Section 2: The Distribution of Earthquakes

Activity #11: AN EARTHQUAKE DEFICIT?

Concept: The lack of accurate records pre-dating modern seismology hinders our ability to understand long-term variations, and thus, possible future trends.

Materials:

Procedure:

This activity deals with a question that has recently been at the forefront of seismological discussion in southern California: Is there an "earthquake deficit"? Put another way, have there been enough earthquakes in the area in historical time to release the amount of strain energy that plate tectonics is constantly supplying to the crust? In 1995, the WGCEP -- Working Group on California Earthquake Probabilities -- published a report suggesting that there had not; southern California, the WGCEP decided, had an "earthquake deficit" that would have to be made up in the future by the occurrence of more frequent large earthquakes. Earthquake insurance rates rose dramatically at the announcement, and a lot of people already rattled by the rash of recent large earthquakes (Joshua Tree, Landers, and Big Bear in 1992, and Northridge in 1994) wondered whether those were only the beginning of shaky times in southern California.

Three years later, a pair of scientists working on the same question came up with a different, more reassuring answer, citing flaws in the original study -- among them, the incomplete nature of our historical records. Which view is more correct? That's a question you'll get to answer for yourself as you work through this activity.

There are two parts to this problem: you must determine the appropriate year to begin your study of our historic earthquake records, and then you must decide if the energy released by past earthquakes has been equivalent to the amount of energy accumulating through the action of plate tectonics over the same number of years. These tasks will be accomplished in Parts I and II of this activity. Part III will be devoted to an analysis of your findings.

Let's now start this activity by determining the proper year to begin a complete historical catalog. How do you do this? Part I will help you figure that out, while providing you with a few simple tools to do the job.

Part I: Undetected Quakes?

How far back can you go into our historical records of large earthquakes before "holes" begin to appear, and certain large earthquakes may have gone unnoticed, or at least, unreported? That's the question you'll attempt to answer in this first part of the activity.

The first step is defining what we mean by a "large earthquake". For various reasons, let's use a "cut-off" magnitude of 6. Anyone experiencing an earthquake that large anywhere near its source would undoubtedly have a story to tell, or damage to report, so we can assume earthquakes of this size were generally noted in newspapers, logs made by railroad operators, etc. -- unless they happened far enough away from these sources to be undetected or unreported.

From looking at our catalog of earthquakes, it's pretty clear that the records can't be complete any earlier than about 1850 -- there are only a few large earthquakes noted anywhere in southern California from before that time. Also, settlements in southern California before 1850 were few and far between, and there were no railroads. Railroads generally kept good records of any major disturbances to occur along their lines.

At the other end of the scale, most parts of southern California were settled by 1910, with railroad lines cutting across many of the more empty sections of the state. So the cut-off line in our records should probably fall between 1850 and 1910.

You will check three different years: 1860, 1880, and 1900. You will be trying to determine the probability of a magnitude 6 earthquake going completely unnoticed in each of these years. The way you'll do this is by looking at randomly generated "magnitude 6 earthquakes" projected onto a background map of southern California, labelled with the locations of newspapers and of railroad lines that existed during the year it represents.

Your first task, then, is to determine these probabilities. To do this, follow each of the three links below. When you first arrive, you will see a background map of southern California labelled with a year in the upper right-hand corner. Somewhere on the map, there will be a semi-transparent orange circle. This circle represents the area that would likely experience enough shaking from a magnitude 6 earthquake to cause minor damage, and raise concern among (or awaken) most people. If this area overlaps any part of a map symbol that represents a newspaper or a railroad, assume that this earthquake was reported, and would be in our historical records. If it totally fails to intersect a map symbol, count it as undetected.

Click on the orange circle to run another random trial on the same map. At the very least, run 10 of these trials; 20 would be better. Keep count of how many earthquakes are "reported," and how many go "undetected," and when you're done with your random trials, record or remember the percentage of "undetected" earthquakes for that year. Do this for all three years, using your browser's "Back" button to return to this page at the end of each.

Run the random earthquake simulator for 1860.
Run the random earthquake simulator for 1880.
Run the random earthquake simulator for 1900.

  1. What percentage of the "magnitude 6 earthquakes" went undetected in each year you studied?

  2. If we decide that a 10% rate of undetected magnitude 6 earthquakes is acceptable, do any of these years meet this criteria? If none did, use the latest year (1900) as your cut-off date (assume personal journals and newspaper reporters "in the field" filled in the few "gaps" there were). If one or more did, use the earliest year that met this criteria as your cut-off date for the catalog.

With your catalog-limiting date determined, you're now ready to move on to Part II: Balancing the Energies.

Part II: Balancing the Energies

Earthquakes are ruptures along fault surfaces that occur when mechanical stresses in the crust build up enough to overwhelm the resistance that crustal rocks have to slipping. Plate tectonics provides the tiny but constant motion responsible for these stresses. Once the rocks finally begin to slip along faults, an earthquake is generated as one section of the crust shifts relative to another, and the stress is relieved. As this happens, much of the tectonically generated stress that was piling up for years and years is released as energy -- some of this energy drives the ground shaking we associate with earthquakes.

