A Monte Carlo approach for estimating tsunami hazard from submarine mass failure along the U.S. East coast Chris Baxter1, Stephan Grilli1, and Teresa Krause1 1 Department of Ocean Engineering, University of Rhode Island, Narragansett, Rhode Island, USA Abstract This work is being conducted as part of the development of tsunami inundation maps for the U.S. East Coast (USEC), as mandated by the National Tsunami Hazard Mitigation Program (NTHMP). Along the USEC, which borders the Atlantic Ocean Basin, tsunami hazard may result from large distant co-seismic sources (e.g., in the Puerto Rico Trench or the Azores convergence zone) or volcanic flank collapse sources (e.g., in the Canary Islands). More importantly, however, tsunami hazard may result from Submarine Mass Failures (SMFs) occurring along the nearby continental shelf break and slope (e.g., 1929 Grand Bank). Indeed, potentially large tsunamigenic SMFs can be triggered by moderate seismic activity, such as could occur along the USEC, and cause large local tsunamis. While many past SMFs have been identified along the USEC and described in various publications (e.g., by USGS), due to the paucity of historical tsunami observations in this area, the associated tsunami hazard and its recurrence probability are largely unknown. To estimate the latter, in earlier work, we developed, validated with field data, and applied a Monte Carlo simulation (MCS) approach (Grilli et al., Marine Geology, vol. 264, p74, 2009) to the upper USEC (north of New Jersey). Here, a similar methodology is applied to the entire USEC. In the present MCSs, distributions of relevant parameters (e.g., seismicity, sediment properties, type and location, volume, and dimensions of slide, water depth) are used to perform large numbers (O(105)) of stochastic stability analyses of submerged slopes (along actual shelf transects), based on standard pseudo-static limit equilibrium methods. The predicted SMF types (i.e., translational or rotational), surface area, and slope angle are found to match published field data quite well along the USEC. For each parameter configuration found to be unstable under a specified ground acceleration (of given return period), the tsunami source characteristic height, and corresponding runup distribution on nearby shores, are calculated using empirical equations based on earlier numerical simulation work. A final statistical analysis of generated runup values yields estimates of overall coastal hazard, from 100 and 500-yr SMF tsunami events. The latter allows identifying regions of the USEC with elevated hazard (and related SMF parameters), where complete and detailed SMF tsunami simulations should be performed. The latter will be the object of the continuation of this NTHMP work, in which inundation from SMF tsunamis thus identified will be combined with that from other tsunami sources, to develop a series of tsunami inundation maps for areas of elevated tsunami hazard along the USEC.

Proposed Methodology for a Probabilistic Tsunami Hazard

Assessment from Submarine Mass Failures

on the U.S. East Coast

Christopher D.P. Baxter, Stephan GrilliChristopher D.P. Baxter, Stephan GrilliDepts. of Ocean/Civil and Environmental Engineering

NRC/USGS Workshop on Landslide Tsunami ProbabilityAugust 19, 2011

Acknowledgements

• National Oceanic and Atmospheric Administration

• Stefan Maretzski

• Oliver Taylor

• Teresa Krause

Grilli, S.J., Taylor, O.-D., Baxter, C.D.P., and Maretzki, S. (2009).

Probabilistic Approach for Determining Submarine Landslide Tsunami

Hazard along the Upper East Coast of the United States, Marine Geology,

264, 74-97.

Krause, T. (2011). Probabilistic Tsunami Hazard Assessment for the East

Coast United States, M.S. Thesis, University of Rhode Island.

Outline

• Introduction

• Description of Monte Carlo Model

• Validation

• Statistical Analysis

• Model Results

• Limitations and Ways Forward

Objectives

• Develop and validate a probabilistic model to assess the

tsunami hazard potential for the U.S. East Coast

• Account for uncertainty at every step of the process

• Use this model as a screening tool for selecting more

detailed deterministic analyses

• Provide guidance for potential source volumes and

locations for deterministic analyses

Methodology – Monte Carlo Approach

• Evaluation of Slope Stability

• Geometry of the slopes

• Seismicity and overpressures as triggering

mechanisms

• Sediment properties• Sediment properties

• Estimate of Initial Characteristic Tsunami Amplitude and

Runup for Each Submarine Mass Failure at each

Coastal Point

• Statistical Analysis to Estimate 100-year and 500-year

Runup for each Coastal Point

Northern

Transects

Coastline simplified by

2400 coastal points

Southern

Transects

Seismicity Data from USGS Hazard Maps

Surficial Sediment Properties from CONMAP

Database

Limit Equilibrium Slope Stability

• Rotational failures were modeled using Modified Bishop’s Method

∑

∑

=

=

−+

∆

=I

i

iiiii

I

i

iui

r

hkWW

lS

FS

1

1

2cossin’ αα

• Translational failures were modeled using Infinite Slope Method

• Pseudostatic coefficient k is assumed to be equal to peak horizontal acceleration (PHA)

