Tsunami Modeling

Permanent URI for this collectionhttps://digital.lib.washington.edu/handle/1773/46677

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Probabilistic Source Selection for the Cascadia Subduction Zone
(2017-03-19) Adams, Loyce; LeVeque, Randall J; Rim, Donsub; Gonzalez, Frank I
This report has been submitted to FEMA Region IX as a final project report for a project on developing new methodologies for Probabilistic Tsunami Hazard Assessment (PTHA). We propose a methodology for taking a large number of realizations of potential future earthquakes (with associated probabilities) and producing good approximations to the resulting hazard curves and maps without doing a computationally- expensive fine-grid tsunami simulation for each realization.
Tsunami Hazard Assessment of Whatcom County, Washington. Project Report - Version 2
(2019-05-19) Adams, Loyce; LeVeque, Randall J; Gonzalez, Frank
This report documents the results of a study supported by the Washington State Emergency Management Division of the tsunami hazard along the coast of Whatcom County. One earthquake source from the Seattle Fault and one from the Cascadia Subduction Zone were considered. Results include inundation depths and times of arrival that will be useful to coastal communities, as well as tsunami current speeds and momentum flux. GeoClaw Version 5.5.0 was used for the modeling, with some modifications as described in the appendices.
Modeled tsunami in Lake Washington from hypothetical ruptures on the Seattle Fault
(2020-03) Richwine, Kathryn
Tsunami deposits from an earthquake on the Seattle fault have been found around the Puget Sound area. Tsunami modeling has been conducted in Puget Sound with the Seattle fault as the initiating event, however published modeling efforts have not investigated the effects of an event from the Seattle fault on the Lake Washington area. The Seattle fault crosses Lake Washington extending east towards Lake Sammamish, and a tsunami generated from this fault could create hazardous conditions along the lake’s shorelines. The parameters of the Lake Washington section of the Seattle fault are applied to create deformation files modeling potential tsunami waves generated from a fault rupture. Four simulations are run with the modern-day lake level and again with the pre-ship canal lake level using the open source software GeoClaw. These eight simulations are analyzed to determine which fault parameters produce a wave that inundates the shoreline. A scenario modeling a 10-meter slip at a depth of 1-km that uses the pre-ship canal lake level and a four-hour runtime determines the extent of inundation and locates potential areas for tsunami deposits. These results show that the shoreline is inundated four times over the first four hours after the earthquake, with maximum tsunami wave heights of 2 m to nearly 4 m arriving within minutes to tens of minutes of the fault rupture. I identify seven low-lying areas susceptible to inundation and suggest three sites for paleotsunami investigation as a test for these models. More extensive modeling of different scenarios and fault parameters is needed to understand the range of possible or likely inundation from a tsunami wave in Lake Washington triggered from the Seattle fault.
Preliminary Modeling Study of a Vertical Evacuation Structure Site for the Aberdeen School District
(2020-02) Adams, L.M.; Gonzalez, F.I.; LeVeque, Randall J
A Maximum Considered Tsunami (MCT) scenario was developed for a magnitude 9 tsunamigenic earthquake on the Cascadia Subduction Zone. The development of this MCT scenario is compliant with our current understanding of the American Society of Civil Engineers (ASCE) Building Code 7 published in 2016, i.e., ASCE 7-16. The results of the numerical simulation support the design of a vertical evacuation structure (VES) as part of the new Stevens Elementary School in Aberdeen, WA. Estimates of key hazard design parameters at the site include seismic subsidence of -2.76 m, 75 years of sea level rise to 0.37 m above the current level, maximum flooding of 2.75 m, and maximum current speed of 1.2 m/s. The arrival times of the leading edge and crest of the first wave to arrive at the site are 80 and 91 minutes, respectively, but several waves of increasing amplitude follow; the largest wave arrives almost 4 hours after the earthquake to create the maximum flooding and hazardous tsunami waves may continue to arrive for several hours beyond the 6-hour simulation. Substantial Aberdeen land area will be lost due to permanent flooding at levels that vary twice a day from 0 m (no flooding) at MLW to a maximum of about 3 m at MHW, depending on the location. It must be kept in mind that the simulated MCT scenario is probabilistic in nature, a single realization of an event with an estimated 2,475-year mean recurrence interval, so that the results discussed in this report cannot be taken literally as an accurate, detailed prediction of what will happen; rather, valuable general guidance is provided on what may happen, but significant uncertainties exist in any seismic or tsunami model result.
