and Figures S2 to S11), the explained variances are predominantly represented by the first two leading EOF modes for all scenarios. These modes depict the most energetic tsunami dynamics in the specified region that can be attributed mainly to the tsunami source, as expected in a typical near-field case. Since the number of extrema on each mode varies for different state variable patterns, we need to determine the appropriate number of extrema required for our application. Yildirim et al. (2009) and Yang MULIA ET AL. OPTIMAL TSUNAMI OBSERVATION NETWORK 12,110

6 Figure 3. Performance comparisons between the EOF-generated, predefined, and randomly distributed observation points. (a) EOF-generated points. (b) Predefined points. (c) Random points (one seed). (d) Comparisons of RMSE for all scenarios between the EOF-generated, predefined, and 10 random point seeds. Result examples using the scenario 1 are shown in Figures 3a 3c: station locations (left), inverted slip (middle), and errors (right). et al. (2010) tried various combinations of EOF modes and the number of extrema to obtain the best result. Similarly, after some trial-and-error, we define that the four largest extrema of the first two EOF modes as our preferred initial locations to place the tsunami gauges. However, we limit the distance between points at 30 km radius (comparable to the S-net) to avoid redundancies; thus, the extrema of the lower mode located within the specified radius are removed. For the most part, spatial distributions of the EOFgenerated points are in line with the location of asperities or large slip regions at each source. This is a reasonable and desired gain, because we intend to capture the main energy of the tsunami that largely characterizes the source. Combining the EOF-generated points from the total 11 scenarios results in several clustered or even collocated points. This means that the locations are considered optimal for more than one sources but may cause superfluous observations for an actual single tsunami event. Therefore, we apply the same threshold of 30 km minimum distance between points, by which the clustered points located within the threshold are replaced by only one representative. As a result, we obtain 30 initial observation points (see Figure 3a). To appraise their performance, we compare the inverted slips from those points against predefined observation locations. Given that the source area is known beforehand, intuitively, one will distribute equidistance points covering the source area as the preferred observation locations. However, it is difficult to determine the number of required points to obtain the desired result. For a fair comparison with the EOF result, here we MULIA ET AL. OPTIMAL TSUNAMI OBSERVATION NETWORK 12,111

7 Figure 4. Performance comparisons between the optimized and existing observation points. (a) Optimized points. (b) Existing points. (c) Comparisons of RMSE for all scenarios between the optimized (EOF + MADS), initial (EOF), and existing observation points. Result examples using the scenario 1 are shown in Figures 4a and 4b: station locations (left), inverted slip (middle), and errors (right). distribute 30 equidistance points covering the source area (Figure 3b). Additionally, we also compare with randomly generated points using the same number of observations and the same threshold radius of 30 km (Figure 3c). We quantify the error in terms of a root-mean-square error (RMSE) and a relative error in percentage as shown in the Figure 3a (right), 3b, and 3c. Figure 3c shows an instance of the random point result, and Figure 3d indicates the RMSE of the EOF results compared to the predefined points, and to that of yielded by 10 random seeds for all scenarios (see Figure S12 for point locations). The results clearly suggest that EOF-generated points are located at the area where the trace of the tsunami should be retrieved for an accurate source characterization. Furthermore, the reasonable initial number of observations will aid the optimization process in the subsequent stage, which is unlikely to be achieved by simply distributing dense equidistance points. As suggested by Robinson and Glenn (1999), sampling from predetermined locations with uniform spatiotemporal scale may be inefficient, because mostly only a small subset of the measurements is required to produce an acceptable result. Voronin et al. (2015) reported that based on synthetic experiments using an ideal flat bathymetry, one can improve the inversion accuracy by increasing the number of observations. However, this is not necessarily true for a real bathymetry and noisy data. Tsunami waveforms recorded in the vicinity of where drastic changes in bathymetric profile exist and accumulation of noise can cause the deterioration of the solution. Voronina (2016) further confirmed the result using real tsunami data. The configuration of our optimization approach leads to identification of such ineffective measurements. Initially, the optimization starts with all of the EOF-generated points are being activated (i = 1 in equation (2)), then it prunes the observations while reducing the cost function. Such an approach had also been used in a previous study to remove redundant Green s functions in the inversion analysis (Mulia & Asano, 2016). The MADS algorithm converges after 31 function evaluations/iterations and results in 23 observation points (Figure 4a). Figure 4c shows that the optimized points (EOF + MADS) produce smaller errors (RMSE m) compared to that of the initial 30 MULIA ET AL. OPTIMAL TSUNAMI OBSERVATION NETWORK 12,112