• Pore pressure ratio (Ru) based loosely on ODP 174

FS =

(γ −1)(1− Ru ) − k γ tanβ

(γ −1) tanβ + k γtanφ'

∑=

i r1 2

Tsunami Generation, Propagation, and Runup

• Generation

• Empirical Equations (Grilli and Watts, 2005 and others)

• Inundation

• Correspondence Principle• Correspondence Principle

• Gaussian Distribution

• Propagation

• Travel Time

• Wave Height at Breaking

• Breaking Distance from shore

• Shoreline simplified by coastal points

Monte Carlo

Model Logic

Distributions of

Input and Run Up

Data

Validation

• Input Parameters:

• Distribution type (normal, log normal) of the Monte Carlo random parameter selections were compared to known distribution types(Density, Depth, Length, etc.)

• Slope Stability

• Compared with results from a commercial slope stability program • Compared with results from a commercial slope stability program (SLOPE-W TM)

• Published Sediment Properties

• Coefficient of variation

• Known Geological Evidence

• Booth et al 1993

• Chaytor et al. 2009

700

750

800

850

900

950

1000

1050

1100

1150

1200

1250

33500 34000 34500 35000 35500 36000 36500 37000 37500 38000

Distance Along Transect [m]

Ground Surface

Model

SLOPE-W

Validation

Statistical Analysis

• Return Periods:

• Based on definitions by FEMA Guidelines for Coastal

Flooding Analyses and Mapping

• An event is defined to have a return period (or • An event is defined to have a return period (or

recurrence interval) of Y years, if their magnitude is

such that it is equaled or exceeded once on average

every Y years.

• The reciprocal of the return period is the probability that

the event is equaled or exceeded in any given year.

Statistical Analysis

• Pf is the probability of a tsunamigenic slope failure

• n is the total number of tsunamigenic slope failure

• N is the total number of MC simulations

n=

• The joint annual probability of a tsunamigenic slope

failure is

N

nPf =

fPHASMF PPP ⋅=

Statistical Analysis (example)

• Using 45 transects and 9,000 simulations per transect:

• N = 405,000 simulations.

• n = 62,782 tsunamigenic slope failures are recorded for ground motions corresponding to a Y = 500-yr earthquake (PPHA =1/Y = 0.2% annual-probability).

• The probability of a tsunamigenic slope failure is:

62782n

• Therefore, the joint annual probability of a tsunamigenic slope failure is:

• The reciprocal of PSMF is the return period of a tsunamigenic slope failure within the study region, i.e. 3,350 years.

• Thus, the generated runup data for each coastal point contains up to a 3,350-yr tsunami runup event.

155.015501.0405000

62782≈===

N

nPf

PSMF = PPHA ⋅ Pf = 0.002 ⋅ 0.155 ≈ 0.0003

Statistical Analysis• The design runup is defined as the 1% value of all the descending

values of runup to the highest possible return period in the study area

• To calculate the magnitude of the desired design runup for a given

coastal point:

• The values of runup collected from the tsunamigenic submarine mass failures affecting the coastal point are first sorted in mass failures affecting the coastal point are first sorted in descending order from 1 to m

• The value of runup for a given probability of exceedance (Pz) then corresponds to the zth data point, determined by:

( )m

P

Pz

SMF

Z ⋅=100

0700

============================================

500 years

3350 years

Location: Lat 39.6 Lon -74.21

5963

Rununp

39.83 16.1 13.03 10.41 9.28 8.31 7.55 6.98 6.59 6.02 5.55 5.27 5.04 4.76 4.57 4.37 4.12 3.94

36.38 15.96 13.03 10.34 9.26 8.3 7.52 6.95 6.58 6.01 5.53 5.26 5.04 4.75 4.57 4.37 4.12 3.93

34.38 15.65 12.67 10.23 9.25 8.27 7.49 6.93 6.58 5.98 5.51 5.24 5.04 4.74 4.55 4.36 4.1 3.93

32.27 15.48 12.62 10.07 9.19 8.27 7.47 6.91 6.56 5.97 5.49 5.23 5.03 4.74 4.55 4.34 4.09 3.93

31.41 15.2 12.35 10.04 9.04 8.23 7.47 6.89 6.53 5.96 5.49 5.23 5.02 4.74 4.54 4.32 4.09 3.93

28.35 15.16 12.01 9.96 9 8.2 7.41 6.89 6.52 5.93 5.48 5.22 5.01 4.71 4.54 4.31 4.09 3.92

Tsunamigenic Slope Failure Return Period

Max Seismic Return Period

Total Number of Data Points

Results for Coastal Point

0.03%-annual-chance

of being exceeded

(3,350 year tsunami)

(z = 60)