Modeling Study of a Proposed Vertical Evacuation Structure Site for the Shoalwater Bay Tribe Final Project Report
(2020-02) Adams, L. M.; González, F. I.; LeVeque, Randall J
A Maximum Considered Tsunami (MCT) scenario was developed that includes projected sea level rise of 0.47 m over 75 years and a magnitude 9 tsunamigenic earthquake on the Cascadia Subduction Zone; development of the scenario is compliant with our current understanding of the 2016 American Society of Civil Engineers (ASCE) Building Code 7, i.e., ASCE 7-16, and was reviewed by a SEFT Peer Review Team and Peer Review Advisory Panel for the project. The results of the numerical simulation support the design of a vertical evacuation structure, a tower located within the city of Tokeland, WA on land purchased by the Shoalwater Bay Indian Tribe. Estimates of key hazard design parameters at the site include 75 years of sea level rise to 0.47 m above the current level, seismic subsidence of -2.5 m, maximum flooding of 5 m and maximum current speed of 6.7 m/s, all referenced to mean high water (MHW). The arrival times of the leading edge and the maximum amplitude of the first wave to arrive at the site are 29 and 36 minutes, respectively. Hazardous tsunami waves continue to arrive for the 6 hours of the simulation and would likely continue for as many more. Most of the peninsula will be flooded twice daily at mean high water to a depth of 1-3 m for decades, assuming that post-seismic uplift eventually raises the land above mean high water.
Effects of Flow Shielding and Channeling on Tsunami-Induced Loading of Coastal Structures
(2020-02-04) Winter, Andrew Owen; Motley, Michael R; Eberhard, Marc O
Prior efforts to numerically model the complex fluid-structure interactions that occur as tsunami inundations pass through coastal communities have failed to consistently reproduce experimentally-measured flow velocities and depths. These deficiencies have led to inaccurate estimates of the forces and pressures acting on individual structures due to shielding and channeling effects caused by neighboring structures, which tend to reduce and increase structural demands, respectively. To address these shortcomings, the primary goals of this dissertation were to produce an experimental data set for a range of neighboring structure configurations from which shielding and channeling effects on force demands were identified as well as to develop an experimentally-validated computational fluid dynamics model that was capable of accurately reproducing the observed effects. Additionally, a parametric study that varied neighboring structure locations was conducted using the validated CFD model in order to develop a streamwise force-prediction design equation, which improves upon the methods provided in the ASCE 7-16 design provisions used to estimate force amplifications due to neighboring structures.
Tsunami Inundation Modeling of Sequim Bay Area, Washington, USA from a Mw 9.0 Cascadia Subduction Zone Earthquake
(2017-06) Lee, Chun-Juei
The Strait of Juan de Fuca and the coastline nearby are prone to tsunami attacks along the Cascadia Subduction Zone (CSZ). Besides the tsunami deposits that exist on the outer coast, the inland geological evidence shows that nine sandy-muddy Cascadia tsunami deposits intrude a 2500-yr-old sequence of peat deposits beneath a tidal marsh at Discovery Bay, Northern Olympic Peninsula, Washington (Williams et al., 2005). Thus, assessing the potential damage for the next CSZ earthquake tsunami event is important. In this study, I conducted tsunami simulations using the GeoClaw numerical model by a scenario earthquake. The earthquake scenario adopted for this study is a Mw 9.0 CSZ earthquake, also known as the “L1” scenario (Witter et al., 2011). Fine-resolution (1/3 arc-second) digital elevation models (DEMs) are used to provide high resolution tsunami inundation results on Sequim Bay area at northern Olympic Peninsula. The numerical gauges which are set around the major Infrastructure and properties provide information of wave height, wave velocity and wave arrival time. Four tsunami waves with 2-meter-height are found over the ten hours simulation. Also, two spits at the entrance of Sequim Bay can diminish and delay the tsunami impacts in the Bay. The modeling results will contribute to public safety administration in the Pacific Northwest as an aid to development of hazard mitigation plans and emergency response.
