Modelling the probability of earthquakes (M >= 5.0) in North Anatolian Fault Zone


Murat Koptur


August 25, 2022

Visualization of earthquake data

Let’s look and visualize the historical earthquake data.

Time Span between Earthquake Occurrences

p <- ggplot(data_diff_between_eq, aes(x=diff)) + geom_histogram(aes(y = ..density..)) + geom_density()

p2 <- ggplot(data_diff_between_eq, aes(x=diff)) + geom_boxplot()

Earthquake Count By Year

p3 <- ggplot(data_count_by_year, aes(x=year, y=count)) + geom_line()

Modelling the probability

Let’s fit Weibull distribution to distribution of days between two earthquakes occurred successively.

plotdist(data_diff_between_eq$diff, demp = TRUE)

Fit the distribution:

# add all data points to 0.1 for avoiding zero division errors
data_diff_between_eq$diff <- data_diff_between_eq$diff + 0.01 <- fitdist(data_diff_between_eq$diff, "weibull")

Check convergence, 0 means procedure was converged:

[1] 0


  • Estimate

    x sd
    shape 0.3647605 0.0294541
    scale 124.4717945 34.3619153
  • Fit quality:

    loglik -618.5651
    aic 1241.13
    bic 1246.494
  • Plots:

Let’s calculate mean occurence period of earthquakes which have magnitudes equal or bigger than 5 (simulation and theoretical mean):

shape.v <- as.numeric($estimate[1])
scale.v <- as.numeric($estimate[2])

simulated_data <- rweibull(100000, shape = shape.v, scale = scale.v)
Simulated mean 535.6679525
Theoretical mean 545.0535056

It is expected to have another earthquake having magnitude equal to 5 or above are average 545 days later than the preceding one.

Let’s plot the CDF:

plot(ecdf(simulated_data), xlim=c(0, 6000))

If we look the data, the last earthquake was occurred at 2006-10-24, so 5753 days passed since last earthquake was occurred. The risk of an earthquake happening today is 98 %.

Full source code:


\(^1\) Earthquake historical data was downloaded from:

\(^2\) Map shape file was downloaded from:

\(^3\) Weibull distribution in earthquake probability modelling: Yilmaz, Veysel & Erişoğlu, Murat & Çelik, H.. (2004). Probabilistic Prediction of the Next Earthquake in The Nafz (North Anatolian Fault Zone), Turkey = Kuzey Anadolu Fay Zonunda (Nafz) Gelecek Depremlerin Olasılıksal Tahmini. Dogus University Journal. 5.

\(^4\) Weibull distribution fitting:

No matching items Protection Status