PROBABILISTIC APPROACH FOR TSUNAMI INUNDATION MAPPING

Transcription

1 UNIVERSITY OF HAWAI'I LIBRARY PROBABILISTIC APPROACH FOR TSUNAMI INUNDATION MAPPING A THESIS SUBMITTED TO THE GRADUATE DIVISION OF THE UNIVERSITY OF HA WAn IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN OCEAN AND RESOURCES ENGINEERING MAY 2008 BY Megan L. Craw Thesis Committee: Kwok Fai Cheung, Chairperson Geno Pawlak Ian Robertson

2 We certify that we have read this thesis and that, in our opinion, it is satisfactory in scope and quality as a thesis for the degree of Master of Science in Ocean and Resources Engineering. THESIS COMMITTEE dz~ e on ~ ii

3 ACKNOWLEDGEMENTS I would like to express my appreciation to my advisor Dr. Kwok Fai Cheung for the opportunity to participate in this work, and for his advice and patience during this process. I am grateful to my committee members, Dr. Geno Pawlak and Dr. Ian Robertson, for their insights and recommendations for further analysis. Thanks and recognition to Mr. George Curtis for his comments and generous technical discussions. Many thanks to Ms. Edith Katada for her help with all the necessary paperwork. I appreciate the friendship of all the Ocean and Resources Engineering students who have provided input and suggestions, specifically Dr. Yong Wei, Yoshiki Yamazaki, Volker Roeber, Sophie Munger, Alejandro Sanchez, Pablo Duarte-Quiroga, Justin Goo, Justin Stopa and Abdulla Mohamed. I would like to thank and acknowledge my parents, family and friends for their generous encouragement and support. Special gratitude goes to Chet, for his love and refreshing perspective. Financial support in the form of a graduate research assistantship was provided by Hawaii State Civil Defense and the University of Hawaii Sea Grant Program. iii

4 ABSTRACT A probabilistic approach is necessary to assess the future tsunami hazard for a given shoreline. Given the complicated nature of tsunamis, it seems intuitive that it is best to perform statistical analysis considering both the generation and far-field effects of a tsunami in a single process. It is important not to mix the frequency-of-occurrence distributions or historic runup data from multiple sources in order to make up for a small sample size, although this is a common approach of current probabilistic tsunami hazard assessment. The method presented in this thesis generates events of equal probability of occurrence by systematic sampling of the source extremal distribution curve and uses a two-dimensional model to propagate the resulting tsunamis across the ocean and compute the inundation on land. The model results are then compiled so an inundation limit with a desired return period can be computed. This methodology is demonstrated with a case study considering the Alaska-Aleutian Seismic Zone (AASZ) and the far-field location on the north shore of Oahu, where historic runup data is used for model calibration. This method yields probabilistic inundation estimates without mixing runup data from different tsunamigenic sources or simulating incomplete data records. This method is uniquely expandable, and can include additional tsunami source locations and mechanisms, each with its own unique probabilistic distribution. This probabilistic approach to tsunami inundation mapping will be very useful for hazard assessments and generating quantifiable results for mitigation efforts. iv

5 TABLE OF CONTENTS List of Tables... vi L IS t 0 ff' 19ures Vll.. Chapter 1. Introduction Previous Approaches Goals and Objectives Chapter 2. Tsunami Source Characterization Tsunamigenic Source Tsunami and Earthquake Catalogs Spatial Distribution of Earthquake and Tsunami Occurrence Source Parameter Configuration Statistical Distributions Chapter 3. Probabilistic Tsunami Inundation Mapping Tsunami Modeling Probabilistic Inundation Grid Chapter 4. Results and Discussion Data Analysis Probabilistic Inundation Maps Additional Considerations Future Application Chapter 5. Conclusions and Future Work References I v

6 LIST OF TABLES Table Page 1. Earthquake and Tsunami Source Data Catalogs Data Catalog Compilation Compiled Data Catalog Analysis Magnitude Grouping Scenarios Catalog Data Used for Probabilistic Analysis Historic Tsunami Event Source Parameters Data Regression Analysis Results and Sampled Magnitude Values Nested Grid Coverage and Resolution Bathymetry Data Sources and Resolution Summary Parameters of Events Tested Sample Fault Weight Factors vi

7 LIST OF FIGURES Figure Page 1. Definition sketch of planar fault mode! Bathymetry, seismic and tsunami events ( ) for the AASZ Earthquake source parameters for the AASZ Seismic events and approximate rupture areas Fault length and width variation with magnitude Constant (a) and variable length (b) fault scenarios Probabilistic analysis curve fitting Numerical model nested grid setup Sketch of probabilistic space Probabilistic grid development Sample inundation lines Probabilistic inundation grid Runup comparison and Probabilistic Inundation Map vii

8 CHAPTER 1 IN1RODUCTION The Hawaiian Islands are prone to natural disasters including hurricanes, earthquakes, floods, and tsunamis. With its unique position in the Pacific Basin, Hawaii is particularly vulnerable to far-field tsunamis generated in the active subduction zones around the Pacific Rim. The eastern part of the island chain is also subject to less frequent, locally generated tsunamis due to seismic activities and underwater landslides. Past far-field tsunamis have been very damaging to Hawaii, with a long history of property damage and loss of over 200 lives in the past century, according to the National Geophysical Data Center (NGDe) Online Global Tsunami Database. The most recent and well-documented destructive tsunamis to Hawaii include the 1946 Aleutian, 1952 Kamchatka, 1957 Aleutian, 1960 Chile, and 1964 Alaska events (Walker, 2004). Common parameters used to define the far-field effects of tsunamis are the inundation limit, which is the maximum horizontal distance a tsunami travels inland, and the runup, which is the elevation of the inundation limit referenced from Mean Sea Level (MSL). Hawaii state and county civil defense agencies have made a significant effort to understand the threat of tsunamis to better prepare for their occurrence. Hawaii was the first state in the U.S. to prepare tsunami evacuation maps. The current Hawaii Tsunami Evacuation Maps were developed by Curtis (1991) and published in the telephone books of each county. The tsunami inundation limit was calculated for Hawaii coastlines using a one-dimensional long-wave model developed by Bretschneider and Wybro (1976). The Hawaii Tsunami Evacuation Maps are currently being updated based on reconstruction of the five destructive tsunamis in the last one-hundred years using two-dimensional modeling techniques (Cheung et al., 2006). The National Tsunami Hazard Mitigation Program called for the use of a credible worst-case scenario in tsunami hazard assessment (Gonzalez et al., 2005). This requires some knowledge of the probability of occurrence of tsunamigenic events. Govermnent

9 agencies, engineers, architects and citizens should be aware of the return periods of destructive tsunamis, including the credible worst-case scenario event. This is in-line with the use of statistical analysis in developing hazard assessment maps called for by the Federal Emergency Management Agency (FEMA). A probabilistic approach is necessary to assess the vulnerability of infrastructure and local populations to tsunamis. Because of Hawaii's susceptibility to tsunamis from many seismic sources with varied geologic characteristics and unequal potential for tsunami generation, the methodology needs to consider tsunami inundation from multiple source locations. In this study, for the purpose of demonstration, one seismic zone is considered, the Alaska Aleutian Seismic Zone (AASZ). This area has generated particularly destructive tsunamis affecting Hawaii, and has a reasonable amount of historic data for validation. Additional seismic sources, each with their own unique distribution can be incorporated, since this method is scalable and able to include additional information as it becomes available. This paper develops a methodology to relate the statistics of tsunami generation at the source with the runup and inundation at a far-field location through numerical modeling and the development of a probabilistic inundation estimate. As will be discussed in more detail, this method is uniquely expandable, and can include additional tsunami source locations and mechanisms with different probabilistic distributions. 1.1 Previous Approaches There have been many different methods used to determine the tsunami hazard for a particular location. Various statistical methods have been applied to the historic runup heights or tsunami amplitudes to determine the maximum expected water level near the shore. Soloviev (1969) investigated tsunami frequency-size distribution in terms of tsunami intensity and determined a classification of tsunami intensity based on the runup. Houston (1977) determined frequency-of-occurrence curves based on the maximum 2