Efficient Tsunami Simulation at Local and Global Scales
(2019-10-15) Qin, Xinsheng; Motley, Michael R.; LeVeque, Randall J.
Tsunami hazard evaluation and mitigation is of great importance to coastal communities around the world, especially after the frequent occurrence of large tsunamis in the past two decades. Many physical phenomena need to be modeled during a tsunami event, e.g. tsunami wave generation and propagation, coastal inundation, and forces on structures. Most of them are nonlinear and involve a wide range of length scales, and thus are challenging to model. In this dissertation, the ability of three-dimensional (3D) and two-dimensional (2D) models to capture tsunami forces on structures and flow through a constructed environment is first analyzed. Then the development of a GPU-accelerated hyperbolic partial differential equation (PDE) solver with adaptive mesh refinement (AMR), with application to solving several PDEs that govern different physical processes arising in tsunamis, is presented and discussed. Tsunami inundation is the final and most destructive phase of tsunami evolution that comes after tsunami wave propagation in the ocean. The numerical modeling of this phase that incorporates the constructed environment of coastal communities is challenging for both 2D and 3D models. Inundation and flooding in this region can be too complex for 2D models to capture properly, while for 3D models a very fine mesh is required to properly capture the physics, dramatically increasing the computational cost and rendering impractical modeling of some problems. To evaluate the capability of the current tsunami inundation models, comparisons are made between GeoClaw, a depth-integrated 2D model based on the nonlinear shallow water equations (NSWE), and the interFoam solver in OpenFOAM, a 3D model based on Reynolds Averaged Navier-Stokes (RANS) equations for tsunami inundation modeling. The two models are first validated against existing experimental data of a bore impinging onto a single square column. Then they are used to simulate tsunami inundation in a physical wave tank model of Seaside, Oregon. The resulting flow parameters from the models are compared and discussed, and these results are used to extrapolate tsunami-induced force predictions and give guidance for the use of numerical models in other similar situations. Numerical modeling of tsunami processes is computationally expensive. Being able to do this faster means we can simulate a problem with higher resolution to potentially get more accurate result, simulate the same problem faster to send out tsunami warning earlier, or perform more tsunami simulations within a given time budget when doing probabilistic hazard assessment or studying the uncertainties of the process. Using Adaptive Mesh Refinement (AMR) as implemented in GeoClaw speeds up the process by greatly reducing computational demands, while accelerating the code using the Graphics Processing Unit (GPU) could do so through faster hardware but has not previously been implemented in GeoClaw. The second part of this dissertation presents an efficient CUDA implementation of the GeoClaw code. The code can model transoceanic tsunami simulation by using AMR and solving the shallow water equations in spherical coordinates. Numerical experiments of the 2011 Japan tsunami and a local tsunami triggered by a hypothetical Mw 7.3 earthquake on the Seattle Fault illustrate the correctness and efficiency of the code. The GPU implementation, when running on a single GPU, is observed to be 3.6 to 6.4 times faster than the original model running in parallel on a 16-core CPU. Three metrics are proposed to evaluate performance of the model, which shows efficient usage of hardware resources.