Since we know how fast the tectonic plates in southern California are slipping past each other, we can calculate the amount of energy that should be released by earthquakes to keep up with the tectonic pace. The figure scientists have calculated is roughly 9 * 1018 Newton-meters (Nm) per year, about the same amount of energy that would be released by a single earthquake of magnitude 6.6 or so.

But how much energy is released, on average, in the course of a year, by earthquakes? As it turns out, large earthquakes dominate the amount of energy released, so we only really need to look at the largest earthquakes. Again, we will use the same lower magnitude limit we used in Part I: magnitude 6.

To find out if the rate of energy released in earthquakes has been keeping pace with the stress build-up from plate tectonic motion (and thus, whether there is an "earthquake deficit" to be made up in the future), you will need to add up the amount of energy released by every large earthquake recorded in southern California since the year our historical records are complete (as determined in Part I). Don't worry, though -- this somewhat daunting task has been made easy for you.

You only need to link to a page with a pre-made checklist of large earthquakes. There, make sure all the earthquakes after the year you chose as your "cut-off" are checked (to help you, all the ones after 1900 are checked by default). Once you've done this, choose the starting year from the pull-down menu at the bottom of the page, and then click the button labelled "Calculate Totals". A script will automatically compute both the expected energy (from the plate tectonic rate of 9 * 1018 Nm per year) and the actual amount of energy released by earthquakes since complete records of large earthquakes (magnitude 6 or greater) have been kept.

When you've finished this, come back to this page, and start the analysis of your results in Part III, below.

Part III: Analysis and Interpretation

Now that you've completed the first two parts of this activity, it's time to look at the results and not only determine what they mean, but what this study might have overlooked. Work through the questions below to wrap up the activity.

  1. Once you had chosen what you felt to be the appropriate starting year, and checked off the corresponding earthquakes in Part II, did the two energy sums balance? If not, did you try using a different starting year? Were the results any closer to being balanced? How far behind the expected total does the actual total fall?

You should have found that the sum of the energy released by earthquakes fell short of the total expected energy release, as calculated from the motion of the tectonic plates. Assuming that the expected figure is correct, this seems to be a real problem, implying that there is an "earthquake deficit" that needs to be made up in the future.

However, what you may not have realized is how heavily the total energy released by earthquakes depends upon the very largest earthquakes in the list.

  1. Go back to the checklist of earthquakes and remove the checkmarks from just two earthquakes -- the two largest: the 1952 Kern County earthquake (M 7.4), and the 1992 Landers earthquake (M 7.3). Then tally the energy released, and compare this with the total you saw previously. How much of a difference did this make?

  2. Given the previous "energy deficit" you found (question 1), and the difference made by removing just the two largest earthquakes (question 2), how many more earthquakes of that size (M 7.3 - 7.4) would be needed to make up the "earthquake deficit"?

  3. Brace yourself for this one: in terms of energy released by an earthquake, there is about a 30-fold increase for every one unit increase of the magnitude scale. This is the main reason our list included earthquakes no smaller than magnitude 6.0; at magnitudes much smaller than that, their energy contribution becomes negligible. Given this, about how many magnitude 6.3 earthquakes (capable of causing serious damage, especially in urban areas) would need to occur to make up the energy deficit? Is it understandable, then, that this question of whether an "earthquake deficit" exists is an important one?

Though major earthquakes are never really good news, there is one detail of southern California seismicity we've overlooked that could banish the "deficit" without requiring the number of extra earthquakes you calculated above. This "detail" is the great, roughly magnitude 8, earthquake that should occur along the San Andreas fault zone every few centuries (often thought of as "The Big One").

The last such earthquake was in 1857, just before our list (from Part II) begins. It is estimated that it released about 800 * 1018 Nm of energy.

  1. Would a single earthquake of this size totally make up for the energy deficit? Would it go beyond that, even -- giving us a "surplus"? Can you see why it's important that you don't neglect this kind of earthquake from your calculations?

Since this kind of earthquake can be expected to recur every few centuries, we can take it as a given that it will, eventually. Thus, while it hasn't occurred within our study's window of time and thus wasn't on our list, you can add to your total of energy released a percentage of its expected energy (use 800 * 1018 Nm) equal to the percentage of its recurrence interval that the study covers. Why? Because if your study lasted as long as the recurrence interval, you'd almost certainly see exactly one such event occur within that period of time -- and thus it would contribute 100% of its expected energy to the total.

Though the average recurrence interval of the San Andreas fault's Mojave segment, north of Los Angeles, was found to be 140 years, let's use a more conservative estimate of 200 years. (We also do this because the ruptures with shorter repeat times that lower the average recurrence interval release less energy than an earthquake like the 1857 rupture. Conversely, we could use a more conservative average energy estimate while keeping the 140-year recurrence interval.)

  1. What percentage of this 200-year recurrence interval did your study cover?

  2. Multiply the expected energy release from this very large earthquake by that fraction. Adding this number to the total energy released that you found in question 1, above, does this roughly balance out the energies? (A total within about 100 * 1018 Nm is well within the uncertainties of these figures.)

  3. Now that you've allowed for the inevitable "Big One" on the San Andreas fault that wasn't within your study's window of time, do you think it's likely there's much of an "earthquake deficit"?

This activity was based upon the following studies:

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