Palabras clave
volcanes de pequeño volumen
geoestadística
intensidad espacial
procesos puntuales
permutaciones volcanic fields
small-volume volcanoes
geostatistics
spatial intensity
point pattern analyses
permutations
Cómo citar
Resumen
Los volcanes de pequeño volumen son los más abundantes en México y el mundo y tienden a agruparse en el espacio (campos volcánicos). Aquí se aplican técnicas de patrones puntuales espaciales para comparar el comportamiento de la intensidad espacial de los campos volcánicos de Sierra Chichinautzin y Los Tuxtlas. Las intensidades espaciales se ajustan con modelos de procesos Poisson no homogéneos. Posteriormente, se aplica una prueba de permutaciones con simulación Monte Carlo y se propone un estadístico de prueba basado en la razón de verosimilitudes de los modelos ajustados. Los resultados de la prueba de permutaciones presentaron evidencia para rechazar la hipótesis de igualdad de intensidades espaciales entre los campos volcánicos de Sierra Chichinautzin y Los Tuxtlas. El intercepto del modelo ajustado del campo volcánico de Los Tuxtlas estima una intensidad (volcanes por unidad de área) de 0.42, mientras que el intercepto del modelo ajustado de la intensidad del campo volcánico Sierra Chichinautzin fue de 0.40 unidades. Se discuten métodos estadísticos alternativos utilizados en la literatura y se compara su utilidad para contestar preguntas en la vulcanología.
Comparison of the spatial intensity of small-volume volcanoes in two volcanic fields in Mexico by using Poisson point pattern analysis
Small-volume volcanoes are the most abundant in Mexico and worldwide, and tend to cluster in space (volcanic fields). Here, spatial point pattern techniques are applied to compare the behavior of the spatial intensity of the Sierra Chichinautzin and Los Tuxtlas volcanic fields. Spatial intensities are fitted with inhomogeneous Poisson process models. Subsequently, a permutations test with Monte Carlo simulation is applied and a test statistic based on the likelihood ratio of the fitted models is proposed. The results of the permutations test delivered evidence to reject the hypothesis of equality of spatial intensities between the volcanic fields of Sierra Chichinautzin and Los Tuxtlas. The intercept of the fitted model of the Los Tuxtlas volcanic field estimates an intensity (volcanoes per unit area) of 0.42 while the intercept of the fitted model of the intensity of the Sierra Chichinautzin volcanic field was 0.40 units. Alternative statistical methods used in the literature are discussed and their usefulness to answer questions in volcanology are compared.
Citas
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Derechos de autor 2023 Francisco Córdoba Montiel