10 expected wave elevation near the shore. Severnl authors have investigated the spatial distribution of tsunami heights along coastlines with extensive historical records, which tend to follow a log-normal distribution (Van Dom, 1965; Kajiura. 1983; and Choi et ai., 2002). Burroughs & Tebbens (2005) suggested that tsunami wave heights follow a power-law curve, similar to the use of the commonly used earthquake frequencymagnitude distribution, the Gutenberg-Richter (G-R) relationship. These studies are less effective if the historic runup record is limited. It is also important to note that the runup records are from a mix of tsunamigenic source regions, which may not have equal tsunami genemting potential. Geist and Parsons (2006) developed the Probabilistic Tsunami Hazard Assessment Method, PTHA, based on integrating computational methods with empirical analysis of historic runup data. This method has a comprehensive error analysis and uses a Monte Carlo simulation to account for historic runup records that are limited, but mixing the runup data from various source regions does not correctly relate the statistics of the single source region considered to the far-field location. Numerical modeling of historic tsunamis is used in regions where there are sufficient earthquake and tsunami runup data (Curtis, 1991, Cheung, et al. 2006). Since the historic data for tsunamis is limited, probabilistic analysis based on seismic data will help to supplement this method. Other studies have investigated the tsunami vulnembility by focusing on local social and economic factors, such as population density, building construction, and distance from coastline (papathoma et ai., 2003; and Dominey-Howes & Papathoma, 2006). This study is useful for community planners and civil defense agencies, but it would be advantageous to have more specific probabilities associated with the tsunami zone classifications. Many subduction zones have been studied to assess tsunami frequency-of-occurrence by relating the generation of tsunamis with the occurrence of seismic activity for a given region (Soloviev, 1970; Rikitake and Aida, 1988; and Orfanogiannaki and Papadopoulos, 3

11 2007). This approach is useful, because not all shallow subduction zone earthquakes generate far-field or even local tsunamis. While earthquake frequency distributions have been studied in detail, the incompleteness of tsunami catalogs including well-documented moderate sized tsunamis can have adverse effects on the probabilistic analysis (Geist and Parsons, 2006; and Orfanogiannaki and Papadopoulos, 2007). There are many variations in the existing methods for the probabilistic analysis of earthquake occurrence itself, as highlighted by Utsu (1999). Several examples include power law distributions (Wadati, 1932), many variations of the famous and widely-used Gutenberg-Richter magnitude-frequency relation introduced in 1944 (Gutenberg and Richter, 1944 & 1949, Gutenberg, 1956; Kanamori & Anderson, 1975; Pacheco & Sykes, 1992a; Okal and Romanowicz, 1994; Sornette, et az. 1996; Kagan and Jackson, 2000; Kagan, 2002), the Weibull distribution (Rikitake and Aida, 1988), the lognormal distribution (Orfanogiannaki and Papadopoulos, 2007), variations of the gamma distribution (Kagan, 1991, 1999), variations of the Pareto distribution (Pisarenko and Somette, 2003), the use of Bayesian statistics (Tsapanos, et az. 2001; Galanis, et at. 2002) and many others. In addition, some authors believe that the factors such as the b-value are universal (Kagan 1997, 1999), while others consider regional differences in the distribution to be significant. Given the many distributions applied with reasonable results, it suggests frequency of occurrence variations between seismic zones will be a significant factor in probabilistic analysis. The method developed for this thesis focuses on numerically simulating a set of tsunamigenic earthquakes based on magnitudes obtained through systematic sampling of the statistical distribution to determine the 100 and 500-year return inundation and runup for a given location. Given the variation of distributions used for the seismic source and the tsunami runup data, it seems intuitive that it is best to perform statistical analysis considering both the generation and far-field effects of a tsunami in a single process. By considering individual seismic zone frequency-of-occurrence distributions and 4

12 numerically simulating the tsunami from the source to the target shore, there is more continuity between the seismic source and the tsunami runup. This method also allows the numerical model to be validated with historic data. Despite the fact that the historic tsunami data is limited compared to other natural phenomena where statistical distributions are applied, such as river flooding, it is important not to mix the frequencyof-occurrence from multiple sources having varied characteristics and to apply a more physics-based connection between tsunami source and far-field locations where possible. 1.2 Goals and Objectives Understanding the potential level of destruction from tsunamis is an aid to planning for and mitigating the impact of future tsunamis. It is important to know not only the expected nearshore tsunami amplitude, but also to understand the variation of how the tsunami will inundate the coast and the likely flow depth within the inundation zone. This tsunami impact must be reported with a probability-of-occurrence or recurrence estimate. This information will aid in mitigation efforts for tsunami hazard mapping, and increase the ability to design new structures or retrofit existing structures to expected tsunami flow conditions. This can be achieved through the probabilistic approach of tsunami modeling, demonstrated here for a section of the island of Oahu. This study utilized the data resources and modeling capabilities of the Hawaii Tsunami Mapping Project to develop a probabilistic method to determine the vulnerability of individual structures within the inundation zone. This thesis presents the development of new methodology used to determine the level of tsunami impact as a function of return period. For this methodology, the objective is to relate the statistics of the tsunami source to the statistics of inundation and runup. This objective can be achieved by gathering and selecting seismic and tsunamigenic source data (Chapter 2); selecting tsunami generation locations (faults) to test (Chapter 2); 5

13 I fitting the selected seismic source data to an extremal distribution curve (Chapter 2); selecting magnitude values from equal intervals of the distribution (Chapter 2); numerically modeling the selected events at multiple locations along the trench (Chapter 3); compiling the numerical results and determining a probabilistic inundation grid (Chapter 3); generating inundation lines with various return periods (Chapter 4). The resulting probabilistic inundation line can be used to determine runup values from the topography, which in turn can be compared to the historic records to confirm the analysis. Specifically, this study aims to develop methodology to determine the recurrence of destructive tsunamis and produce a demonstration of 100 and SOD-year probabilistic tsunami inundation maps. This study is a demonstration of the methodology, and uses only one tsunami source region, the Alaska-Aleutian Seismic Zone (AASZ). The nearshore area of focus is the north shore of the island of Oahu, Hawaii, utilized for its large historic runup dataset. Applications of this approach will lead to a better estimate of the risk of future tsunami damage to critical infrastructure. Knowledge gained from these results can be utilized by state and local agencies to better protect residents and property, and this method can be expanded to include multiple source regions. This methodology will also be important to facilities storing hazardous material within the inundation zone, and can potentially help limit pollution by an increased understanding of the tsunami phenomena and likelihood of occurrence. 6

14 CHAPTER 2 TSUNAMI SOURCE CHARACTERIZATION Tsunamis are long-period oceanic gravity waves generated by a large disruption of the entire water column, most notably via seafloor deformation resulting from a seismic event. Typically tsunamis are generated by large, shallow submarine earthquakes, but submarine landslides or volcanic activity and, rarely, even an asteroid impact can generate a tsunami. To make the best use of all available data and to account for the limited and possibly mixed records, where possible, the statistical analysis should be performed with the tsunami and seismic source data, which reflects the intensity of tsunami events originating at each source location. The runup records can be used to calibrate a numerical model for each source location, thereby accounting for limitations in the runup record, tsunami generation source mechanisms and numerical error during propagation and inundation. There are good records of the historical seismic events, available for statistical analysis of earthquake magnitude. Given the variety of available distributions, the equation best-fitting the data will be used and applied to the selected earthquake magnitude values. Analysis of the tectonic structures at the source regions complements the published seismic data for tsunami modeling (Wei et at. 2003; Yamazaki et at. 2006; and Sanchez and Cheung, 2007). 2.1 Tsunamigenic Source Further considering the seismic tsunami generation, Satake and Tanioka (1999) have classified tsunamigenic earthquakes in subduction zones into three categories: typical interplate earthquakes, intraplate earthquakes, and 'tsunami earthquakes'. Interplate events occur when accumulated stress at the interface between the subducting and overlying plate is released, typically km below the seafloor. These are the more 7

