Abstract. In order to perform probabilistic tsunami hazard assessment (PTHA) based on subduction zone earthquakes, it is necessary to start with a catalog of possible future events along with the annual probability of occurance, or a probability distribution of such events that can be easily sampled. For nearfield 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-Lo\`eve 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.
Keywords. Probabilistic tsunami hazard assessment, seismic sources, Karhunen-Lo\`eve expansion, subduction zone earthquakes
Journal article: [doi:10.1007/s00024-016-1357-1] ... Open access view-only version
Accepted manuscript: KLslip.pdf
Earlier preprint (before substantial revisions): arxiv.org/abs/1605.02863
Code:
bibtex entry:
@article{LeVequeWaagan2016:KLslip,
author="R. J. LeVeque and K. Waagan and F. I. Gonzalez and D. Rim and G. Lin",
title="Generating Random Earthquake Events for Probabilistic Tsunami
Hazard Assessment",
journal = "Pure Appl. Geophys.",
doi="10.1007/s00024-016-1357-1",
year="2016"
}