Cuadernos Reproducibles de Conocimiento del Riesgo

Los Cuadernos Reproducibles de Conocimiento del Riesgo tienen el objetivo de compartir datos, herramientas y flujos de trabajo para fomentar la investigación y tecnologías reproducibles y reutilizables en gestión del riesgo de desastres.

Los cuadernos son un espacio para el intercambio de ideas, trabajos recientes e impactos dentro de la comunidad profesional y de investigación en riesgos de desastres en Colombia. Bajo la sombrilla de plataforma Riesgos, busca que estudiantes, investigadores y profesionales compartan sus investigaciones más recientes y aplicaciones que emplean el modelado y la simulación computacional para comprender y reducir los riesgos de desastres.


### Spatial Distribution

The spatial distribution of earthquakes reveals two main clusters:

**Cluster 1 - Shallow/Intermediate (8-15 km depth)**
- Located beneath the central part of the island
- Associated with crustal magma reservoir
- Earthquake magnitudes typically ML 2.0-3.5

**Cluster 2 - Deep (20-35 km depth)**  
- Located slightly offshore to the west
- Associated with mantle reservoir and deep magma ascent
- Earthquake magnitudes typically ML 1.5-4.5

```{figure} spatial_distribution.png
---
name: fig-spatial
width: 100%
---
Spatial distribution of earthquakes colored by depth. The shallow cluster (red) is located beneath the island, while the deep cluster (blue) extends offshore. The eruption site is marked with a star.

Depth Distribution¶

The depth distribution analysis confirms the two-reservoir model:

N(z) = A_1 \exp\left(-\frac{(z-z_1)^2}{2\sigma_1^2}\right) + A_2 \exp\left(-\frac{(z-z_2)^2}{2\sigma_2^2}\right)

(1)

Where: - $z_1 = 12 \pm 2$ km (crustal reservoir depth) - $z_2 = 28 \pm 4$ km (mantle reservoir depth) - $A_1, A_2$ are amplitude parameters - $\sigma_1, \sigma_2$ are depth uncertainties

Magnitude-Frequency Analysis¶

The Gutenberg-Richter relationship for La Palma seismicity follows:

\log_{10} N = a - bM

(2)

Where: - $N$ = cumulative number of earthquakes ≥ magnitude $M$ - $a = 4.2 \pm 0.1$ (activity parameter) - $b = 1.1 \pm 0.1$ (slope parameter)

The b-value of 1.1 is typical for volcanic environments and indicates a high proportion of smaller earthquakes relative to larger ones McNutt (2005).

```{figure} magnitude_frequency.png 31b8e172-b470-440e-83d8-e6b185028602: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:31b8e172-b470-440e-83d8-e6b185028602

Magnitude-frequency distribution for La Palma earthquakes. The plot shows the characteristic power-law relationship with a b-value of 1.1, typical for volcanic seismicity.


## Statistical Analysis

### Seismic Rate Changes

We applied change-point analysis to identify significant changes in seismic rate:

```python
import ruptures as rpt

# Prepare time series data
daily_counts = df.groupby(df['datetime'].dt.date).size()
signal = daily_counts.values

# Change-point detection
algo = rpt.Pelt(model="rbf").fit(signal)
result = algo.predict(pen=10)

print(f"Change points detected: {result}")

The analysis identified three major change points: 1. May 2020: Transition from background to elevated activity
2. July 2021: Onset of pre-eruptive intensification 3. September 19, 2021: Eruption onset

Correlation Analysis¶

Cross-correlation between shallow and deep seismicity reveals:

r(τ) = \frac{\sum_{t} [x_s(t) - \bar{x}_s][x_d(t+τ) - \bar{x}_d]}{\sqrt{\sum_t [x_s(t) - \bar{x}_s]^2 \sum_t [x_d(t+τ) - \bar{x}_d]^2}}

(3)

Where $x_s(t)$ and $x_d(t)$ are shallow and deep earthquake counts at time $t$ .

Results show maximum correlation at τ = 0 days with r = 0.72, indicating synchronized activation of both reservoir levels.

Discussion¶

Magma System Dynamics¶

The seismic data supports a model where:

Deep reservoir activation (2017-2020): Slow magma accumulation at mantle depths
Crustal reservoir charging (2020-2021): Magma ascent and storage at crustal levels\
Final ascent (September 2021): Rapid magma transport to surface

Hazard Implications¶

The analysis has important implications for volcanic hazard assessment:

Key Findings :class: important

Early warning: Deep seismicity provides months of advance warning
Eruption timing: Shallow swarms indicate imminent eruption (days to weeks)
Duration prediction: Correlation between pre-eruptive seismic energy and eruption duration :::

Comparison with Other Systems¶

La Palma’s seismic patterns are similar to those observed at other ocean island volcanoes:

Volcano	Deep Swarm Depth	Shallow Swarm Depth	Lead Time
Kilauea	30-60 km	3-8 km	Weeks-Months
Etna	20-30 km	5-15 km	Days-Weeks
La Palma	20-35 km	8-15 km	Months
Stromboli	10-20 km	2-6 km	Hours-Days

: Comparison of seismic patterns at ocean island volcanoes {#tbl-comparison}

Conclusions¶

The 2021 La Palma eruption was preceded by a complex pattern of seismic activity that provides insights into the magma plumbing system:

Two-reservoir system: Seismicity confirms mantle (20-35 km) and crustal (8-15 km) magma reservoirs
Long-term precursors: Deep seismicity began increasing in 2017, providing years of warning
Short-term precursors: Shallow seismicity intensified weeks before eruption
Synchronized activation: Strong correlation between deep and shallow earthquake rates

These findings have important implications for: - Volcanic monitoring: Multi-depth seismic networks essential for eruption forecasting - Hazard assessment: Different phases of unrest require different response protocols\

Scientific understanding: Confirms conceptual models of ocean island volcano plumbing systems

Future work should focus on: - Real-time implementation of change-point detection algorithms - Integration with other monitoring techniques (geodesy, gas emissions) - Development of probabilistic eruption forecasting models

Acknowledgments¶

The authors thank the Instituto Geográfico Nacional (IGN) for providing the earthquake catalog data. We also acknowledge the staff at the Observatorio Geofísico Central for their continuous monitoring efforts during the crisis.

Data Availability¶

The earthquake catalog data used in this study is available from the IGN at https://www.ign.es/web/ign/portal/sis-catalogo-terremotos. Processing scripts and analysis code are available at https://github.com/curvenote/la-palma-seismicity.

References¶

McNutt, S. R. (2005). Seismic monitoring and eruption forecasting of volcanoes: a review of the state-of-the-art and case histories. Monitoring and Mitigation of Volcano Hazards, 99–146. 10.1007/978-3-642-80087-0_3