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

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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