15 widely known large shailow thrust earthquakes, from which most transoceanic tsunamis are generated. Intraplate events are tsunamigenic earthquakes that occur in the outer rise of the subducting plate, or within the subducting slab or overlying crust. The term tsunami earthquake refers to a seismic event that generates a much larger tsunami than typicaily expected, as coined by Kanamori (1972). Adding to the complexity of the tsunami source is the occurrence of multiple source mechanisms contributing to the generation of a tsunami, such as the combination of a submarine landslide and earthquake, as theorized by several authors regarding the 1946 Aleutian earthquake and tsunami (Sykes, 1971; Kanamori 1985; and Shepard, 1950) or as a submarine landslide only (Fryer et al. 2004). The time sequence of the coupling between seafloor deformation and tsunami generation is an area of current research, which could dramaticaily influence hydrodynamic analyses. For very large tsunami events, it is more likely that variations of the displacement of a fault (slip) affect tsunami generation and earthquake rupture velocity has more influence on the tsunami propagation (Song et al. 2005). Ohmachi et al. (2005) postulates that the dynamic coupling of the seabed and the overlying water column-which has a significant impact on the tsunami propagation and arrival times-is a shortcoming of the currently used hydrodynamic models. Nearshore transformation of a tsunami is strongly influenced by the bathymetry and topography (Loomis, 1966). Tsunami waves generaily take two characteristic forms nearshore: forming a bore--a vertical wail of water---or behaving as a very rapidly rising tide. If the coast has a very gentle slope, the floodwater may travel very far inland, but produce a smail runup height. The nearshore bathymetry also influences tsunami waves by focusing energy at headlands or spreading energy in an embayment. Because of the complex nature of tsunami generation, propagation, and inundation, runup values for the same tsunami may vary greatly at different nearshore locations and do not provide an adequate indication of the tsunami characteristics. There is also significant variability in runup records, which may be a mix of nearshore wave heights, high water marks, tide 8

16 gauge records of tsunami amplitude, and actual runup values marking the maximum inundation of the tsunami (Loomis, 1976). A recent study shows that resonance in the Hawaiian Island chain can significantly affect tsunami wave amplitude (Munger and Cheung, 2008). AIl of these factors contribute to the complexity of applying a probabilistic approach to tsunami hazard assessment 2.2 Tsunami and Earthquake Catalogs There are many catalogs recording earthquake and tsunami events, and catalog completeness has a large impact on statistical analysis, especiaily when there is a limited record of events available. Just as there are many frequency-magnitude relationships for earthquakes, there are many different approaches used for catalog development and magnitude determination. This stems from slight changes in magnitude definitions, and the methods and instrumentation used to determine various magnitudes. Several authors have given detailed studies of various magnitude scales and determination methods, most notably Kanamori and Anderson (1975), GeIler (1976), Kanamori (1977,1978), and Utsu (2002). Common magnitudes available in many catalogs that are used for tsunami analysis include the surface-wave magnitude Ms, the local magnitude, ML, the body wave magnitude, mb, the moment magnitude Mw, and the tsunami magnitude, MT. Many variations of the formulas used for various magnitude types can be found in Utsu (2002). The surface wave magnitude is based on the amplitude of the 20-second period seismic surface waves and was first introduced by Gutenberg (1945). Both the United States Geological Survey (USGS) and the International Seismological Center (ISC) use a definition of Ms as given by Vanek et al. (1962) in their catalogs known as the Prague formula Ms = log(a/t)m logA+3.3 (1) where A (~m) and T (s) are the amplitude and period of the horizontal surface wave 9

17 component, and ~ is the epicentral distance measured in degrees (Utsu, 2002). It is important to note that slight differences in the conditions used to implement this formula can produce slightly different Ms values reported by the USGS and the ISC for the same earthquake (Utsu, 2002). Larger differences in reported Ms values can also occur because of increasing epicentral distance. The values of Ms, ML, and mb saturate at large magnitudes (Ms "" 8.3, ML and mb "" 7) because of the finite bandwidth available in the instrumentation to capture the gross fuulting characteristics and when the rupture dimension of the earthquake is greater than the wavelength of the seismic waves used for magnitude determination (5-50 Ian) (Kanamori, 1977; and Hanks and Kanamori, 1979). To overcome this saturation phenomenon, the moment magnitude, Mw, is used. The moment magnitude is based on the seismic moment, Mo of an earthquake, which represents the strain energy release of an earthquake. Seismic moment is defined as Mo = lids (2) where!l is the rigidity, D is the average fuult offset or slip, and S is the fault area which is typically characterized by a rectangle oflength, L and width, W, as shown in Figure 1. The seismic moment is the basis of the moment magnitude, Mw, which sterns from the Gutenberg-Richter magnitude-energy relation (Gutenberg, 1956), loge = 1.5M (3) where E is the energy released in seismic waves in ergs and M is the earthquake magnitude. Kanamori (1977) used this relationship to develop the famous moment magnitude scale, where E is replaced by the strain energy drop, Wo which is estimated from the seismic moment, -MoI(2x ) for cases when the stress drop is complete. The most general form of the seismic moment magnitude relation is Mw = (IogMo /1.5)-10.7 (4) with Mo in dyne-ern, as given by Kanamori (1978). 10

18 This study investigates tsunamis generated in the Alaska-Aleutian Subduction Zone (AASZ) in the last century, and therefore looks to the distribution of the AASZ earthquakes for further insight. Several reliable earthquake and tsunami catalogs are compiled and compared to take advantage of the largest amount of seismic data possible, as well as to evaluate how the data varies from one catalog to the next. These catalogs include: Seismic Moment Catalog of Large Shallow Earthquakes, 1900 to 1989 (pacheco and Sykes, 1992a); Alaska Earthquake Information Center; National Geophysical Data Center (NGDC) Historical Tsunami Database; USGS Preliminary Determination of Epicenters (PDE); USGS Significant Worldwide Earthquakes (SWE); USGS Significant U.S. Earthquakes (SUS) catalogs; Global Centroid-Moment-Tensor (CMT) Catalog (formerly known as the Harvard CMT Catalog). Table 1 lists the period, source region, and number of records in these catalogs. All catalog searches are magnitude 7-9.5, depth 0-70 km, and a date range of when available. These catalogs do not report all earthquake events and often show different magnitudes and parameters for the same event. In this paper, record refers to a given catalog entry, while event refers to a specific earthquake that has been recorded in one or many catalogs. Table 2 is a summary of the number of records that were reported in multiple catalogs. For example, there is only 1 event that was reported in all seven catalogs, which was the May 7, 1986 earthquake and tsunami. On the other hand, there are 28 seismic events that are reported in only I of the 7 catalogs. Of the 238 total records, there are 34 additional repetitive records that are not included in the data selection. Of the 14 tsunamis with runup recorded, 1 event was very unlikely to be an 11

19 actual tsunami. The variation of number of events reported in multiple catalogs demonstrates the differences in catalog completeness and the importance of crossreferencing multiple data sources, since not all events are reported in multiple catalogs. Records are grouped into events by matching the date, time and location. Table 3 shows the subsequent breakdown of the magnitude type data for the 87 available seismic events with magnitude (Ms or Mw) greater than 7.0. The purpose of this data compilation is to determine the variation among the total seismic and tsunami data available, as well as to gather and utilize all relevant data. Because not au events have records for Mw, which is used in most tsunami numerical modeling and statistical analysis, there is a choice between using only true Mw values, which limits the total number of events used in statistical analysis, or assuming that the Ms and Mw scales may be mixed to fill the data catalog. Since the Mw record for events before the 1970's is fairly limited for statistical analysis, Ms must be used to have a statistically reasonable amount of data points. Four magnitude selection scenarios were compared from the entire data catalog: (a) Mw only; (b) Ms only; (c) Mixing Mw & Ms; and (d) Mw supplemented with Ms, when needed or available. Since each event does not have the same reported magnitude in different catalogs, the minimum, maximum, average could be considered as the final value used for statistical analysis. Table 4 shows the resulting number of events for each method available for statistical analysis. The number of events available varies slightly between (c) and (d) scenarios. This is because averaging Mw & Ms tends to yield lower values, since Mw values tend to be higher than Ms. Of the 29 events available with Mw ~ 7.5, only 23 were considered for the probabilistic analysis, and will be discussed in further detail. The full earthquake magnitude dataset for scenario (d), Mw supplemented with Ms, with the maximum value of Mw ~ 7.5 is used for the probabilistic analysis, and is given in Table 5 and shown in Figure 2. Where an event had a range of earthquake magnitude 12

