March/April 1999


Discussion on the characteristic earthquake model vs. the Gutenberg-Richter (G-R) relationship leaves me with some uneasiness. The Gutenberg-Richter relation is a traditional, basic one of seismology with an origin that can be traced back to Ishimoto and Iida's empirical power law formula in 1939 describing the frequency of maximum amplitudes of observed seismic waves. The G-R relationship is unambiguously defined by a simple formula, but some ambiguities about the G-R relation exist as well. For example, possible sources of ambiguity are how to define the maximum magnitude since we have an Earth of finite size (and hence the maximum possible magnitude must be finite also), and how to truncate the relationship at the maximum magnitude. On the other hand, the relatively new idea of the characteristic earthquake model appears to have many loose ends. Does it include any specification on the temporal earthquake distribution, or does it specify only a magnitude-frequency distribution? What is the allowable range of variation in magnitude for the characteristic earthquake? What is the minimum gap in magnitude between the characteristic earthquake and the largest of the other possible earthquakes? How can spatial extent be specified for the application of this model?

There could be many definitions for the characteristic earthquake model, and no consensus seems to exist even among its supporters. My feeling of uneasiness probably comes from this contrast: a somewhat ambiguous new idea versus a clear-cut one of basic seismology. Although the G-R relationship represents one end member of the behavior of earthquake occurrences, the characteristic earthquake model does not seem to be the other end member. This point may not seem to be well recognized, but it must be a starting point of more fruitful discussion. What then is the other end member of the spectrum?

Believe it or not, the other end member, the extreme end of the characteristic earthquake behavior, is the world of the one and only one Almighty Earthquake. The Almighty Earthquake ruptures an entire plate boundary at once and leaves no stress which could produce any other kind of earthquake. Neither foreshocks nor aftershocks. Neither small earthquakes nor microearthquakes. The one and only one. Always exactly the same size. And probably the repeat time does not vary, if the plate motion is steady. This may not be science, but religion. One might argue whether or not it is physically realizable. What would be the physical state of the plate boundary which enables an existence of the Earthquake? Is it really possible to erase all barriers which are obstacles for a rupture propagating along the plate boundary? Certainly geometrical barriers cannot be removed unless only smooth plate boundaries are artificially produced on a hypothetical Earth, which is not a geophysically or geologically viable idea. Think about all the heterogeneities within the crust. It appears impossible to suppress the generation of every tiny earthquake which releases a stress concentration caused by the heterogeneities. No doubt we are far from this extreme end of earthquake models.

Recent developments in the simulation of seismic activity show how the power-law type size distributions can be produced from relatively simple homogeneous dynamic systems. It is now well known that the G-R relationship can be obtained from a state of self-organized criticality. This is a totally chaotic world, and the largest earthquakes are randomly generated by the system. The existence of dependent shocks such as aftershocks is certainly a most prominent feature in earthquake statistics, but we often find Poisson-type randomness after removal of those dependent shocks. Since the worldwide earthquake statistics favor the G-R relationship, our planet as a whole probably stays in a totally chaotic world. Then why the characteristic earthquake model?

The concept of the characteristic earthquake model originated from earthquake statistics in a spatially limited region. The characteristic earthquake is the largest event in the region and often shows a quasiperiodic feature of recurrence. Other earthquakes, including aftershocks of this main event, are much smaller in size than this characteristic earthquake. The so-called "runaway" event produced by some simulations with simple dynamic systems appears to show features similar to the characteristic earthquake. With certain properties for rupture propagation a huge event can be produced, and it can be terminated only when its periphery reaches the end of the simulation field. These runaway events take place somewhat regularly in time because they move the system out of the critical state and because a certain period of time is necessary for the accumulation of energy within the system after a significant energy loss by such events. The event size is nearly constant because it is determined by the size of the simulation field.

A worldwide survey of strike-slip faults (Stirling et al., Geophys. J. Int. 124, 833-868, 1996) suggests that fault trace complexities evolve with time. A fractal network of fractures at the beginning of the development of a fault system will end up with a single smooth fault. This observation suggests that the G-R relation holds for immature fault systems. The departure from the G-R relation increases with maturity since there are fewer complexities of the fault system. Wearing processes working on the fault gradually smooth its surface, and sometimes barriers may break abruptly, allowing separate faults to be connected to form a single fault. Fractures which efficiently release accumulating strain become dominant. More repetition of slips on selected faults rather than on surrounding minor faults gradually forms the mainstream of strain release. In a closed system the evolutionary growth of incipient faults may finally lead to a single smooth fault, and thus the Almighty Earthquake. If all plate boundaries stay the same--which is unrealistic, though, as plate tectonics shows us--the present system of tectonic stress release may evolve toward the world of the Almighty Earthquake.

It seems to me that we are somewhere in the evolutionary path, a little bit off the starting point of total chaos but far from the world of the Almighty Earthquake. The seismicity of the Earth as a whole obeys the G-R relationship. But a significant departure from the G-R relation can be found locally, especially near mature faults. This is because for a smaller area an evolutionary clock can tick fast, but it goes more slowly in a larger region. The characteristic earthquake model is an attempt to describe a feature of seismicity in this half-boiled world. Thus, there could be many different definitions of characteristic earthquakes according to the different evolutionary stages of fault systems.

One important question is what kind of parameter we can use for describing the different stages of the evolutionary path of fault systems. One candidate is the fault complexity, which appears to be useful for strike-slip faults. How important would be the interaction between a particular fault system and the surrounding systems, and how can we quantify that interaction? Probably no unique characteristic earthquake model exists. We need a quantity which characterizes the degree of "characteristicness."

Kunihiko Shimazaki
Earthquake Research Institute
University of Tokyo
1-1-1 Yayoi, Bunkyo-Ku
Tokyo 113-0032

To send a letter to the editor regarding this opinion or to write your own opinion, contact Editor John Ebel by email or telephone him at (617) 552-8300.

Posted: 7 April 1999