La Palma Earthquakes

In [1]:

library(tidyverse)

── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.1.2     ✔ readr     2.1.4
✔ forcats   1.0.0     ✔ stringr   1.5.0
✔ ggplot2   3.4.2     ✔ tibble    3.2.1
✔ lubridate 1.9.2     ✔ tidyr     1.3.0
✔ purrr     1.0.1     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

In [2]:

eruptions <- tibble(
  year = c(1492, 1585, 1646, 1677, 1712, 1949, 1971, 2021)
)
n_eruptions <- nrow(eruptions)

In [3]:

avg_years_between_eruptions <- eruptions |>
  filter(year != 2021) |>
  mutate(
    year_lag = lag(year),
    diff = year - year_lag
  ) |>
  summarize(avg_diff = mean(diff, na.rm = TRUE)) |>
  pull()

Based on data up to and including 1971, eruptions on La Palma happen every 79.8 years on average.

Studies of the magma systems feeding the volcano, such as (Marrero et al. 2019), have proposed that there are two main magma reservoirs feeding the Cumbre Vieja volcano; one in the mantle (30-40km depth) which charges and in turn feeds a shallower crustal reservoir (10-20km depth).

In [4]:

ggplot(eruptions, aes(x = year, y = 0)) +
  geom_text(label = "|") +
  theme_minimal() +
  labs(y = NULL) +
  theme(
    panel.grid = element_blank(),
    axis.text.y = element_blank()
  )

Figure 1: Timeline of recent eruptions on La Palma

Eight eruptions have been recorded since the late 1400s (Figure 1).

Data and methods are discussed in Section 1.

Let \(x\) denote the number of eruptions in a year. Then, \(x\) can be modeled by a Poisson distribution

\[ p(x) = \frac{e^{-\lambda} \lambda^{x}}{x !} \tag{1}\]

where \(\lambda\) is the rate of eruptions per year. Using Equation 1, the probability of an eruption in the next \(t\) years can be calculated.

Table 1: Recent historic eruptions on La Palma

Name	Year
Current	2021
Teneguía	1971
Nambroque	1949
El Charco	1712
Volcán San Antonio	1677
Volcán San Martin	1646
Tajuya near El Paso	1585
Montaña Quemada	1492

Table 1 summarizes the eruptions recorded since the colonization of the islands by Europeans in the late 1400s.

Figure 2: Map of La Palma

La Palma is one of the west most islands in the Volcanic Archipelago of the Canary Islands (Figure 2).

1 Data & Methods

References

Marrero, José M., Alicia García, Manuel Berrocoso, Ángeles Llinares, Antonio Rodríguez-Losada, and Ramón Ortiz. 2019. “Strategies for the Development of Volcanic Hazard Maps in Monogenetic Volcanic Fields: The Example of La Palma (Canary Islands).” Journal of Applied Volcanology 8 (1). https://doi.org/10.1186/s13617-019-0085-5.