20 values reported in multiple catalogs, the maximum value is used to utilize the maximum number of events. In Table 5 the events in blue are not considered. Figure 2b shows that there is somewhat of a gap of seismic events near Mw = 7.0. This leads to the use of Mw = 7.5 as a lower cutoff magnitude for statistical analysis, which is used by several other researchers including Gica (2005), and Geist & Parsons (2006). In addition to compiling the earthquake and tsunami data into a catalog, the erroneous points had to be removed. The points with longitude values greater than 2200E were excluded, because of the changes in the tectonic structures. As mentioned previously, the erroneous data points specified in the data source were also removed Figure 2 illustrates the earthquake and tsunami events that are considered in this analysis, corresponding to the information provided in Tables 3 and 5. The maximum number of available seismic events is n = 29. Events significantly far from the Aleutian trench were not considered in the probabilistic analysis. The total number of tsunamigenic events is 18. By considering only the tsunamigenic events and Mw <! 7.5 in order to capture trans-pacific tsunamis, the number of available events fell to 13, and only II of the selected seismic events created tsunamis that reached Hawaii. These sample sizes are too small for reasonable statistical analysis. The scenario of n = 23 seismic events with Mw <! 7.5 is considered for statistical analysis. 2.3 Spatial Distribution of Earthquake and Tsunami Occurrence Figure 2a shows the locations of earthquakes and tsunamis in the Alaska-Aleutian source region from Several events are from erroneous entries into the data catalog, for example the 1903 event at N, E from the NODC Catalog. This event is listed as a very unlikely tsunami, which is reasonable given the inland location of the epicenter. Earthquake magnitude variation with the longitude of the trench is given in Figure 2b. This figure demonstrates that not all large, shallow subduction zones generate trans-oceanic tsunamis, though many do. This discrepancy complicates the tsunami 13

21 frequency analyses, and there are several approaches to remedy the issue. One solution is just to consider only tsunamigenic events for probabilistic analysis, but then the question arises of data completeness and statistical significance. This issue is addressed in a probabilistic study by Orfanogiannaki and Papadopoulos (2007), who take into account the ratio of tsunami generating earthquakes to the total number of earthquakes in considering the conditional probability of tsunami occurrence. The rate of tsunami occurrence for the 23 selected earthquake events is 78%. In this study, for the earthquake magnitude scenario of Mw supplemented with Ms, it is assumed that all earthquakes above Mw = 7.5 will generate a tsunami. If the probabilistic distribution used for this analysis is reduced by approximately 20%, the slip would have to be increased by an unrealistic value to generate any inundation. Because there is uncertainty about the tsunami source, local oceanic crust variability, it is better to utilize all of the available seismic data, and calibrate the tsunami model according to the historic runup data, rather than to manipulate the source data further. To account for the expected number of tsunamis can be taken into account in the probabilistic grid calculations at the target farfield shore location. 2.4 Source Parameter Configuration Figure 1 illustrates the planar fault model and the source parameters for tsunami generation. The earthquake rupture surface is commonly represented by a rectangular area with a definable length and width and referred to as the fault area, fault plane, or simply fault. The parameters depth (d), strike (4)), dip (I» and rake (A.) define the location and orientation of the fault plane. The slip, u, is the vertical dislocation that describes the movement along the fault plane. Often multiple faults, or subfaults, are used to characterize the slip distribution of tsunamigenic events. Several researchers have characterized the AASZ into a continuous distribution of potential interplate faults. The Pacific Marine Environmental Laboratory (PMEL), a 14

22 division of the National Oceanic and Atmospheric Administration (NOAA) uses a uniform set of subfaults with a length of 100 km and width of 50 km, where the plate interface is represented by a continuous line of subfaults that is two subfaults wide ( Figure 3 shows the strike, dip and focal depth fault parameters used by PMEL, Wei et al. (2003) and the parameters used for this thesis. Where only one line appears, the parameters have identical values. A rake angle of 90 is common to subduction zone thrust earthquake and therefore tsunami modeling, and is used for this paper. The dip and depth angles are constant for all earthquake faults configured for this paper in order to reduce the number of variables in the probabilistic analysis. The rake, dip and depth parameters are not as critical to the resulting tsunami wave as the slip, length and width parameters of the faults (Gica, et al. 2007). An additional sensitivity analysis of the seismic source parameters to this probabilistic method is an area for further investigation. The selection of the strike, length, and width fault parameters are described in the following paragraphs. Wesson et al. (1999) show the rupture area for the major tsunamigenic events in the last century, which is reproduced in Figure 4. This figure demonstrates that the majority of the AASZ trench has ruptured within the past 100 years. Johnson (1999) made a comprehensive study of Alaska-Aleutian faults based on an inverse analysis of tsunamigenic earthquakes including the 1938, 1946, 1957, 1964, 1965 and 1986 events. Wei et al. (2003) developed and refined the faults with additional inverse analysis and numerical modeling to define a continuous distribution offaults along the trench. Two fault configurations are chosen for the probabilistic analysis, and shown in Figure 5. The distribution of multiple earthquake fault locations allow a given earthquake magnitude to be tested along the entire trench. Both scenarios are based on historic data and the work of Johnson (1999), Wei et al. (2003) and the source parameters given in Table 6. The first fault configuration is to assign a fault of constant length and width at different locations along the trench. The length (L) and width (W) of each fault 15

23 is the average of the historic event source parameters given in Table 6: L = 500 krn and W = 150 krn. Figure 5 shows the variation oflength and width with magnitude as given in Table 6. The linear regression of length and Mw is given in equation 5. The fault locations are selected to best fit the entire trench, and 6 fault locations are used, as shown in Figure 6a. For the constant fault-area configuration, the slip varied with the Mw values tested. The second configuration used was one where the length varied linearly with Mw, based on the same data from Table 6. For the variable length fault setup, the faults each have the same center point, strike and width as the constant area scenario, and is shown in Figure 6b. The variable length relationship is L = Mw R2 = (5) The low correlation coefficient demonstrates the variability of fault area for a given earthquake magnitude. There is also large variation in the historic event fault parameters determined for each event, as shown in Table 6. For large, shallow thrust-type earthquakes, as earthquake magnitude increases, fault width tends to saturate while length keeps increasing, since the width is limited by the down-dip extent of the subduction zone (Geist, 1999). A typical fault length:width ratio of 2: I (Geller, 1976) could be assumed, but does not correlate well with the historical event data given in Table 6. Geist and Parsons (2006) used an empirical relationship presented by Wells and Coppersmith (1994) for fault length that was not designed for subduction zone earthquakes. This study considers equal probability of occurrence of tsunami genic events along the trench that does not take into account trench variability such as seismic gaps. The entire length of the trench does not rupture in the 50Oxl50 krn scenario, so in a sense gaps are somewhat arbitrarily included. Trench variability can be accounted for by applying a distribution of occurrence along the trench, which could be based on the spatial locations of the earthquakes or tsunamis. This is tested by applying a weighted probability to each fault and accounted for during the probabilistic grid calculation, as discussed in the data 16

24 analysis section (5.2). This is another example of the expandable characteristic of this probabilistic analysis method. 2.5 Statistical Distributions The basis of the probabilistic analysis method developed for this paper is to fit data to an extremal distribution function and relate that distribution to the resulting inundation distribution at a far-field location. This is achieved by systematically sampling the source distribution curve at intervals of equal occurrence probability. For each interval under the source distribution curve, the median Mw value has an equal likelihood of occurring anywhere along the trench. The selected magnitude values are used to numerically model tsunami events at multiple locations along the trench of a given seismic zone. The results of these tsunami events can be compiled so an inundation with a desired return period can be computed. As mentioned previously, many statistical distributions have been applied to determine the frequency of occurrence of seismic events. The Weibull and lognormal distributions are both frequently used distributions in earthquake statistical analysis, and the Gutenberg-Richter distribution is one of the most famous earthquake size distribution functions. All three of these distributions are applied to find the best fit of the available Datasets, considering the (c) and (d) earthquake magnitude grouping scenarios. The cumulative distribution function (cdj) of the Weibull distribution is given as F{x) = l-exp[ -( X~BJ] B s x < 00 (6) where x is the extreme variate ( earthquake magnitude), A is the scale parameter, B is the location parameter and k is the shape parameter. The probability density function (pdf) lognormal distribution (Goda, 2000) is f(x) = 1 exp[ (lnx-by].j21cax 2A2 o<x<oo (7) 17

