Timing of major earthquakes

Case Studies in Statistical Thinking

Justin Bois

Lecturer, Caltech

Models for earthquake timing

Exponential: Earthquakes happen like a Poisson process

Gaussian: Earthquakes happen with a well-defined period

Stable continental region earthquakes

¹ Data source: USGS Earthquake Catalog for Stable Continental Regions

The Nankai Trough

Earthquakes in the Nankai Trough

Date	Magnitude
684-11-24	8.4
887-08-22	8.6
1099-02-16	8.0
1361-07-26	8.4
1498-09-11	8.6
1605-02-03	7.9
1707-10-18	8.6
1854-12-23	8.4
1946-12-24	8.1

ECDF of time between Nankai quakes

Formal ECDFs

ECDF(x) = fraction of data points $\le$ x

Formal ECDFs

# time_gap is an array of interearthquake times
_ = plt.plot(*dcst.ecdf(time_gap, formal=True))
_ = plt.xlabel('time between quakes (yr)')
_ = plt.ylabel('ECDF')

# Compute the mean time gap
mean_time_gap = np.mean(time_gap)

# Standard deviation of the time gap
std_time_gap = np.std(time_gap)

# Generate theoretical Exponential distribution of timings
time_gap_exp = np.random.exponential(mean_time_gap, size=100000)

# Generate theoretical Normal distribution of timings
time_gap_norm = np.random.normal(
  mean_time_gap, std_time_gap, size=100000
)

# Plot theoretical CDFs
_ = plt.plot(*dcst.ecdf(time_gap_exp))
_ = plt.plot(*dcst.ecdf(time_gap_norm))

Model for Nankai Trough

Let's practice!

Case Studies in Statistical Thinking