The history, hydraulics, and geomorphic impact of outburst floods in the eastern Himalaya
(2019-10-15) Turzewski, Michael David; Huntington, Katharine W
Outburst floods have shaped many landscapes on Earth and represent a significant geologic hazard, but they are relatively infrequent, and we must rely on the sedimentary record to study the most extreme events that have occurred. The eastern Himalaya has a record of various magnitude outburst flood events, including landslide-dam outburst floods (>10^5 m^3/s) and ancient glacial-outburst megafloods (>10^6 m^3/s) that have done substantial amounts of geomorphic work on the landscape throughout the Quaternary. This dissertation investigates outburst floods in the eastern Himalaya with a combination of fieldwork, remote sensing, numerical flood modeling, and geochronology to study the timing, hydraulics, and net erosional impact of these events. Numerical flood simulations of the year 2000 Yigong River outburst flood help characterize flood hazard in the Siang River valley, India, and are used to examine the relationship between outburst flood hydraulics and geomorphic change observed along the >450 km rugged flood pathway that cuts through the >2 km deep Tsangpo Gorge. Simulated outburst flood hydraulics differ from non-flood flows and show that valley topography exerts a strong control on the distribution of shear stress and the patterns of erosion and deposition produced from the flood. Zircons collected from ancient slackwater flood deposits in the region characterize the age of rocks eroded from flood source terrains in Tibet and from the Tsangpo Gorge. Statistical analyses of these data support the previous hypothesis that megafloods erode more rock from Gorge compared to smaller flows, but also show substantial variability among different megaflood deposit samples. These data suggest that megafloods rework sediments from previous events, which is a result supported by luminescence age data from megaflood deposits that influences the interpretation of detrital outburst flood samples. Radiocarbon and luminescence dating methods constrain the timing of at least 9 megaflood events over the last 42 ka, showing the potential for repeated megaflood events from glacial-lake sources in Tibet. The work presented here advances our knowledge about hydraulics during outburst floods, patterns of preferential erosion, chronology of megafloods, and processes of sediment reworking, altogether improving our understanding of the impact of extreme outburst floods in the region.
Issues Encountered with ASCE Compatibility Criteria
(2019-05) Adams, Loyce; Gonzalez, Frank; LeVeque, Randall J
The State of Washington is assisting at-risk coastal communities that have included the design and construction of tsunami vertical evacuation structures in their hazard mitigation plans. Washington State has not formally adopted the ASCE 7-16 Chapter 6 standard; however, past VES projects have made the decision to meet these standards, as well as TLES-approved ASCE 7 Change Proposals to revise Chapter 6 of the 2022 version, ASCE 7-22 (e.g., Chock, et al., 2018) in anticipation of possible formal approval by the ASCE 7 Main Committee and adoption by the State. As a result, Washington State has been a very active user of the standard, which continues to evolve as the TLES reviews and develops and votes on 7-22 Change Proposals. The purpose of this brief report is to contribute to the ASCE 7 TLES process of improving ASCE Chapter 6 guidance by identifying issues we have encountered with these standards and providing appropriate suggestions that we hope will improve the guidance and ease of use by practitioners.
