Finite Element Models of Volcano Deformational Systems Having Structural Complexity

Abstract

The main focus of this work is to build 3-D FEM models with structural complexities in order to simulate volcanic systems in a more realistic way. We use Rabaul as an example to show the application of the methods and strategies proposed to an active volcano.

Rabaul caldera is a volcanic system whose dynamics still need to be understood to effectively predict the behavior of future eruptions. In comparison to the simplified analytic models used so far, more realistic models, such as Finite Elements Models (FEMs), are needed to more accurately explain recent deformation and understand the magmatic system. By inverting InSAR data collected between 2007 and 2010 (using linear inversions based on FEMs), we investigate the sources of surface displacement and provide insights about the actual shallow magmatic system.

FEMs are numerical models that let us include realistic features such as topography and mechanical heterogeneities. We provide strategies to use geophysical and geological information to build complex 3-D parts and assemble them into 3-D models. We then compare the effects of different material properties configurations and of different source shapes on the deformational signal and on the strength source estimates (fluid flux or pressure).

Ultimately, we provide a strategy for performing a linear inversion based on an array of FEM sources that allows us to identify a distribution of flux of fluid (or change in pressure) over a volume, without imposing an a-priori source shape and depth. We use Rabaul as an example to show the 3-D model’s validity and applicability to active volcanic areas. The methodology is based on generating a library of forward numerical displacement solutions, where each entry is the displacement generated by injecting a mass of fluid of known density and bulk modulus into a source of the array. The sources are simulated as fluid-filled cavities that can accept a specified flux of magma. As the array of sources is an intrinsic geometric aspect of all forward models and the sources are activated one at a time, the domain only needs to be discretized once. This strategy precludes the need for remeshing for each activated source and greatly reduces computational requirements. By using an array of sources, we are not investigating the geometric and pressure parameters of a simplified, unique source with a regular shape. Instead, we are investigating a distribution of flux of fluids over a volume of potential sources responsible for the pressure changes in the medium as dictated by the data. The results allow us to image the complex shape of the deformation source without having to use any a-priori or simplified sources. This takes source modeling a step towards more realistic source models.

The application of the methodology to Rabaul shows a shallow magmatic system under the caldera made of two interconnected lobes located at the two opposite sides of the caldera. These lobes are suggested to be the feeding reservoirs of the ongoing Tavuvur volcano eruption, on the eastern side, and of the past Vulcan volcano eruptions, on the western side. The interconnection and spatial distribution of sources find correspondence in the petrography of the products described in literature and in the dynamics of the single and twin eruptions that characterize the caldera.

The good results obtained from the application of the method show that the proposed linear inversion based on the FEM array of sources can be considered suitable for generating models of the magmatic system. It can be easily applied to any volcano, because it accounts for volcano deformation without having to specify the shape of the deformation source prior to inversion.

El objetivo principal de este trabajo es la construcción de modelos de elementos finitos (FEMs) 3-D con complejidades estructurales con el fin de simular sistemas volcánicos de manera más realista. Como ejemplo de aplicación se ha escogido la caldera de Rabaul, un sistema volcánico cuya dinámica no se comprende por completo. Invirtiendo los datos de InSAR recogidos durante los años 2007-2010, investigamos las fuentes de desplazamiento de la superficie y proporcionamos claves de relevancia sobre el sistema magmático superficial real. Incluyendo características realistas, como la topografía y heterogeneidades mecánicas, usamos las informaciones geofísicas y geológicas para construir modelos de FEMs complejos en 3D. En última instancia, proporcionamos una estrategia para llevar a cabo una inversión lineal basada en una matriz de fuentes que nos permite identificar una distribución de flujo de fluido a través de un volumen de posibles fuentes responsables de los cambios de presión en el medio según lo dictado por los datos, sin imponer a priori una forma de fuente específica y su profundidad.

Los resultados permiten generar imágenes de la forma compleja de la fuente que da lugar a la deformación, en el espacio y en el tiempo, sin tener que utilizar ninguna fuente con una forma excesivamente simplificada a priori. Esto lleva el modelado de fuentes un paso adelante hacia modelos más realistas.

En el caso de Rabaul, la aplicación de la metodología discutida anteriormente, muestra un sistema magmático superficial formado por dos lóbulos interconectados localizados bajo la caldera y en posiciones diametralmente opuestas. La interconexión y la distribución espacial de las fuentes encuentran correspondencia en la petrología de los productos descritos en literatura y en la dinámica de las erupciones que caracterizan la caldera. Los resultados obtenidos mediante la aplicación del método son satisfactorios y demuestran que la inversión lineal basada en la matriz de fuentes de FE propuesta puede ser considerada adecuada para generar modelos de sistemas magmáticos. Se puede aplicar fácilmente a cualquier volcán, ya que tiene en cuenta la deformación del edificio sin tener que especificar la forma de la fuente de deformación antes de la inversión.