A Stochastic Model for Potential Tsunamis in the Pacific Northwest

Beyond Scaling Relationships

In the first phase of research (88 kb) on potential tsunamis that may occur along the Pacific Northwest coast, we showed that the individual parameters of earthquake rupture (e.g., geometry of faulting, orientation of slip) have a significant effect on the local tsunami wavefield. For this reason, even though local tsunami runup generally increases with earthquake magnitude, there is substantial variation or scatter in this scaling relationship, as evidenced by average and maximum statistics of local observations.

Two observations are apparent in the figures above:

1. for a given earthquake magnitude, local runup is substantially greater for tsunami earthquakes (88 kb) than for non-tsunami earthquakes;
2. the degree of scatter is critical for estimating local tsunami hazards--comparison of earthquakes of similar magnitude (1944 Tonankai and 1986 Aleutian, for example) illustrates the discrepancy of maximum runup that could occur.

It is also important to note that these observations pertain to local tsunamis. There is considerably less scatter in the scaling relationship for distant tsunamis because of the smoothing effect of tsunami propagation on small-scale variations of the earthquake rupture process.

The observed scatter in the relationship between local runup and earthquake magnitude shown above is caused by several different factors including water depth at the source, hypocentral depth, and rupture geometry (aspect ratio). In this study we focus on perhaps the largest source of this scatter: variation in the amount of slip throughout the rupture area.

Fundamental Effects on Slip Variations

We often think that during an earthquake, the fault slips a fixed amount. It serves not only as a common conception but also as a working assumption for many tsunami models (including models employed during the first phase (88 kb) of this study). An alternative and, perhaps, a more useful conception of earthquake rupture is that of a crack in which slip decreases to zero at the crack tip or at the edge of earthquake rupture. In Geist and Dmowska (1999) we demonstrate that incorporating "natural" slip variations into our tsunami generation model has a measurable effect on the local tsunami wavefield, in comparison to models that assume uniform slip throughout the rupture area. Moreover, we can use the slip distribution of an earthquake determined from global seismic observations to reconstruct the generated tsunami. Although reconstructing past tsunamis is a significantly worthwhile scientific endeavor for understanding the relationship between earthquakes and tsunamis (e.g., Geist and Zoback, 1999 (140 kb)), an essential product of tsunami research is tsunami hazard assessments which we discuss next...

Forecasting Local Tsunami Hazards: A Collaborative Effort

The problem of forecasting tsunami hazards then is determining the range of tsunamis that can be produced by different combinations of source parameters. Even if all of the geometric parameters of a "scenario earthquake" are prescribed, there would be a large uncertainty in determining the ensuing tsunami because of the difficulty in formulating a "characteristic" slip distribution. (See, for example, the variety of distributions for earthquakes in California at a repository of slip models housed at the Pasadena office of the USGS). While seemingly random, earthquake slip distributions can be thought of in terms of fractals. A source model can be developed to construct an infinite number of different slip distributions that statisfy common observations of earthquakes. These slip distributions then can be used to gauge the range the possible tsunamis from an earthquake of a particular magnitude and location. Two examples of stochastic slip distributions are shown below (warm colors represent high amounts of slip).

The tsunami that is generated from the slip distribution in the top figure for a hypothetical subduction earthquake in the Pacific Northwest is shown below.

Please Note: The tsunami shown here is one of many possible tsunamis, both in terms of location and details of the wavefield.

This tsunami is available to view as a VRML model.
VRML 2.0 plugin is required for viewing this model.
Warning: Cumulative file size at this link approx. 2.8 MB

Here is what the tsunami wavefield looks like for this scenario after 20 minutes:

You can also view QuickTime animations of this tsunami at two different resolutions:

Low Resolution Animation
Warning: Cumulative file size at this link approx. 2.2 MB

High Resolution Animation
Warning: Cumulative file size at this link approx. 11.3 MB

To determine the range of possible tsunami amplitudes for a given earthquake magnitude and location, a Monte Carlo-type simulation can be run, involving a large number of slip distributions. Statistics from the simulation could then be used for hazard planning. An example showing minimum, average, and maximum nearshore tsunami amplitude (not runup) for a section of the Pacific Northwest coastline is given below. The horizontal gridpoint axis is distance measured parallel to the shoreline (approx. 3.5 km/gridpoint).

It is important to note that the technique described above only accounts for nearshore tsunami amplitude variations caused by different slip distributions. A complete hazard analysis would include variations in other source parameters, the effects of which are discussed in the first phase (88 kb) of our study of potential Pacific Northwest tsunamis.

The stochastic/Monte Carlo method provides the groundwork for an alternative way of forecasting local tsunami hazards. The third phase of our study focuses on forecasting tsunami hazards that also includes the probability of earthquake occurrence that would most likely involve methods similar to those used to formulate probabilistic estimates of ground shaking from earthquakes (see the USGS National Seismic Hazard Maps). Developing tsunami hazards maps in future will rely on the broad collaboration among the many scientific disciplines that are involved in tsunami research.

Related Publications

1. Geist, E. L., 1999, A stochastic source model for estimating local tsunami hazards: Seismol. Res. Lett., v. 70, p. 221
2. Geist, E. L., and Dmowska, R., 1999, Local tsunamis and distributed slip at the source: Pure Appl. Geophys., v. 154, p.