Page 7 - 1052-5173-27-11

AB Goldfinger et al. (2012). Earthquake prob-
ability issues can be explored from discus-
Paleoearthquake History sions in Stark and Freedman (2003),
Parsons (2008), Matthews et al. (2002), and
recent cluster Kagan et al. (2012).

8000 BCE 6000 BCE 4000 BCE 2000 BCE 0 2000 CE The take-home message for students is
that saying “the probability of an earth-
D Earthquake probability quake is N%” involves specifying the
in next 50 years assumptions made. Different plausible
assumptions yield different probabilities.
C Annual earthquake probability 40% This situation may seem frustrating, but it
lets instructors explain how limitations in
0.004 2017- Time dependent our knowledge give young scientists
2067 opportunities for major advances.
30%
Recent cluster ACKNOWLEDGMENTS
Recent cluster
0.002 We thank Michael Hubenthal and three reviewers
20% for helpful comments.
All data
Time independent REFERENCES CITED

10% Time independent Time Goldfinger, C., Nelson, C.H., Morey, A.E.,

0 All data Dependent Johnson, J.E., Patton, J.R., Karabanov, E.,
1700 Gutiérrez-Pastor, J., Eriksson, A.T., Gràcia, E.,
1900 2100 2300 2500 2700 0% 1700 1800 Date 1900 2000 Dunhill, G., Enkin, R.J., Dallimore, A., and
Vallier, T., 2012, Turbidite event history—
Date Methods and implications for Holocene
paleoseismicity of the Cascadia subduction zone:
Figure 1. (A) Geometry of the Cascadia subduction zone. (B) Paleoearthquake history from turbidite USGS Professional Paper 1661-F.
deposits. (C) Probabilities of an earthquake in the next year as a function of time assuming a Gauss- Goldfinger, C., Ikeda, Y., and Yeats, R.S., 2013,
ian distribution of recurrence times with mean and standard deviation corresponding to the recent Superquakes, supercycles, and global earthquake
cluster (red/dashed lines) or the entire paleoearthquake record (blue/solid lines). Shaded area clustering, 7 Jan. 2013: Earth, https://www.
under the curves corresponds to the probability in next 50 years. (D) Conditional probability of an earthmagazine.org/article/superquakes-
earthquake in next 50 years, given that last was in 1700, for the four cases discussed. supercycles-and-global-earthquake-clustering-
recent-research-and-recent-quakes (last accessed
However, assuming that we are still in the subduction zone. Each choice yields a dif- 17 Aug. 2017).
recent cluster gives a probability ~6 times ferent probability estimate. Kagan, Y.Y., Jackson, D.D., and Geller, R.J., 2012,
larger: 0.41 or 41%. The higher probability Characteristic earthquake model, 1884–2011,
results from the smaller mean recurrence A baseball analogy illustrates these R.I.P.: Seismological Research Letters, v. 83,
time and standard deviation. ideas. Whether to assume that we are in p. 951–953, doi:10.1785/0220120107.
the cluster is like whether to assume that a Matthews, M.V., Ellsworth, W.L., and Reasenberg,
Figure 1D also shows flat lines starting hitter’s performance in the next game is P.A., 2002, A Brownian model for recurrent
at 1700 CE, corresponding to time-inde- better described by his lifetime batting earthquakes: Bulletin of the Seismological
pendent models. If the time-dependent average or by the past few games, because Society of America, v. 92, p. 2233–2250,
model predicts higher probability than the he may be hitting unusually well or in a doi:10.1785/0120010267.
time-independent model, an earthquake slump. Choosing between time‐indepen- Parsons, T., 2008, Earthquake recurrence on the
can be considered “overdue,” which occurs dent or time-dependent models is like south Hayward fault is most consistent with a
if we are in the cluster. assuming either that the player’s hitting is time dependent, renewal process: Geophysical
the same from year to year or that it Research Letters, v. 35,
IMPLICATIONS AND changes systematically over his career. The doi:10.1029/2008GL035887.
OPPORTUNITIES probability of a hit in the next game Schulz, K., 2015, The really big one: The New
depends on the assumptions. Yorker, 20 July, p. 20.
Comparing these cases shows how Stark, P.B., and Freedman, D., 2003, What is the
earthquake probability estimates depend There are many opportunities for delv- chance of an earthquake?, in Mulargia, F., Geller,
on the probability model chosen and the ing further. Students can explore different R.J. eds., Earthquake Science and Seismic Risk
data used to choose the model parameters. assumptions using the data and spread- Reduction: Dordrecht, Netherlands, Kluwer.
Other plausible choices are possible. sheet at http://www.earth.northwestern. Stein, S., and Stein, J., 2014, Playing against nature:
Various probability density functions can edu/people/seth/Educational/eqprob.html integrating science and economics to mitigate
be used. The data can be treated in more or write spreadsheets or programs using natural hazards in an uncertain world:
complex ways: considering different sub- formulations in Stein and Wysession (2003) Washington, D.C., American Geophysical
sets, assigning different magnitudes to or Stein and Stein (2014). Instructors or Union, and New Jersey, Wiley, 278 p.
different paleoevents, and assuming that students interested in Cascadia paleo­ Stein, S., and Wysession, M., 2003, Introduction to
different events broke different parts of the seismology and probabilities can consult seismology, earthquakes, and earth structure:
New Jersey, Wiley-Blackwell, 510 p.

Manuscript received 3 July 2017
Revised manuscript received 29 July 2017
Manuscript accepted 9 Aug. 2017

www.geosociety.org/gsatoday 7