Adjoint-Guided Adaptive Mesh Refinement for Hyperbolic Systems of Equations
(2018-11-28) Davis, Brisa; LeVeque, Randall J
One difficulty in developing numerical methods for time-dependent partial differential equations is the fact that solutions contain time-varying regions where much higher resolution is required than elsewhere in the domain. The open source Clawpack software implements block-structured adaptive mesh refinement to selectively refine around propagating waves in the AMRClaw and GeoClaw packages. In particular, GeoClaw is widely used for tsunami modeling, the application that motivated this work. For problems where the solution must be computed over a large domain but is only of interest in one small area (e.g. one coastal community when doing tsunami modeling, or the location of a pressure gauge when doing acoustics modeling), a method that allows identifying and refining the grid only in regions that influence this target area would significantly reduce the computational cost of finding a solution. The adaptive mesh refinement approach currently implemented in AMRClaw and GeoClaw often refines waves that will not impact the target area. To remedy this, we seek a method that enables the identification and refinement of only the waves that will influence the location of interest. In this work we show that solving the time-dependent adjoint equation and using a suitable inner product with either the forward solution, or the estimated one-step error in the forward solution, allows for a more precise refinement of the relevant waves. We present the adjoint methodology first in one space dimension for illustration and in a broad context since it could also be used in other adaptive software, and for other tsunami applications beyond adaptive mesh refinement. We then show how this adjoint method has been integrated into the adaptive mesh refinement strategy of the open source AMRClaw and GeoClaw software and present linear variable coefficient acoustics and tsunami modeling results showing that the accuracy of the solution is maintained and the computational time required is significantly reduced through the integration of the adjoint method into adaptive mesh refinement. The adjoint method is compared to adaptive mesh refinement methods already available in the AMRClaw software, and the advantages and disadvantages of using the adjoint method are discussed. Other capabilities of the adjoint method such as focusing on specific time ranges of interest, sensitivity analysis, and source impact analysis and design are also presented. The new algorithms are incorporated in Clawpack and code for the examples presented in this work is archived on Github.
Green's Law and the Riemann Problem in Layered Media
(2018-07-31) George, Jithin Donny; LeVeque, Randall J
The propagation of long waves onto a continental shelf is of great interest in tsunami modeling, where understanding the amplification of waves during shoaling is of significant importance. When the linearized shallow water equations are solved with the continental shelf modeled as a sharp discontinuity, the ratio of the amplitudes is given by the transmission coefficient that can be obtained from the solution of a Riemann problem. On the other hand, when the slope is very broad relative to the wavelength of the incoming wave, then amplification is governed by Green's Law, which predicts a larger amplification than the transmission coefficient, and a much smaller reflection than given by the reflection coefficient of a sharp interface. Exploring the relation between these results offers a perspective that allows us to view the solution to the shallow water equations as combinations of infinitely many transmitted and reflected waves. The thesis focuses on an asymptotic approximation to this solution, general enough for continuous non-homogeneous media, and presents some interesting results and scenarios along the way. The same phenomena and similar results exist for other physical settings described by wave equations, including those of linear acoustic waves and electromagnetic waves.
GeoClaw Model Tsunamis Compared to Tide Gauge Results Final Report
(2018-11-03) Adams, Loyce M.; LeVeque, Randall J
The purpose of this project is to compare GeoClaw tsunami model results to detided tide gauge results at multiple destinations for each of several tsunamis. In particular, we are interested in the suitability of GeoClaw for calculating tsunami amplitudes with enough precision to be used for forecasting, especially in the context of ensemble modelling. In each of our comparison plots, we also include a sample MOST tsunami result which is useful to see the reasonableness of GeoClaw in regions where tide gauge data is missing or has insufficient resolution. The methodology behind GeoClaw can be found in [1] and [5], and its performance on the 2011 NTHMP problems in [4] and [6]. For a description of the MOST model see [7]. Here, we give a quick summary of our progress on such comparisons for the Japan 2011, Samoa 2009, Kuril 2007, Chile 2010 and HaidiGwaii 2012 tsunamis at tide gauge destinations at Crescent City, Arena Cove, Port Orford, Hilo, Midway Island and Pago Pago. In the next sections, we provide more details.