25 The Gutenberg-Richter equation (8) as defined by Utsu (1999) is F(x) = I-exp[- BX] (8) The more common form of the equation is expressed in equation (9), where M is the earthquake magnitude, n is the number of events, a is the intercept and b is the slope of the line. 10gn(M)=a-bM, B=blnlO (9) The data fitting analysis method follows Goda (2000). The scale and shape parameters ( A, ij) are solved from the least-squares fit of the data to a straight line of the form (10) where the r.educed variate, YR is a function of the return period, R and the mean rate, A. defined by equation 11. (II) The mean rate, A., is the number or events occurring during a given time period, which is also the inverse of the recurrence interval. The results of the data analysis are given in Table 7, where datasets of 29 and 23 seismic events are analyzed and the wellness of fit of each distribution is given. The root-mean-square error (r) value is used to determine the fit of the data. The Gutenberg-Richter distribution was ultimately chosen due to the frequency of use in the seismological community and a reasonable fit. Figure 7a shows the best fit of the selected seismic events to the G-R distribution. The best fit line is used to determine intervals with equal areas under the curve (equal percentage intervals) which are shown in Figure 7b. The magnitude values to use for the numerical modeling and probabilistic grid generation are calculated from the slope of the best fit line and the median locations of each interval (Figure 7c). Using equations (10-11), the 100-year return earthquake magnitude can be established. A significant mistake in probabilistic analyses would be to calculate the

26 year earthquake magnitude, model a tsunami using the 100-year magnitude at various locations along the trench or even multiple source regions, and then take the 100-year tsunami inundation to be the maximum inundation from all those events. This essentially alters the probability of the probabilistic inundation line, because the 100-year earthquake is counted multiple times. The likelihood of occurrence depends on both the magnitude and source location of the event. As shown in section 5.1, the location of the tsunami source can yield very different inundation for the same input magnitude. 19

27 CHAPTER 3 PROBABILISTIC TSUNAMI INUNDATION MAPPING FEMA specifies the use of annual exceedance probabilities of 1 % and 0.2% in the Flood Insurance Rate Maps that correspond to 100 and SOO-year return periods and also calls for the use of probabilistic method for tsunami hazard assessment (Wallace et ai., 2005). Probabilistic analysis is a well known and used technique in flood and seismic risk assessment, where historic data is abundant. Tsunamis are relatively infrequent compared to seismic and flooding events, thus applying probabilistic analysis to tsunamis presents a challenge. The best-fit distribution can be systematically sampled over selected intervals of equal occurrence probability in order to determine magnitude values to use for the numerical modeling and probabilistic grid generation. The sampled magnitudes can then be tested at multiple locations along the source trench and aggregated into a probabilistic inundation grid to determine the 100 and SOO-year inundation limits. 3.1 Tsunami Modeling This study uses a two dimensional long-wave numerical model to generate, propagate and calculate tsunami inundation and runup. The model characterizes the initial tsunami wave from the probabilistic earthquake magnitude and the earthquake fault parameters of strike, dip, focal depth, fault length and width, which are illustrated in Figure 1. The seafloor deformation is calculated from the vertical dislocation (slip) on the fault area using the Okada formula (1985). The initial sea-surface deformation is taken to be identical to the seafloor deformation. The initial wave dimensions are linearly proportional to the fault dimensions and the initial wave amplitude is linearly proportional to the slip. The still water level is used for the initial surrounding sea surface. 20

28 A modified leap-frog fmite difference scheme is used to solve the depth-integrated long-wave equations, as described by Liu et al. (1995). The linear governing equations of continuity and momentum are, as given in spherical coordinates, as + I [a Q + a(pcosb)] = 0 at RcosB at ab aq + gd at R cos B a;., as jp=o (14) (15) (16) where t is time, ~ is the water surface elevation, d is water depth, R is the earth's radius, B is longitude, A. is latitude, P and Q are the velocity fluxes in the latitudinal and longitudinal directions, and f is the Coriolis parameter, 2nsinA.. The earth's angular velocity, n, is taken as 7.29 x S I. As expressed in Cartesian coordinates (x, y), the non-linear form of the equations are given by (17) (18) (19) where D = (~+d) is flow depth, the fluxes P and Q are now defined in the x and y directions and t"x, t"y are the respective bottom shear stresses. The model uses a four-layer nested grid that solves the long-wave equations linearly for open-ocean wave propagation in spherical coordinates and non-linearly for wave transformation, runup and inundation in Cartesian coordinates. The Coriolis force is 21

29 considered in the first layer (linear) calculations only. For the non-linear calculations, bottom shear stresses in the x and y-directions are computed from the Marming's friction coefficienl The water surface elevation and velocity fluxes are calculated at each time step. The time step,!>t, must satisfy the Courant-Friedrichs-Levy stability condition, as given by (20) where ~ is the horizontal grid spacing. The coverage and grid spacing of the four nested grids are given in Table 8 and shown in Figure 8. The increasing resolution of the nested grids captures the increasing non-linear effects as the tsunami approaches nearshore areas. The input bathymetry datasets are compiled from several different data sources, as given in Table 9. The bathymetry data was compiled, merged and used for the Hawai'i Tsunami Mapping Project (Cheung et af. 2006). All bathymetry data is referenced to Mean Sea Level (MSL) and the WGS 84 datum. All water levels are referenced from MSL. As mentioned previously, with this numerical scheme there are limitations and errors in the earthquake source parameters estimations, the tsunami generation mechanism, and small numerical errors during propagation, which could lead to incorrect runup calculations if not accounted for. The current approach to remedying this situation is to adjust the initial tsunami wave amplitude by increasing the slip value, so that the modeled tsunami inundation matches the historic records. An amplification factor of five is used for the calculations presented in this paper. This is an average amplification factor of the 1946 Aleutian, 1957 Aleutian and 1964 Alaskan tsunami events as modeled by Cheung et af. (2006). 3.2 Probabilistic Inundation Grid To characterize the potential tsunami inundation generated from the entire subduction 22

30 zone, the distribution can be applied to multiple locations along the trench, as shown in Figure 9. By testing specified magnitude values at multiple locations along a seismic zone, it is necessary to compile the inundation from each test, and convert it into a probabilistic grid in order to maintain the probability of a given interval. Thus, if the chosen interval size is 2%, if there is one fault representing the trench, one may model the given magnitude from the specified interval at one location having a 2% chance of occurring. However, for this paper there are 6 representative faults for a given seismic zone, each of the faults having a 0.33% chance of occurring. This method allows for a varying number of fault scenarios to be tested without "multiple counting" the impact of a given magnitude, which in turn alters the specific probability of that event. A varying distribution can also be applied to the likelihood of event location along a given seismic zone. Systematic sampling of the earthquake statistics over intervals of equal probability of occurrence results in a number of representative events for tsunami inundation modeling. The tsunami model outputs the maximum wave elevation at each (x, y) location in each layer of nested grids. By compiling these results a cumulative exceedance probability, Q, can be calculated at each (x, y) location. The exceedance probability is simply related to the number oftimes each point was inundated over a given number of total events (niln). With 2% intervals and 6 faults, the total number of events is 300, from which the top 60 are simulated. The procedure of vertical grid compilation is illustrated in Figure 10. This grid of exceedance probability can then be contoured to obtain an inundation line with a given return period, using the following formulation. The recurrence interval, r is equivalent to the inverse of the mean rate, A., as defined by Goda (2000), and given in equation (12), where T is the data duration and n is the number of events that have occurred. The return period, R of a given event is a function of the recurrence interval and the exceedance probability. 23

31 T I r=-=n A R=!... Q (12) (13) A I % annual probability of exceedance or Q = om is the probability associated with a 100-year return event, whether it is an earthquake, flood, or any other event, where there is a I-in-IOO chance of that particular event occurring in a given year. For the case of the probabilistic grid, using n = 23 earthquake events and d = 106 years of data as an example, Q = 0.01 is equivalent to a 461-year event. To obtain the probability of a given return time, equation (13) is simply solved for Q given a selected R. A contour of the probabilistic grid at the obtained value of Q is then the R-year inundation line. Results for the specific test cases are discussed in section 5.1. This method to develop a probabilistic grid has similarities to the method used to apply the PTHA (Geist and Parsons, 2006, Tsunami Pilot Study Working Group, 2006). The Tsunami Pilot Study Working Group study (2006) use a numerical model to simulate several characteristic earthquakes whose recurrence probability is determined with the G-R distribution. From the selected events, they next compute a hazard curve (cumulative frequency of exceedance vs. tsunami wave height) at every nearshore grid point to determine the probabilistic inundation. The resulting grid is based on sampling of the source distribution curve over unequal intervals that is not an accurate characterization of the distribution. While the calculation of a return value from an extreme distribution is possible, and used frequently for wave analysis, there is significant variability in the estimation of the return value when it is calculated from the maximum values of the extreme distribution (Goda, 2000). In the case of tsunamis, an earthquake magnitude with a specific return value can be calculated, such as a 100-year return earthquake magnitude value. Since this 100-year magnitude value can be applied at multiple locations along the trench, the 100-year earthquake magnitude is not necessarily the same as the 100-year tsunami 24

