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Generating Random Earthquake Events for Probabilistic Tsunami Hazard Assessment

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Abstract

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.

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Notes

  1. We follow http://earthquake.usgs.gov/aboutus/docs/020204mag_policy.php and use \(M_w = \frac{2}{3} (\log _{10}(M_o) - 9.05)\) where the seismic moment \(M_o =\)length \(\times\) width\(\,\times\) (average slip)\(\,\times \,\)(rigidity) and set the rigidity to \(3.55\times 10^{10}\) N-m for this calculation.

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Acknowledgments

The initial phase of this work was performed when GL was employed at Pacific Northwest National Laboratory (PNNL) and KW was a postdoctoral fellow supported in part by PNNL and by the University of Washington (UW). This work was also supported in part by NSF Grants DMS-1216732 and EAR-1331412, funding from FEMA, and the Applied Mathematics Department of UW. The authors have benefitted from discussions with many applied mathematicians and geoscientists concerning the approach developed in this paper, including in particular Art Frankel, Finn Løvholt, Martin Mai, Siddhartha Mishra, Diego Melgar, and Hong Kie Thio. Numerous suggestions from the referees improved the quality of this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Washington, Seattle, WA, USA

    Randall J. LeVeque & Donsub Rim

  2. Forsvarets Forskningsinstitutt, Oslo, Norway

    Knut Waagan

  3. Department of Earth and Space Sciences, University of Washington, Seattle, WA, USA

    Frank I. González

  4. Department of Mathematics, Purdue University, West Lafayette, IN, USA

    Guang Lin

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  1. Randall J. LeVeque
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Correspondence to Randall J. LeVeque.

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LeVeque, R.J., Waagan, K., González, F.I. et al. Generating Random Earthquake Events for Probabilistic Tsunami Hazard Assessment. Pure Appl. Geophys. 173, 3671–3692 (2016). https://doi.org/10.1007/s00024-016-1357-1

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