8 points by the EOF alone (RMSE m) for all scenarios. The inverted slips using the optimized 23 observation points for the scenario 2 to 11 are shown in Figures S13 and S14. From these results, it is evident that the MADS algorithm can further improve the accuracy of the EOF results and reduce the observation points simultaneously. Finally, we compare our result with the existing observation stations consisted of 60 cabled OBP gauges (including the DONET systems) and eight GPS buoys shown in Figure 4b (left). Both the 30 initial points and the 23 optimized points can produce better accuracies than the 68 existing observation stations (RMSE m). Figure 4c indicates that the existing stations produce relatively smaller errors only at scenarios where the large slip regions are located at the eastern part of the domain (>135 E). This is an anticipated outcome because the station locations are concentrated at that area, whereas there are only a few stations at the western part. Our resulted points, on the other hand, are spread sufficiently to capture the EOF modes. Furthermore, several of the existing stations may not provide substantial information required for the inversion analysis, which is similar to the initial EOF-generated points removed after the optimization process by the MADS algorithm. However, it should be noted that some of the existing observing systems are also equipped with instruments for measuring and monitoring seismic activities. Therefore, our design is optimal specifically in a sense of tsunami observations. Acknowledgments This study is conducted under the Japan Society for the Promotion of Science (JSPS) fellowships for an international research fellow, as well as KAKENHI JP17F The bathymetry data are available from The British Oceanographic Data Centre ( systems/gebco_gridded_bathymetry_ data). The optimization code is part of the OPTI Toolbox downloaded from OPTI/. The EOF code is provided by Chad A. Greene of the University of Texas Institute for Geophysics (UTIG) downloaded from eof. The authors would like to thank Shingo Watada, M. Jakir Hossen, and Yuchen Wang for their constructive comments on the initial draft. 7. Discussion and Conclusions The 11 source scenarios used in our study represent a wide range of realistic slip distributions and account for plausible key features of the future Nankai Trough tsunamigenic earthquakes. However, a considerable increase of source variations is necessary to fully quantify the uncertainties associated with the characteristics of the anticipated future tsunamis in the region. Goda et al. (2017) proposed stochastic source models by combining the 11 CDMC sources with a spectral synthetic method for megathrust subduction earthquakes. The large amount of slip patterns resulted from the stochastic simulation can facilitate the assessment of uncertainty. In their study, the accounted source uncertainties are then related to probabilistic tsunami hazard and risk analyses in the coastal areas. We believe that such an approach can also be used to enhance the reliability of the designed tsunami observation networks, and thus, future efforts should be directed toward it. In view of the efficacy of the tsunami waveform inversion, our design is particularly developed to accurately estimate the fault slip distribution in the area of interest. Nevertheless, the accurate source characterization can also lead to accurate tsunami forecasts. Further investigations should be carried out if one intends to emphasize on a practical tsunami early warning system. This can be achieved by introducing appropriate constraints to the solution (Schindelé et al., 2008; Spillane et al., 2008; Omira et al., 2009). For example, a timely warning dissemination is strongly related to the location of observations relative to the shoreline or highly populated areas. Such a condition should be incorporated in the formulation of the optimization algorithm in order to advocate an effective warning. Additionally, complementary scenarios from far-field cases are probably necessary, so that the design is suitable for more regional events. Together with the uncertainty quantification, these will be considered in the future study to produce effective and efficient observations for both tsunami source estimation and forecasting. We have demonstrated the use of properly configured