32 inundation. For this reason, it is necessary to test a specific magnitude at various locations along the trench, and incorporate the resulting inundation into a probabilistic grid that does not alter the probability of a given magnitude. By modeling the tsunami from the source to the far-field shore in one step there is a physics-based connection between the statistical distributions of the seismic source and the inundation at a far-field location. 25

33 CHAPTER 4 RESULTS AND DISCUSSIONS The areas tested nearshore are on the north shore of Oahu from Kaena Point to Haleiwa and are simulated with two nearshore grids given in Figure 8 and Table 8. This area is particularly vulnerable to destructive tsunamis from AASZ, due to the proximity, directivity and frequency of tsunami events. There are also many historic runup records to compare the probabilistic events. Each tsunami was modeled for a total time of 7 hours to capture the entire length of the event. Initial waves typically reach the Hawaiian Island Chain 3 Ya - 4 hours after a tsunami is generated in the AASZ. Table 10 gives a summary of the magnitudes tested at each fault, for both of the fault configurations (constant and variable). By considering the top 20% of the distribution subdivided into 2% equal area intervals and applied at each of the 6 faults, the resulting total of 60 simulated tsunami events are repeated for two nearshore domains: Haleiwa and Mokuleia. In order to fully capture the extreme tail of the distribution, the top % interval was further subdivided to model magnitudes from 98-99% and % intervals for the variable fault scenario. In order to capture the energy of the earthquake magnitude, the constant length fault scenario caused the slip to become unreasonable large, so only the variable length scenario is considered for the final probabilistic inundation grid. 4.1 Data Analysis To investigate the variability of a tsunami originating at various locations along the trench, Figure Iia shows a comparison of the inundation from the constant and variable fault scenarios for the 90-92% interval of the earthquake distribution (Mw = 9.03). The colors for the lines correspond to the faults shown in Figure 6. The resulting inundation from tsunamis with the same initial magnitudes and different locations along the trench 26

34 show considerable differences in inundation. This also shows that using a characteristic earthquake at a single location in a subduction zone may not be sufficient, which reiterates the importance of systematically sampling and testing the source distribution. The difference in inundation illustrates the influence of source location and directivity. Figure II b-c show the difference in inundation generated by the constant (b) and variable (c) length scenarios. For the smaller events (80-96%) the variable length faults give slightly more inundation, though the results are very similar. This results from higher slip values for shorter fault lengths, to obtain the same amount of initial energy as the constant fault length scenario. For the larger events, the constant length scenario events yield greater inundation than the variable length faults. As Figure lla demonstrates, the trench location has a greater impact on the far-field inundation than the fault length. This data supplements the different sensitivity analysis studies that have been conducted to determine the earthquake parameters that most influence the tsunami inundation and runup (Titov et at. 1999, Gica 2005, Cheung et al. 2006, Gica et at. 2007). For each of the fault length configurations, probabilistic grids are generated with each fault weighted equally at a 0.33% chance of occurrence over a recurrence interval of 4.61 years. The 1 OO-year return inundation line is a contour of the probabilistic grid using Q = The SOO-year return inundation is based on Q = The 100-year return inundation from the probabilistic grid is less than the maximum inundation of the 100- year magnitude tested at multiple locations along the trench. One of the advantages of this method is that it is readily expandable. For each seismic zone, an earthquake distribution can be used to model a set of tsunamis, which can be counted in the fmal probabilistic grid with its own individual likelihood of occurrence. Within a seismic zone, additional consideration can be given to the spatial probability of occurrence. As a demonstratioli., the spatial weighting of individual faults along the AASZ is included as one of the test cases for this study. 27

35 By sampling the number of seismic or tsunami events that occur at each fault, a weighted probability is incorporated into the probabilistic grid calculations. For an equal probability of occurrence along the trench each grid point receives a count of I (0.33%) if it is inundated and 0 if the cell is dry, during the calculation of the exceedance probability grid. Then the probabilistic inundation at any (x, y) location or grid point is the accumulated count of inundation over the total number of possible events. For six faults, 50 intervals of the distribution there are 300 total possible events. Since the top 20% of the distribution was modeled, the maximum probability of exceedance value of the grid will be 0.2. Figure 12a shows the probabilistic grid result based on an equal probability of occurrence along the trench. As grid points are inundated less frequently, the probability of exceedance decreases, which is intuitive: only very large, unlikely tsunamis will travel very far inland. To take into account the additional distribution along the trench, each fault can be assigned a weight factor, and the sum of these weight factors must equal the number of faults. Various potential weight factors are given in Table II. For each of the fault length scenarios, the probabilistic grid was generated based on both equal and weighted probabilities for each fault. Testing different fault and weighted distribution scenarios also gives insight into the sensitivity of the source to the probabilistic inundation. Figure 12 also shows the comparison of probabilistic inundation grids for the variable length fault configurations and 3 weighted distributions: equal spatial likelihood, spatial likelihood based on n = 23 earthquakes, spatial likelihood based on n = 18 tsunamis. As given in Table 11, using the weight factor based on n = 18 tsunamis eliminates the westernmost fault (green) from the calculations, which decreases the probability of exceedance for the entire grid. Testing the spatial likelihood distributions along the trench is an area for further investigation. 4.2 Probabilistic Inundation Maps 28

36 Figure 13a presents the final probabilistic inundation map resulting from the development of this method, using an equal likelihood of occurrence along the trench, The inundation lines are the same as shown in Figure 12a. The I ~O-year return inundation is very similar to the envelope of the maximum inundation from the 1946 Aleutian, 1957 Aleutian and 1964 Alaskan tsunamis calculated by the Tsunami Mapping Project Group (Cheung, 2006). The dots on Figure 13a are the locations where historic runup data is available. In Figure 13b, the runup values of I ~O-year return inundation are compared to the maximum runup values of the 1946 Aleutian, 1957 Aleutian and 1964 Alaskan tsunamis. Because there is 100 years of tsunami data available, it is reasonable that the computed IOO-year probabilistic runup would be similar to the maximum inundation extent of the tsunami runup from the past 100 years. This expectation is based on the assumption that the events which occurred in the past 100 years have the same likelihood of occurrence in the next 100, which is equivalent to asking if the events that occurred over the past 100 years are truly events with a 1 % armual chance of occurring. For the development of this method, it is assumed that the magnitude of the 1 ~O-year return event is within the range of the past 100 years of data, as discussed in section 2.5. The IOO-year tsunami runup is similar to the historic tsunami runup records, given by Walker (2004). Because of the variability of near-shore tsunami characteristics and the historic runup records (Loomis, 1976) there is more potential for error in fitting a probabilistic distribution to the runup or tsunami wave height values coilected along a coastline. Statistical analysis of the runup records only can partiaily account for some of the effects of local bathymetry, differences in tsunami waves due to directivity and nonlinear effects, especiaily if the historic runup record is limited or the runup records are. from tsunamis generated in various subduction zones with different frequency-ofoccurrence distributions. Houston et al. (1977) determined nearshore tsunami-wave elevation estimates with a frequency of occurrence of I-in-l 00, or 1 ~O-year return values ranging from 4-9 m. Geist and Parsons (2006) consider the runup to be equal to twice 29

37 the nearshore tsunami wave amplitude. The historic runup from the 1946, 1957 and 1964 events ranges from 2-11 m. When the amplification factor of 2 is used to convert the nearshore wave amplitude into runup heights, the 100-year return tsunami runup values derived by Houston et al. (1977) are larger than the historical runup records or the results of this study. Four of the events tested have inundation similar to the 100-year return inundation line: yellow fault event with Mw = 9.04 (96-98% interval); blue fault event with Mw = 8.82 (94-96% interval); white fault events with Mw = 8.67 (92-94% interval) and Mw = 8.56 (90-92% interval). This illustrates the importance of modeling tsunami events at multiple locations along a source region for a given magnitude, and that the 100-year earthquake calculated from the best fit of the distribution is not necessarily the same as the 100-year tsunami inundation. Figure 13c shows maximum flow depth for the 100-year probabilistic tsunami inundation. The darker blue gives deeper flow depth on land. In this figure the affect of many land features are evident. For instance at W near the Dillingham Airfield, there is very little water on top of the air strip, but the surrounding drainage ditches are flooded. Having an idea of not only how far on land the tsunami waves are likely to reach, but an estimate of the water depth is a very useful tool for building design and civil defense agencies concerned with hazard mitigation. 4.3 Additional Considerations One obvious aspect of the tsunami hazard assessment that deserves additional investigation is the affect of the tides on the probabilistic analysis. In Hawai'i the tides are mixed, which presents a large variation in amplitude over time, though the tide range 30

