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

# Visualization of earthquake data

Let’s look and visualize the historical earthquake data.

## Time Span between Earthquake Occurrences

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

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

## Earthquake Count By Year

```
```{r}
<- ggplot(data_count_by_year, aes(x=year, y=count)) + geom_line()
p3
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
$diff <- data_diff_between_eq$diff + 0.01
data_diff_between_eq
<- fitdist(data_diff_between_eq$diff, "weibull")
wei.fit ```
```

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}
<- as.numeric(wei.fit$estimate[1])
shape.v <- as.numeric(wei.fit$estimate[2])
scale.v
<- rweibull(100000, shape = shape.v, scale = scale.v)
simulated_data ```
```

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