The relationship between the parameters that define earthquake rupture and local tsunamis is complex. For distant tsunamis that have traveled far from the origin of the earthquake, the magnitude of the earthquake is a good measure of the size of the tsunami. For local tsunamis, however, more knowledge than the magnitude is needed to calculate the eventual runup of the tsunami. This study was designed to calculate how local tsunamis are affected by variations in earthquake source parameters specific to faulting along the Cascadia subduction zone.
What Aspects of Earthquake Rupture Affect Tsunamis?
The nature of earthquake rupture is defined by many different parameters that can vary spatially and with time. Here we show how the following parameters affect local tsunamis:
Amount of Average Slip
During an earthquake, one side of the fault moves vertically and/or horizontally with respect to the other side. The distance the two sides move averaged over the rupture area is what we will call average slip. The relationship between fault slip and the permanent offset of the seafloor after earthquake rupture is linear. That is, if average slip for one earthquake (EQ 1) is twice that for another earthquake (EQ 2), the seafloor offset and the initial tsunami will be different also by a factor of two. Owing to propagation effects, however, there is a greater than linear relationship between the amplitude of the tsunami near shore and the amount of average slip. Therefore, the difference in the near-shore amplitude of the tsunamis generated by EQ 1 and EQ 2, for example, will be slightly greater than a factor of two.
The amount of slip throughout the rupture area of an earthquake has the largest influence on the size of the local tsunami. Is the average amount of slip related to the magnitude of the earthquake? Generally, slip increases with the magnitude of the earthquake. However, because other parameters such as the rupture area and physical properties of the rocks surrounding the rupture determine the magnitude of an earthquake, we cannot calculate the amount of slip associated with an earthquake without knowing these other parameters. For example, shown below is the average slip associated with many subduction zone earthquakes around the world. Although slip generally increases with magnitude, there is significant scatter in the data:
In the above figure, a distinction is made between tsunami earthquakes and non-tsunami earthquakes. The term tsunami earthquakes is used to designate those earthquakes that generate larger than expected tsunamis relative to the magnitude of the earthquake (see also online article by Dr. Kenji Satake). As evident above, the average slip during rupture of a tsunami earthquake appears to be larger than a non-tsunami earthquake of the same magnitude.
Depth of Rupture
The size of the local tsunami also depends on how deep the earthquake ruptured within the earth. Shallow rupture will result in larger offset of the seafloor and hence, a larger initial tsunami, than a deep rupture earthquake. An example is shown below. The left part of the figure shows the portion of a fault that ruptures in green. The local tsunami that is generated from this rupture is shown below as a synthetic marigram (wave amplitude as a function of time). Fault C, shown in the second set of figures, ruptures much shallower in the earth and generates a substantially larger tsunami.
Test Case 1: Rupture on Fault B
Test Case 2: Rupture on Fault C
Orientation of Slip Vector
The figures above show a type of faulting known as thrust faulting, in which the overlying block moves upward and over the underlying block. Considered in 3 dimensions, however, the fault blocks could also move in-and-out of the page (screen) as shown by the perspective figure below:
Oblique faulting such as this can occur in a subduction zone when the downgoing plate is moving at an oblique angle (theta) relative to the overriding plate. The obliquity of the slip vector (D) in the fault plane of dip (delta) is measured by the angle (lambda) that the slip vector makes with a horizontal line in the fault plane.
Why would such details of rupture be important in terms of generating local tsunamis? When oblique faulting as described occurs, the vertical offset of the seafloor is considerably different than for the case of simple thrust faulting. The result is the generation of secondary tsunamis that initially travel in a different direction than the deep-ocean and local tsunamis shown in Panels 2 and 3 at the top of this page. Let's look at an animation of a tsunami generated from oblique faulting to better understand the different waves generated by this type of earthquake:
GIF Animation (110 kB)
The image above is the last time step of the animation. Peaks in the tsunami waves are shown by red intensity, whereas troughs are shown by blue intensity. For a tsunami generated by pure thrust faulting, only the primary wavefronts would be evident: one moving toward the deep ocean and one moving toward the local shoreline. As shown here, fault movement parallel to the convergence direction between the Juan de Fuca and North American plates results in the generation of secondary wavefronts. Most obvious is the isolated secondary wavefront propagating to the southeast. In addition, there is a secondary wavefront propagating to the northeast that is a continuation of the shoreward primary wavefront. Both of the secondary wavefronts initially travel parallel to shoreline, but their paths of travel curve (refract) toward shore. Thus, the length of shoreline inundation from this type of tsunami is significantly greater than inundation calculated from the primary wavefronts alone.
The parameters used to create this image are merely for illustrating the effect of oblique rupture on tsunami propagation. Certainly, variations in the chosen parameters would affect the amplitude of the tsunami and the physical location of coastal inundation.
These examples illustrate the complex relationship between the parameters that characterize earthquake rupture and the local tsunami that is generated. Presently, it is exceedingly difficult to devise likely scenarios of rupture along the Cascadia megathrust. Much work is presently under way by seismologists to determine the nature of earthquake rupture along major plate boundary faults. As more is learned about the nature of possible earthquakes in Cascadia, the hazards from local tsunamis can be better defined. See second phase (155 kB) and third phase (USGS OFR 1661-B) of this research project.
- Geist, E., and Yoshioka, S., 1996, Source parameters controlling the generation and propagation of potential local tsunamis along the Cascadia margin: Natural Hazards, v. 13, p. 151-177.
- Geist, E. L., 1999, Local tsunamis and earthquake source parameters: Advances in Geophysics, v. 39, p. 117-209.