Tsunamis and sea levels of the past millennium in Puget Sound, Washington
(2017-10-26) Garrison-Laney, Carolyn; Atwater, Brian F
Tidal marsh deposits in the Puget Sound area contain evidence for multiple earthquakes and tsunamis over the past 1,000 years. This dissertation focuses on evidence beneath a salt marsh at Lynch Cove, at the head of the Hood Canal about 40 kilometers southwest of Seattle. Previous work at this marsh described stratigraphic evidence for coseismic uplift and liquefaction from a crustal earthquake or earthquakes about 1,000 years ago. New findings from Lynch Cove include two anomalous silt layers interpreted as tsunami deposits that postdate the earthquake uplift and liquefaction. These layers are better explained by tsunamis than by storms or river floods, based on the layer morphology, extent, sedimentology, and microfossils. Radiocarbon ages of the two silt layers at Lynch Cove are 1690–1830 A.D. (120–260 cal yr BP, layer A), and 1170–1230 A.D. (720–780 cal yr BP, layer B). These ages more closely align with the ages of two Cascadia earthquakes than with any other known earthquake in the Puget Sound region within the last 1,000 years. These the silt layers may have been deposited by tsunamis generated by Cascadia subduction thrust earthquakes, as were likely correlative deposits at another tidal marsh at Discovery Bay, along the tsunami path between the Pacific Ocean and Hood Canal. This study improves the age ranges of the youngest six tsunami deposits at Discovery Bay, and compares them to layers A and B at Lynch Cove, and to the ages of known earthquakes and their secondary effects, including tsunamis and slope failures, of the last 1,200 years in the Pacific Northwest. Beds 1 and 3 at Discovery Bay are attributed to Cascadia subduction thrust tsunamis, and have radiocarbon ages that overlap with the ages of layers A and B at Lynch Cove. Discovery Bay Bed 2 has now been dated to 560-630 cal yr BP (1320-1390 A.D.). It is unclear why no corresponding deposit is present between layers A and B at Lynch Cove, and why no known 14th-century coseismic subsidence or tsunami is preserved at any of the Pacific coast estuaries of southern Washington. The source of the tsunami that deposited Discovery Bay Bed 2 remains to be determined. If the source was a rupture along the Cascadia subduction thrust, it may have been limited to an area offshore southern British Columbia and northern Washington, on the northern end of the subduction zone. To test whether Cascadia tsunamis could have deposited the silt layers at Lynch Cove and Discovery Bay, numerical tsunami simulations were run for three different rupture styles of great Cascadia earthquakes, a local Seattle fault tsunami, and a transoceanic tsunami from Alaska. The Cascadia earthquake tsunami simulations produced flow depths and current speeds sufficient to deposit the silt layers at both Lynch Cove and Discovery Bay, while the Seattle fault simulation did not. The Alaska tsunami simulation also produced flooding at Lynch Cove and Discovery Bay, in agreement with historical observations from 1964. Using the inferred tsunami deposits at Lynch Cove as time markers for great Cascadia earthquakes, the paleoecology of the last ~1,000 years is reconstructed using fossil diatoms to test whether Lynch Cove, 240 km inland of the deformation front, records any Cascadia earthquake cycle deformation. A diatom transfer function was developed by statistically comparing the fossil diatoms at Lynch Cove to a training set of modern intertidal diatoms from Puget Sound. Using this method, 31 paleomarsh surface elevations were reconstructed, and with radiocarbon ages, a relative sea level curve was constructed. An overall rise in relative sea level of about 2.5 m is estimated at Lynch Cove over the last 1,000 years, a rate that is faster than rates estimated by other Puget Sound studies. Superimposed on this overall relative sea level rise, paleomarsh surface elevations are observed to rise by about 25 cm prior to the deposition of both layers A and B. While these may record Cascadia preseismic deformation, these rises are within the error range of adjacent data points, so are inconclusive. Because of this, Lynch Cove marsh is interpreted as a location that probably does not record Cascadia earthquake cycle vertical deformation. Lynch Cove is the only forearc data point of vertical interseismic deformation for the Cascadia subduction zone, and these negative results provide an inland limit of earthquake cycle deformation. The findings of this research help to better understand hazards from Cascadia earthquakes and tsunamis in the Puget Sound region. The identification of paleotsunami deposits in Hood Canal identifies a tsunami hazard that was previously unknown. The tsunami simulations corroborate the geological evidence, and identify some areas in Puget Sound with greater tsunami hazard. This study also places constraints on the inland limit of Cascadia earthquake deformation. This is important for accurate estimates of areas of strong shaking, which influence earthquake hazard maps, and for geophysical models. This research also influences estimates of earthquake recurrence. If Bed 2 at Discovery Bay is from a northern Cascadia earthquake, recurrence rates at the northern end of the subduction zone may be shorter than current estimates.
