Generating Random Earthquake Events for Probabilistic Tsunami Hazard Assessment

  • Randall J. LeVequeEmail author
  • Knut Waagan
  • Frank I. González
  • Donsub Rim
  • Guang Lin
Part of the Pageoph Topical Volumes book series (PTV)


To perform probabilistic tsunami hazard assessment for subduction zone earthquakes, it is necessary to start with a catalog of possible future events along with the annual probability of occurrence, or a probability distribution of such events that can be easily sampled. For near-field events, the distribution of slip on the fault can have a significant effect on the resulting tsunami. We present an approach to defining a probability distribution based on subdividing the fault geometry into many subfaults and prescribing a desired covariance matrix relating slip on one subfault to slip on any other subfault. The eigenvalues and eigenvectors of this matrix are then used to define a Karhunen-Loève expansion for random slip patterns. This is similar to a spectral representation of random slip based on Fourier series but conforms to a general fault geometry. We show that only a few terms in this series are needed to represent the features of the slip distribution that are most important in tsunami generation, first with a simple one-dimensional example where slip varies only in the down-dip direction and then on a portion of the Cascadia Subduction Zone.


Probabilistic tsunami hazard assessment seismic sources Karhunen-Loève expansion subduction zone earthquakes 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Randall J. LeVeque
    • 1
    Email author
  • Knut Waagan
    • 2
  • Frank I. González
    • 3
  • Donsub Rim
    • 1
  • Guang Lin
    • 4
  1. 1.Department of Applied MathematicsUniversity of WashingtonSeattleUSA
  2. 2.Forsvarets ForskningsinstituttOsloNorway
  3. 3.Department of Earth and Space SciencesUniversity of WashingtonSeattleUSA
  4. 4.Department of MathematicsPurdue UniversityWest LafayetteUSA

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