Section 1: What is an Earthquake?

Activity #9: RECURRENCE INTERVAL

Materials:

• the San Andreas fault rupture graph template
  
• (optional) graph paper and colored pencils
  
• scratch paper and/or a calculator for making calculations
  

Procedure:

The exercises below cover some fairly simple examples of determining recurrence interval. They should provide you with a good idea of how valuable the concept can be in risk assessment, and of a few of the problems associated with determining and correctly applying recurrence intervals in fault studies.

Exercise 1A Hypothetical Fault Study

Imagine you belong to a group of geologists studying the (hypothetical) Salt Wash fault, a moderate-sized, pure strike-slip fault in the Mojave. Through your studies of the fault's history, you have determined that the fault has experienced 1.4 km of right-lateral slip in the past 5.0 million years. You have also discovered evidence that the most recent major rupture occurred approximately 400 years ago, and caused the fault to slip 2.1 meters.

Now you must report your findings and draw a few conclusions based on the evidence you've uncovered. Thus, using the information above, answer the following questions:

1. What is the slip rate of this fault?
   Does that seem slow (for the slip rate of an active fault)?
   What does that suggest, qualitatively, about the recurrence interval?
   

2. Compute a likely recurrence interval, using the data from the last major rupture. While this may seem like a very long repeat time, it is actually quite normal for real-life right-lateral faults in the Mojave.
   

3. Given the time of the previous rupture and your calculation from question #2, do you think your findings would worry or reassure those people who live very close to the surface trace of the Salt Wash fault?

Exercise 2The San Andreas Fault

Studies at Pallett Creek and other locations along the Mojave section of the San Andreas fault have revealed a rough chronology for that section of the fault over the last 1500 years -- much longer than that covered by historic reports and records.

A compilation of this data is shown in the table below.

Previous San Andreas fault ruptures at Pallett Creek (Mojave section)

1. Using the data in the third column above, calculate the average time (in years) between major ruptures of the San Andreas fault at Pallett Creek. (You should ignore the first and last values in the column when making this calculation. (They will be useful later, however!))
   

2. According to this average recurrence interval, is the Mojave section of the San Andreas fault at Pallett Creek due, not yet due, or well overdue, for a major rupture?
   

3. Looking back at the table, note the difference between the shortest interval and the longest. How much greater than the apparent recurrence interval is the longest interval between events? How much smaller is the shortest interval? Does this give you more or less confidence about your answer to question #2 (above)?
   

4. If you have a good eye for patterns, you may have noticed something intriguing about the data above. Study it carefully. Can you see how long rupture intervals (greater than or equal to 200 years) seem to divide the table into a pattern where one or two short rupture intervals are followed by a much longer interval, which is followed again by one or two short intervals, and so on? The effect is especially easy to pick out if you make a graph of the data in the second column, above. Using the graph template and instructions provided (you will either need to print out the template, or draw a copy by hand), construct this graph now. Then come back to answer the last question.
   

5. With your graph completed, can you now see how there might be a long-period pattern of clusters and gaps in the recurrence of earthquakes at Pallett Creek? If such a pattern can be believed, then, given that over 140 years have passed since the last earthquake ruptured this area, is it more likely that we are currently in a gap, or a cluster? (In other words, how long is a typical "gap", as opposed to the average time between earthquakes in a "cluster"?) Does this support or oppose the first conclusion you came to (in question #2)?
   

No one is sure whether the idea hinted at by your graph is true. This example should show you, in any case, how taking a closer look at recurrence interval data can be more useful than simply doing an average calculation. In this case, if there is a larger pattern, it might occur because the San Andreas fault seems to act as a series of smaller, connected fault segments. Perhaps one segment can influence the timing of the ruptures on adjacent segments? This may be true, but as noted before, no one is certain.

Table data from:
Sieh, K., Stuiver, M. and Brillinger, D. (1989). A More Precise Chronology of Earthquakes produced by the San Andreas Fault in Southern California. Journal of Geophysical Research, Vol. 94, No. B1, pp. 603-623.

Exercise 3Longer Fault = Longer Recurrence Interval?

Very long faults with high slip rates (like the San Andreas fault in southern California) probably seem the most worrisome -- that is, potentially dangerous -- of faults. This makes sense, given that they are very active, and capable of producing large earthquakes. However, the average slip of a very long fault rupture will be much greater than the average slip of a shorter rupture. Think about the significance of that fact, in terms of recurrence intervals, as you work through the exercise below.

1. Let's compare two fault segments in southern California: the Mojave section of the San Andreas fault (as in Exercise 2), and the northern half of the Imperial fault. For simplicity, we will model these two fault segments in a very basic way -- in other words, this will not be an entirely accurate exercise, but it is grounded in reality. The properties we will compare are fault length (which, for the purposes of this exerise, we will equate with rupture length), slip rate, and the characteristics of a particular historic earthquake on each segment, which we will consider a "typical" major rupture. Study the table below to compare and contrast the two (idealized) fault segments.

   Fault segment: Length: Slip Rate: Selected Rupture: Average Slip: Magnitude:

   San Andreas (Mojave) 250 km 35 mm/yr January 9, 1857 (Great Fort Tejon quake) 4.5 meters Mw 8.0 (approx.)

   Imperial (north half) 30 km 20 mm/yr October 15, 1979 (Imperial Valley '79 quake) 0.7 meters Mw 6.4

2. Now, using the information above and your previous studies, compute the approximate rupture intervals for these fault segments.

3. Which segment would rupture more often? Does this example make clear how the slip rate of a fault should not be the only measure of how active (in producing damaging earthquakes) it is? (Keep in mind, though, that both faults in the example above have very high slip rates.)
   

As you've just seen above, more slip needs to accumulate for a very long fault rupture to occur than is needed to produce a rupture of shorter length, and this additional accumulation requires more time. While the long rupture will produce a very strong earthquake (greater than magnitude 7 or 8), the shorter rupture can still produce a damaging earthquake (greater than magnitude 6). Thus, if the faults responsible for these ruptures have roughly the same slip rate, the fault experiencing the shorter ruptures will rupture more often. Though the earthquakes produced by these shorter ruptures will not be as severe as those of a longer rupture, they can still be damaging. In this light, which of two such faults should really be considered the more hazardous? The answer to that is entirely dependent upon your outlook.

Return to the Text