Uncertainty Quantification Problems in Tsunami Modeling and Reduced Order Models for Hyperbolic Partial Differential Equations
(2017-08-11) Rim, Donsub; LeVeque, Randall J; Uhlmann, Gunther A
In this thesis, we consider an uncertainty quantification (UQ) problem that arises from tsunami modeling, namely the probabilistic tsunami hazard assessment (PTHA) problem. The goal of PTHA is to compute the probability of inundation at coastal communities, and the uncertainty originates from the unknown slip distribution of potential tsunamigenic earthquakes. First, we show that the Karhunen-Lo`eve (K-L) expansion can be used to gener- ate a wide range of random earthquake scenarios that represent this uncertainty well. Then we propose a multi-resolution approach to estimate the inundation: since it is computation- ally expensive to accurately estimate the inundation resulting from each scenario by using only fine-grid runs, many cheap coarse-grid runs are used instead to bulid an approximation. For physical models that involve hyperbolic partial differential equations (PDEs), dimen- sionality reduction techniques such as the K-L expansion or multi-resolution approaches face limitations due to the fact that snapshot matrices built from solutions often exhibit slow de- cay in singular values, whereas fast decay is crucial for the success of many projection-based model reduction methods. To overcome this problem, we build on previous work in symme- try reduction [Rowley and Marsden, Physica D (2000), pp. 1-19] and propose an iterativealgorithm we call transport reversal that decomposes the snapshot matrix into multiple shift- ing profiles, each with a corresponding speed in 1D. Its applicability to typical hyperbolic problems is demonstrated through numerical examples, and other natural extensions that modify the shift operator are considered. Transport or wave phenomena are much more complicated in multiple spatial dimensions, and in our approach to extend the transport reversal algorithm to higher dimensions it becomes crucial to generalize the large time-step (LTS) operators [LeVeque, SIAM J. Numer. Anal. (1985), pp.1051-1073]. For this purpose, we introduce a dimensional splitting method using the Radon transform, that enables the transport reversal introduced above for 1D to be extended to higher spatial dimensions. This dimensional splitting is of interest in its own right, and its applications to the solution of acoustic equation, absorbing boundary condition and displacement interpolation are illustrated. This splitting method requires inverting the Radon transform, and a method for inversion using conjugate gradient algorithm will be discussed.
Tsunami Hazard Assessment of the Strait of Juan de Fuca
(2015-09-24) Gonzalez, Frank I.; LeVeque, Randall J; Adams, Loyce M.
This report documents the results of a study supported by the Washington State Emergency Management Division of the tsunami hazard along the Strait of Juan de Fuca. Results include inundation depths and times of arrival that will be useful to communities along the Strait as well as speeds, momentum, momentum flux, and minimum water depths that are useful for harbor masters and the major shipping and ferry industries that operate within the Strait of Juan de Fuca.
Spectral Methods for Partial Differential Equations that Model Shallow Water Wave Phenomena
(2014-10-13) Fabien, Maurice S.; LeVeque, Randall J.
Mathematical models for waves on shallow water surfaces has been of interest to researchers dating back to the 1800's. These models are governed by partial differential equations, and many of them have rich mathematical structure as well as real world applications. This thesis explores a class of numerical techniques for partial differential equations called spectral methods. One can use these spectral methods to approximate solutions to many partial differential equations that model wave type phenomena. Of particular interest are the KdV, BBM, Camassa-Holm, Boussinesq systems, Shallow Water, and Serre Green- Naghdi equations. For all examples presented Matlab code is provided. These files will be uploaded to the GitHub page https://github.com/msfabien/.