algorithms to design an optimal tsunami observation network. First, the determination of the EOF spatial modes has helped to quantitatively identify the optimal initial locations for placement of measurement devices, which is largely associated with the tsunami energy distributions characterizing the source. Second, the optimization by the MADS can lead to the improvement of inversion accuracy by removing redundant or ineffective measurements from the EOF-generated points. We expect that such detailed algorithmic descriptions on the methodology will provide additional valuable information to the common approach in deciding tsunami observation locations based on historical events and other relevant factors. Moreover, further developments of the method are expected to ultimately provide a universal blueprint for deployments of future tsunami observation networks. References Abe, I., & Imamura, F. (2013). Problems and effects of a tsunami inundation forecast system during the 2011 Tohoku earthquake. Journal of Japan Society of Civil Engineers, 1(1), Araki, E., Kawaguchi, K., Kaneko, S., & Kaneda, Y. (2008). Design of deep ocean submarine cable observation network for earthquakes and tsunamis. In OCEANS 2008-TS/IEEE Kobe Techno-Ocean (pp. 1 4). Kobe, Japan: IEEE. MULIA ET AL. OPTIMAL TSUNAMI OBSERVATION NETWORK 12,113

9 Audet, C., & Dennis, J. E. Jr. (2006). Mesh adaptive direct search algorithms for constrained optimization. SIAM Journal on Optimization, 17, Barnes, C. R., Best, M. M., & Zielinski, A. (2008). The NEPTUNE Canada regional cabled ocean observatory. Technology (Crayford, England), 50. Bernard, E., & Titov, V. (2015). Evolution of tsunami warning systems and products. Philosophical Transactions of the Royal Society A, 373(2053), Björnsson, H., & Venegas, S. A. (1997). A manual for EOF and SVD analyses of climatic data. CCGCR Report, 97(1), Central Disaster Management Council (2003). Risk Assessment Results of Tokai-Tonankai-Nankai Earthquake Disaster. Cabinet Office of the Government of Japan, Tokyo. Retrieved from Central Disaster Management Council (2012). Working Group Report on Mega-Thrust Earthquake Models for the Nankai Trough, Japan. Cabinet Office of the Government of Japan, Tokyo. Retrieved from Cohen, K., Siegel, S., & McLaughlin, T. (2003). Sensor placement based on proper orthogonal decomposition modeling of a cylinder wake. In 33rd AIAA Fluid Dynamics Conference, Orlando (Vol. 4259, pp ). Orlando, FL: AIAA. Goda, K., Yasuda, T., Mai, P. M., Maruyama, T., & Mori, N. (2017). Tsunami Simulations of Mega-Thrust Earthquakes in the Nankai Tonankai Trough (Japan) Based on Stochastic Rupture Scenarios. Geological Society of London, Special Publications, 456, SP González, F. I., Bernard, E. N., Meinig, C., Eble, M. C., Mofjeld, H. O., & Stalin, S. (2005). The NTHMP Tsunameter network. Natural Hazards, 35(1), Gusman, A. R., Murotani, S., Satake, K., Heidarzadeh, M., Gunawan, E., Watada, S., & Schurr, B. (2015). Fault slip distribution of the 2014 Iquique, Chile, earthquake estimated from ocean-wide tsunami waveforms and GPS data. Geophysical Research Letters, 42, org/ /2014gl Imamura, F., Yalciner, A. C., & Ozyurt, G. (2006). Tsunami modelling manual. UNESCO IOC international training course on Tsunami Numerical Modelling. Inazu, D., Waseda, T., Hibiya, T., & Ohta, Y. (2016). Assessment of GNSS-based height data of multiple ships for measuring and forecasting great tsunamis. Geoscience Letters, 3(1), Kanazawa, T. (2013). Japan trench earthquake and tsunami monitoring network of cable-linked 150 ocean bottom observatories and its impact to Earth disaster science. In Underwater Technology Symposium (UT), 2013 IEEE International (pp. 1 5). Tokyo, Japan: IEEE. Kaneda, Y., Kawaguchi, K., Araki, E., Matsumoto, H., Nakamura, T., Kamiya, S., Takahashi, N. (2015). Development and application of an advanced ocean floor network system for megathrust earthquakes and tsunamis. In Seafloor Observatories (pp ). Berlin: Springer. Kawai, H., Satoh, M., Kawaguchi, K., & Seki, K. (2013). Characteristics of the 2011 Tohoku tsunami waveform acquired around Japan by NOWPHAS equipment. Coastal Engineering Journal, 55(03), Le Digabel, S. (2011). Algorithm 909: NOMAD: Nonlinear optimization with the MADS algorithm. ACM Transactions on Mathematical Software (TOMS), 37, Maeda, T., Furumura, T., Sakai, S., & Shinohara, M. (2011). Significant tsunami observed at ocean-bottom pressure gauges during the 2011 off the Pacific coast of Tohoku earthquake. Earth, Planets and Space, 63, Mulia, I. E., & Asano, T. (2016). Initial tsunami source estimation by inversion with an intelligent selection of model parameters and time delays. Journal of Geophysical Research: Oceans, 121, Mulia, I. E., Inazu, D., Waseda, T., & Gusman, A. R. (2017). Preparing for the future Nankai Trough tsunami: A data assimilation and inversion analysis from various observational systems. Journal of Geophysical Research: Oceans, 122, JC Mungov, G., Eblé, M., & Bouchard, R. (2013). DART