38 is small (-2ft) so for Hawai'i including the tidal variation is not as critical as locations with large tide ranges. The tsunami-tide interaction is a dynamic process, and there are several things to consider when incorporating tidal probabilities. Not only should the tide level at the initial tsunami arrival be considered, but also the appropriate tidal phase, and appropriate evidence for that selection. It is possible to choose a worst case tide scenario according to tsunami arrival time, but an increase in tide level does not automatically yield a linear increase in runup values, since the tsunami inundation is strongly influenced by the nearshore characteristics such as bathymetry slope and dissipation over coral reefs. Since the velocity of tsunami propagation is much greater in the nearshore area than the changing water level due to tides, the assumption of mean sea level as a static background water level is not unreasonable, for the purpose of developing this probabilistic approach. Also considering background storm wave conditions would be another area that could influence the runup and inundation. Since the coupling of these effects is non-linear, simply increasing the water depth during tsunami propagation could introduce more relative error than can be accounted for, given the uncertainties of tsunami. As mentioned previously, additional tsunamigenic mechanisms can be included in future work. Since the historic data for tsunami earthquakes, local tsunami events, landslide-generated tsunamis and asteroid-impact tsunamis is limited and the probability of occurrence over 100 years is low, they were not considered in this paper. Although the slip distribution within a rupture area may have limited effects on far-field tsunamis (Sanchez and Cheung, 2007), increasing the constraints of earthquake source parameters and the tsunami generation calculations will decrease the uncertainties of the probabilistic calculations. For the application of this method to areas where historic data is limited, extra care will need to be taken in selecting a source distribution and trench characteristics. Though the role of tides or storm waves may be small compared to the tsunami wave, 31

39 there is potential to reduce the uncertainty in the tsunami runup and inundation estimates. Investigating the dynamic coupling of tsunami, tidal and storm wave components, considering both water level variations and the current interactions, spatial likelihood of earthquake or tsunami occurrence along a seismic zone and additional tsunamigenic mechanisms are subj ects where there is significant need for further research. 4.4 Future Application One prominent application of this method is to develop probabilistic inundation maps for the State of Hawaii and other coastal areas vulnerable to tsunamis. The methodology presented in this paper can also be applied and incorporated into the Flood Insurance Rate Maps developed by FEMA. Maps including this probabilistic tsunami inundation data can be used to assess vulnerability of local populations and infrastructure, can be used to develop new building codes or future land use policy. In the event of a natural disaster, energy and electricity play a vital role in the emergency response and recovery of a community. According to the 2005 Annual Report of the State of Hawaii Energy Resources Coordinator, imported petroleum accounts for 89% of Hawaii's primary energy. In addition, electric power generation is heavily dependent on oil. About 78% of the electricity produced by the State's primary electric utility, Hawaiian Electric Company (HECO), is from petroleum. There is a pressing need to utilize latest data and research methods to determine the vulnerability of critical infrastructure such as oil refineries and storage facilities in Hawaii. On the island of Oahu, both oil refineries, power plants, and other critical facilities are located in Campbell Industrial Park. For this reason, the coastline of the southwest Oahu including Campbell Industrial Park is a prime location where potential tsunami impacts need to be thoroughly investigated and quantified, and is a potential case study to demonstrate the usefulness of this method. 32

40 CHAPTERS CONCLUSIONS AND FUTURE WORK This study demonstrates that it is possible to relate the statistics of the tsunami source and resulting runup and inundation through a systematic sampling and modeling approach. A seismic source region is characterized to determine frequency of occurrence distributions, which is sampled at intervals with equal probability of occurrence. These representative events are then numerically modeled and the results are compiled into a probabilistic grid, capable of incorporating additional distributions. The approach of modeling a tsunami from the source to the far-field shore provides a rational approach to account for local variation of tsunami inundation. This method can also determine probabilistic inundation estimates without mixing runup data from different tsunamigenic sources or simulating incomplete data records. This probabilistic approach to tsunami inundation mapping will be very useful for vulnerability studies and generating quantifiable results. One specific area that will be very useful for improving tsunami-ready building codes will be to determine probabilistic flow depth and velocity, from which the tsunami impact on structures can be factored in with more accuracy. As tsunami modeling efforts and the understanding of tsunami generation is improved, the probabilistic analysis method presented here will be refined further. For a more complete analysis, tsunami inundation can be included from different seismic zones, each with its own unique distribution. Other events such as local tsunamis and landslide generated tsunamis should be considered as well, which can be expanded and refined as models are improved and more data is analyzed. Further analysis and understanding of the seismic source zone, the tsunamigenic process and refinements in the overland flow numerical calculations will improve the probabilistic estimates developed with this method. 33

41 Table 1. Earthquake and Tsunami Source Data Catalogs. Catalog Date Source Region Number Runup Range of Location Records Pacheco & Sykes (1992) Alaska (incl. Aleutian Islands) 35 Global Central Moment Tensor (CMT) N 48 N 135 W 168 E 14 Alaska Earthquake Information Center N 48 N 135"W 168 E 80 NEIC Significant US Earthquakes N 48 N 135 W 168 E 44 NEIC SignHicant Worldwide Earthquakes N 48 N 135 W 168 E 24 NEIC Preliminary Determination of Epicenters N 48 N 135 W 168 E 18 NGDC Historical Tsunami Database Alaska (incl. Aleutian Islands) 14 Hawaii (3 searches) N 48 N 135 W 168 E Alaska (Incl. Aleutian Islands) 23 34

42 Table 2. Data Catalog Compilation. Number of Catalogs Events Reported Equivalent In Multiple Number of Catalogs Records Total Events Events with No Data 3 10 Total Earthquake Events

43 Table 3. Compiled Data Catalog Analysis. Catalog Category Number of Percentage of 87 Events, n Total Events Only Ms Available 60 69% Only Mw Available 4 5% Both Mw and Ms Available 23 26% Both Mw and Ms Available Mw ~ % Tsunamis Recorded in Hawaii 14 16% Tsunamis Recorded in Hawaii Mw ~ % Local Tsunami Evenm 8 9% Total Tsunamis Generated 22 25% Earthquake Evenm with Mw ~ % Total Usable Tsunamis 18 21% Tsunamis with Mw ~ % Usable Tsunamis with Mw ~ % Local Tsunami Events with Mw ~ % TsunamlslEarthquakes with Mw ~ % 36

44 Table 4. Magnitude Grouping Scenarios. Number of Events M ~ 7 Number of Events M ~ 7.5 Magnitude Used Minimum Maximum Average Minimum Maximum Average (a) M"Only (b) MsOnly (c) MixM,,&Ms (d) M" supplemented with Ms

45 Table 5. Catalog Data Used for Probabilistic Analysis. * Listed as an unlikel y tsunami event in the NGDC catalog. MW, fill with MS Tsunami Number max min median average range year Generated of Records Latitude Longitude? per Event (ON) eel Y Y Y * Y Y Y Y Y Y Y 5 38

46 Table 5. continued MW, fill with MS Tsunami Number max min median average range a year Generated of Records Latitude Longitude? per Event (ON) (OE) Y Y Y Y Y Y

47 Table 6. Historic Tsunami Event Source Parameters from the AASZ. L = fault length, W = fault width, D = focal depth, cp = strike,!) = dip, I.. = rake Year Date Lat. Lon. L W D ~ Ii A Slip Rigidity Moment Mw Me Ref. (O) {") (kin) (Ian) (Ian) {") (O) {") (m) (N/m 2 ) (102" Nm) Ox10'u x1 0' c c d k c Aleutian x10'o Ox10'u k Ox10'o Ox10'u Aleutian Ox10'o 68 B x10'o m a c d f k 40

48 Table 6. continued Year Date Lat. Lon. L W D IJl /I I.. Slip Rigidity Moment Mw Ms Ref. e) (0) (Iem) (Iem) (Iem) (0) e) (0) (m) (NIm 2 ) (1cfO Nm) xl0' b Alaskan c Oxl0' h xl0' B.4 k Oxl0' c B.7 B c 50 BO / References: a. Utsu (1962), b. Kanamori (1970), c. Sykes (1971), d. Johnson & Satake (1993), e. Johnson & Satake (1994), f. Johnson, et al. (1994), g. Christensen & Beck (1994), h. Holdahl & Sauber (1994), i. Abe (1995), j. Johnson & Satake (1997), k. Johnson (1999), 1. Tanioka & Seno (2001), m. Lopez & Oka! (2006). 41