28.35 15.16 12.01 9.96 9 8.2 7.41 6.89 6.52 5.93 5.48 5.22 5.01 4.71 4.54 4.31 4.09 3.92

24.25 15.07 11.73 9.93 8.95 8.09 7.41 6.85 6.49 5.91 5.48 5.2 5 4.69 4.52 4.3 4.08 3.91

23.19 15 11.66 9.92 8.91 8.08 7.38 6.84 6.48 5.89 5.48 5.18 5 4.69 4.51 4.3 4.08 3.91

22.91 14.81 11.65 9.86 8.78 7.96 7.33 6.82 6.48 5.86 5.47 5.17 4.98 4.68 4.5 4.28 4.08 3.9

20.17 14.76 11.63 9.84 8.74 7.93 7.26 6.8 6.48 5.83 5.46 5.16 4.96 4.68 4.49 4.27 4.06 3.87

19.52 14.52 11.54 9.82 8.73 7.91 7.26 6.79 6.47 5.8 5.44 5.15 4.94 4.68 4.48 4.25 4.04 3.86

19.49 14.49 11.32 9.74 8.68 7.84 7.25 6.72 6.43 5.8 5.42 5.14 4.94 4.68 4.47 4.24 4.04 3.85

19.41 14.48 11.29 9.67 8.67 7.82 7.25 6.72 6.41 5.79 5.42 5.14 4.94 4.67 4.47 4.24 4.04 3.83

19.34 14.46 11.12 9.62 8.56 7.81 7.2 6.71 6.37 5.71 5.38 5.14 4.92 4.66 4.47 4.22 4.03 3.82

19.32 14 10.95 9.53 8.56 7.8 7.15 6.71 6.36 5.67 5.37 5.14 4.9 4.65 4.46 4.22 4.03 3.81

18.15 13.91 10.9 9.53 8.53 7.76 7.13 6.67 6.35 5.66 5.37 5.13 4.9 4.65 4.45 4.21 4.03 3.81

17.74 13.89 10.86 9.51 8.53 7.73 7.12 6.65 6.28 5.62 5.37 5.13 4.86 4.61 4.44 4.16 4.03 3.81

17.51 13.88 10.73 9.51 8.51 7.65 7.09 6.63 6.26 5.62 5.35 5.11 4.85 4.61 4.44 4.15 4.02 3.8

17.32 13.83 10.7 9.49 8.49 7.63 7.06 6.62 6.2 5.61 5.3 5.07 4.85 4.59 4.43 4.13 4.02 3.79

17.08 13.75 10.68 9.38 8.49 7.62 7.03 6.62 6.17 5.59 5.3 5.06 4.83 4.58 4.42 4.13 4.01 3.78

16.72 13.68 10.61 9.37 8.43 7.58 7.03 6.6 6.14 5.59 5.3 5.06 4.81 4.58 4.41 4.12 4 3.78

16.66 13.39 10.52 9.36 8.37 7.58 6.99 6.59 6.11 5.58 5.27 5.05 4.81 4.58 4.39 4.12 3.99 3.78

16.47 13.3 10.41 9.31 8.34 7.56 6.98 6.59 6.09 5.57 5.27 5.05 4.81 4.57 4.39 4.12 3.98 3.77

0.2%-annual-chance

of being exceeded

(500 year tsunami)

(z = 398)

Results

New Jersey

X

Cape Cod Blake Nose

Results

New Jersey

X

Cape Cod Blake Nose

What do we do with these results?

Possible Source Characterization

X XX X

Summary

• Monte Carlo Model

• Based on:

• Known or estimated physical parameter distributions

• Actual bathymetry

• Stochastic Approach was utilized to generate:

• Slope Failures

• Tsunami Inundation data

• Tsunami Travel Time and Wave Height Data

Summary (cont.)

• Statistical Analysis

• Derived from current methodologies (FEMA, USGS, NOAA)

• Estimates the return period for tsunamigenic failures within the region

• Approximately 3,350-yr

• Quantifies tsunami hazard in terms of annual-probability of exceedence

• Identifies two regions of elevated risk• Identifies two regions of elevated risk

• Long Island, NY (~3-m peak at a 500-yr event)

• New Jersey Coastline (~4-m peak at a 500-yr event)

• Model Validation

• In all cases reasonably good agreement was achieved between the model and the validation benchmark:

• Known distribution types

• Standard limit equilibrium software

• Published geological evidence

Limitations and Future Improvements

• Applicability of USGS PHA offshore

• Use of surficial sediment data for geotechnical

properties

• Large uncertainties in stratigraphy• Large uncertainties in stratigraphy

• Limitations of limit equilibrium methods to model

progressive failure or multiple failure scenarios

• Simplified estimates of runup (correspondence

principle, no breaking waves)

Potential Improvements to Stratigraphy

USGS, 2010

Potential Improvements to Sediment Properties

T h a n k Y o uThank You