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

Modelling distribution of days between two earthquakes occurred successively.
Author

Murat Koptur

Published

August 25, 2022

Visualization of earthquake data

Let’s look and visualize the historical earthquake data.

Time Span between Earthquake Occurrences

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

```{r}
p2 <- ggplot(data_diff_between_eq, aes(x=diff)) + geom_boxplot()
p2
```

Earthquake Count By Year

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

Modelling the probability

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

```{r}
plotdist(data_diff_between_eq$diff, demp = TRUE)
```

Fit the distribution:

```{r}
# add all data points to 0.1 for avoiding zero division errors
data_diff_between_eq$diff <- data_diff_between_eq$diff + 0.01

wei.fit <- fitdist(data_diff_between_eq$diff, "weibull")
```

Check convergence, 0 means procedure was converged:

```{r}
print(wei.fit$convergence)
```
[1] 0

Results:

  • Estimate

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

    value
    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):

```{r}
shape.v <- as.numeric(wei.fit$estimate[1])
scale.v <- as.numeric(wei.fit$estimate[2])

simulated_data <- rweibull(100000, shape = shape.v, scale = scale.v)
```
value
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:

```{r}
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: https://github.com/mrtkp9993/MyDsProjects/tree/main/EarthQuakeProbability

References

\(^1\) Earthquake historical data was downloaded from: http://deprem.afad.gov.tr/depremkatalogu

\(^2\) Map shape file was downloaded from: https://gadm.org/

\(^3\) 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: https://stats.stackexchange.com/questions/230937/how-to-find-initial-values-for-weibull-mle-in-r

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Citation

BibTeX citation:
@online{koptur2022,
  author = {Murat Koptur},
  title = {Modelling the Probability of Earthquakes {(M} \textgreater=
    5.0) in {North} {Anatolian} {Fault} {Zone}},
  date = {2022-08-25},
  url = {https://www.muratkoptur.com/MyDsProjects/Analysis.html},
  langid = {en}
}
For attribution, please cite this work as:
Murat Koptur. 2022. “Modelling the Probability of Earthquakes (M >= 5.0) in North Anatolian Fault Zone.” August 25, 2022. https://www.muratkoptur.com/MyDsProjects/Analysis.html.