Probabilistic Tsunami Hazard Assessment (PTHA) for Crescent City, CA
(2014-09-11) Gonzalez, Frank I.; LeVeque, Randall J; Adams, Loyce M.; Goldfinger, Chris; Priest, George R.; Wang, Kelin
This report builds on and supercedes Phase I of a demonstration Probabilistic Tsunami Hazard Assessment (PTHA) study of Crescent City, California [23], which developed an improved methodology for PTHA and associated products that addressed only tsunami flooding depth. The study documented in this report was originally conceived as a follow-on that simply extended Phase I products to include additional tsunami parameters associated with tsunami flow in particular, current speed and momentum flux. As this study was underway, however, it was reviewed by the California Probabilistic Tsunami Hazard Analysis Work Group (CA PTHA WG) [25] that included experts on various PTHA issues, most notably the critical issue of seismic source specification. Subsequently, the CA PTHA WG review concluded that the CSZ sources used in the Phase I work was not adequately consistent with the 2014 Update to the National Seismic Hazard Maps (NSHM) [54]. Consequently, an improved suite of CSZ sources had to be developed that was more consistent with the NSHM, as discussed in Section 7.6. As a consequence, the entire set of inundation model simulations had to be repeated and new PTHA flow depth products were developed. The results presented here thus supercede the results presented in the Phase I report [23]. Both Phase I [23] and this study were funded by BakerAECOM and motivated by FEMA’s desire to explore methods to improve products of the FEMA Risk Mapping, Assessment, and Planning (Risk MAP) Program. Here we briefly summarize the goals, deliverables, technical challenges, additional work, primary results and conclusions, and recommendations of this study.
Finite volume methods for Tsunamis generated by submarine landslides
(2014-04-30) Kim, Jihwan; LeVeque, Randall J., 1955-
Submarine landslides can generate tsunamis, and the generated waves can be catastrophic when a large volume of landslide material is involved. Moreover, large earthquakes are often accompanied by submarine landslides that can enhance the magnitude of the resulting tsunamis. In this thesis, numerical schemes are developed to solve the wave propagation problems generated by submarine landslides. Assuming the landslides in a flow regime, depth-averaged models are studied, and finite volume methods are extended to the fully coupled multi-layer shallow water equations. From the fully coupled model, an efficient simplified approach is derived that is often appropriate for tsunamis generated by submarine landslides. These waves can have relatively short wavelength, and another class of equations may be necessary that can handle the dispersion of waves. Several types of the Boussinesq equations have been reviewed and implemented with a hybrid of high-resolution finite volume and finite difference methods. Stability analysis and convergence tests have been performed for the hybrid scheme. The develpoment has been done in the context of the textsc{Geoclaw} framework, a code designed to handle the single-layer shallow water equations, that uses adaptive mesh refinement to model tsunami propagation on a global scale with inundation of specific regions on a fine grid. The newly developed methods, tested on the exact solutions, are validated by comparing to laboratory experiments and by applying to historic events such as the Papua New Guinea 1998 and Storegga slides. Possible scenarios of submarine landslides and resulting tsunamis on the Washington coast were investigated.
Tsunami Hazard Assessment of the Ocosta School Site in Westport, WA
(2013-09-11) Gonzalez, Frank; LeVeque, Randall J; Adams, Loyce
The Westport Ocosta School District is proposing the construction of a new building to replace the current Ocosta Elementary School (Educational Service District 112, 2012). Since the Walsh et al. (2000) study, there have been significant advances in tsunami modeling and our understanding of potential CSZ earthquake events. Consequently, this study was commissioned and funded by the Washington Emergency Management Division to meet the need for an updated assessment of the tsunami hazard at the Ocosta School campus.

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