49 Table 7. Data regression Analysis Results and Systematically Sampled Magnitude Values. Interval Sampled Magnitude Values Sampled Magnitude Values ClaSSification from n = 29 dataset from n = 23 dataset k i r I ~oo I I Distribution We!buIJ Welbull Weibull G-.g lllgnonnaj i We!buIJ We!buIJ WeJbull Gutenberg Lognormal RIchter, RIchter i Plotting Position a b c a a I, a b c a a 80-82% !, % % % % % % % % % a. F = I-m/(n+l) b. F = 1-(m-O.3)/(n+O.4) c. F = l-(m-a)/(n+b). where a and b are the slope and intercept of the best fit line I 42

50 Table 8. Nested Grid Coverage and Resolution. Nested Grid Layer Coverage Grid Spacing 1 Pacific 62 on 10 on 115 OW 115 E 2 min 2 Hawaiian Islands 23 on 18 on 154 OW 160 E 15 sec 3 O'ahu 21.8 on 21.2 on OW OW 3 sec 4 Haleiwa on on OW OW 0.3 sec 4 Mokulela ON ON OW ow 0.3 sec 43

51 Table 9. Bathymetry Data Sources and Resolution. Dataset Horizontal Coverage Source Resolution General Bathymetric Chart of the 1 min Global British Oceanographic Data Center Oceans (GEBCO) Earth-Topography-Two-Minute 2 min Global National Geophysical Data Center (ETOP02) (NGDC) GEBCO-ETOP02 mixing 1 min Global NOAA Laboratory for Satellite Altimetry Coastal Relief (U.S.) 3 sec U.S. National Geophysical Data Center (NGDC) HawaII Regional Bathymetry 5 sec Hawaii Japan Marine Science and Technology Center (JAMTEC) and U.S. Geological SUivey (USGS) Scanning Hydrographic Operational 4m U.S. Shore to U.S. Army Corps of Engineers Alrbome UDAR Survey (SHOALS) 40m depth (USACE) Photogrammetrlc Data 5 ft (vertical) O'ahu City and County of Honolulu UDAR Topography 2m U.S. Coastline NOAA Coastal Service Center GPSData 2m Parts of O'ahu Dept. of Ocean and Resources Engineering, University of Hawaii 44

52 Table 10. Summary Parameters of Events Tested. Interval Mw Variable Percentage Length (Ion) 80-82% % % % % 8.4B % % % % % % 9.34 n %

53 Table 11. Sample Fault Weight Factors. Fault Weight Factor n.'.. '.- ~ -... ' equal probability

54 z ,,,,,,,,,,,,, y Seafloor,,, i" ~ X,, ~ ,,,,,,,,,,,,,, depth, d North < ) length, L Figure 1. Deftnition sketch of planar fault model. 47

55 62"N U " I ~/;J}fi 'E'~.,.. ~.,. I Coastline I ~:~_ij:"'i_l" J., ~ ' '\ _~~F» t, "'''-_ 6O"N 58"N --AJeul ian Trench Earthquakes Mw~ 7.5 o Tsunamigenic Earthquakes a Tsunamigenic Earthquakes with Runup in HI Eva nts not considered )If a 1»W 9.5 r-r- ~ _, I EarthquOikes Mw ~ 6.5 Ea rthq uakes Mw ~ Tsunamigenic Earthquakes o Tsunamigenic Eart hquakes with Runup in HI 8.5 H X Events not con sidered I ~ I' ~.. s b 6,~ 1 7~ 1~ 17';""" 1sd-w Figure 2, Bathymetry, seismic and tsunami events ( ) for the Alaska-Aleutian Seismic Zone (AASZ), 48

56 3J) C280 ~ ~260 U5 240,-.~ --Wei et 01. (2003) --PMEL --Present Study ~ '- -~ -... r- -, I I!, / O"E 17D"E 100" 171l'W l6o"w l6o"w '-. 14O"W r- C 15 ~ is 10 5 r- l~e r--, ' " '---. I Wei ot 01 _ (2003) --PMEL --Present Stud y I 17D"E ~-, I 100",,, \ \ \ \ \ I I I \ 171l'W l6o"w 150'W O"W 20 ' ~------_,r_------~ ,_ ,_ ~ --Wei et 01 (2003) -;; 10 --PMEL ~ --Present Study 5 [ I I I /\ I --- 1~ 1~ 100" 1~ l6o"w lou"w I I I I O"W Figure 3. Earthquake source parameters for the Alaska-Aleutian Seismic Zone (AASZ). 49

57 76 0 ' t: l?o '~.~ 180'.\f'l \~(0 170W 160'W '\50 'IN,0.(0 170W 160'W Figure 4. Seismic events and approximate rupture areas. Reproduced from Wesson, et al. (1999). 50

58 1500,,- Mw E 1000 Ms ~ --Linear Regression 1 c, c: ' 0 1 I, ~ ~ Magnitude 300 PDt M, IT;]..t:: ~ I 100 [; Magnitude Figure 5. Fault length and width variation with magnitude. Data is also given in Table 6. 51

59 62"N 1 x~*i.l ~!.,.... -~~~ 6O"N 58"N..J...:; 'oj.., a 1'JJW <l.: 17O"E 1 Ell" 17rTW lfxfw, 50"\\1 '4f1'W 1'JJW Figure 6. Constant (a) and variable length (b) subfault scenarios. b 52

60 ~ 85 r Selected Seismic Events 100 yr return magnitude. Mw = linaar Regression. a = b = r 2 = f ~ _ 1l X 1 I 0.4 I I I I 06 o B 1 2 Reduced Vari ate. In(O) I T -, I 1.4 ~ I I Probability Density Function. pdf 10% Division Interval 2% Division Interval 2% Division Interval Median. x a 2 O: t 0 I. I. I. I. I. I I 80 B2 B4 B6 B Equal Interval Percentage DMsions 98 b 100 ~ ~ 10 ~ 9.5 U Mw ;; a + bx I.8 ~ '" => 9 f- ~ 8.5 f- 'C ".3 8 f-." '" ~ I I I I I I I I I BO 82 B4 B6 BB Equal lnterva\ Percentage Divi sions I - - -i c...,.l Figure 7. Probabilistic analysis curve fining, linear regression (a), equal percentage interval determination (b), magnitude values to test (c). 53

61

62 \ v "", \! \ I.... ~<J> "t>.;... '. ~'. ~ o

63 80-82% rt'x,y) ::: 11/ <'N 215~'5~ mm, ~ '> :oc:::: "N < <W 'W "W "W w <W Figure 10. Probabilistic grid development. 56

64 z <'<! ~ N z 19 ~ N,) ~ - r~' ,C'P~ <.). r ' -. r::" ~ _". ~. '. '_, _, ''0.l'\~~.~~.,..;-~---.~ ;~~~""' ~ r-,'" _/'(.I.../' '' - '''--~ '. \ c "... ""-vr ~'''''- r '.; _I ( -.~. '.,., J-...,-r ~ ;;.!~ -'. ".. '.,.,.!11 z ~ r::r='--'-- -'-_ " N W W W W W W W W W W W W z '" ~ N % % 88,90% 92-94% -- 82,84% 86-88% z CO '" ~ N z ~ t ' N W W W W W W W W W W W W ~ ~~;, ================================~ ~ N z 19 ~ N z - 80, 82% % % 88-90% 92-84% ~ r::t=---''-- -'--' N W W W W W W W W W W W W Figure II. Sample inundation lines. 57

65 1 ~O-year Inundation Limit year Inundation Limit -- Q = Exceedance Probability Figure 12. Probabilistic inundation grids. S8

66 z 10 ~ Historic Runup Reoords year Probabilistic Inundation N z 19 ~ N year Probabilistic Inundation -- Q = 0.Q1 Probabilistic Inundation z, co "' N 158.3' W ' W ' W ' W ' W 158.2' W ' W ' W ' W ' W 158.1' W ' W 15 E 10 Q. ::> c: ::> Ct: 5 0' 'I I b ~ z, :g ~ N z fg Flow Depth (m) 8 N 158.3' W ' W ' W ' W ' W ' W ' W ' W ' W ' W Figure 13. Runup comparison and Probabilistic Inundation Map. 59

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