tsunameter retrospective and real-time data: A reflection on 10 years of processing in support of tsunami research and operations. Pure and Applied Geophysics, 170(9-10), Nosov, M., & Kolesov, V. (2007). Elastic oscillations of water column in the 2003 Tokachi-oki tsunami source: In situ measurements and 3-D numerical modelling. Natural Hazards and Earth System Sciences, 7, Okada, Y. (1985). Surface deformation due to shear and tensile faults in a half-space. Bulletin of the Seismological Society of America, 75(4), Omira, R., Baptista, M. A., Matias, L., Miranda, J. M., Catita, C., Carrilho, F., & Toto, E. (2009). Design of a sea-level tsunami detection network for the Gulf of Cadiz. Natural Hazards and Earth System Sciences, 9, Percival, D. B., Denbo, D. W., Eblé, M. C., Gica, E., Mofjeld, H. O., Spillane, M. C., Titov, V. V. (2011). Extraction of tsunami source coefficients via inversion of DART buoy data. Natural Hazards, 58, Rabinovich, A. B., & Eblé, M. C. (2015). Deep-ocean measurements of tsunami waves. Pure and Applied Geophysics, 172(12), Robinson, A. R., & Glenn, S. M. (1999). Adaptive sampling for ocean forecasting. Naval Research Reviews, 51(2), Saito, T., Satake, K., & Furumura, T. (2010). Tsunami waveform inversion including dispersive waves: The 2004 earthquake off Kii Peninsula, Japan. Journal of Geophysical Research, 115, B Satake, K. (1987). Inversion of tsunami waveforms for the estimation of a fault heterogeneity: Method and numerical experiments. Journal of Physics of the Earth, 35(3), Satake, K. (2015). Geological and historical evidence of irregular recurrent earthquakes in Japan. Philosophical Transactions of the Royal Society A, 373(2053), Satake, K., Baba, T., Hirata, K., Iwasaki, S. I., Kato, T., Koshimura, S., Terada, Y. (2005). Tsunami source of the 2004 off the Kii Peninsula earthquakes inferred from offshore tsunami and coastal tide gauges. Earth, Planets and Space, 57, BF Satake, K., Fujii, Y., Harada, T., & Namegaya, Y. (2013). Time and space distribution of coseismic slip of the 2011 Tohoku earthquake as inferred from tsunami waveform data. Bulletin of the Seismological Society of America, 103(2B), Schindelé, F., Loevenbruck, A., & Hébert, H. (2008). Strategy to design the sea-level monitoring networks for small tsunamigenic oceanic basins: The western Mediterranean case. Natural Hazards and Earth System Sciences, 8, Spillane, M. C., Gica, E., Titov, V. V., & Mofjeld, H. O. (2008). Tsunameter network design for the US DART arrays in the Pacific and Atlantic Oceans (NOAA Tech. Memo., OAR PMEL-143) (165 pp.). Tang, L., Titov, V. V., Bernard, E. N., Wei, Y., Chamberlin, C. D., Newman, J. C., Gica, E. (2012). Direct energy estimation of the 2011 Japan tsunami using deep-ocean pressure measurements. Journal of Geophysical Research, 117, C MULIA ET AL. OPTIMAL TSUNAMI OBSERVATION NETWORK 12,114

10 Tanioka, Y., & Satake, K. (2001). Detailed coseismic slip distribution of the 1944 Tonankai earthquake estimated from tsunami waveforms. Geophysical Research Letters, 28, Titov, V. V. (2009). Tsunami forecasting. In The Sea, Volume 15: Tsunamis (chap. 12, pp ). Cambridge, MA: Harvard University Press. Tsushima, H., Hino, R., Tanioka, Y., Imamura, F., & Fujimoto, H. (2012). Tsunami waveform inversion incorporating permanent seafloor deformation and its application to tsunami forecasting. Journal of Geophysical Research, 117, B JB Tsushima, H., & Ohta, Y. (2014). Review on near-field tsunami forecasting from offshore tsunami data and onshore GNSS data for tsunami early warning. Journal of Disaster Research, 9(3), Voronin, V. V., Voronina, T. A., & Tcheverda, V. A. (2015). Inversion method for initial tsunami waveform reconstruction. Natural Hazards and Earth System Sciences, 15(6), Voronina, T. A. (2016). Recovering a tsunami source and designing an observational system based on an r-solution method. Numerical Analysis and Applications, 9(4), Weatherall, P., Marks, K. M., Jakobsson, M., Schmitt, T., Tani, S., Arndt, J. E., Wigley, R. (2015). A new digital bathymetric model of the world s oceans. Earth and Space Science, 2(8), Yang, X., Venturi, D., Chen, C., Chryssostomidis, C., & Karniadakis, G. E. (2010). EOF-based constrained sensor placement and field reconstruction from noisy ocean measurements: Application to Nantucket Sound. Journal of Geophysical Research, 115, C doi.org/ /2010jc Yasuda, T., & Mase, H. (2012). Real-time tsunami prediction by inversion method using offshore observed GPS buoy data: Nankaido. Journal of Waterway, Port, Coastal, and Ocean Engineering, 139(3), Yildirim, B., Chryssostomidis, C., & Karniadakis, G. E. (2009). Efficient sensor placement for ocean measurements using low-dimensional concepts. Ocean Modelling, 27, Zhang, Z., Yang, X., & Lin, G. (2016). POD-based constrained sensor placement and field reconstruction from noisy wind measurements: A perturbation study. Mathematics, 4(2), MULIA ET AL. OPTIMAL TSUNAMI OBSERVATION NETWORK 12,115