The migration of magma within a volcano produces a deformation signature at the Earth’s surface. Inverse models of geodetic data estimate parameters that characterize the magma migration. These characterizations are tied to the specific model that relates migration to the observed deformation. A model is a simplified representation of a natural system. A modeler is tasked with the challenge of designing a model that represents the system, in the context of the available data and purpose of the model. This chapter presents a systematic approach to quantitatively simulate geodetic data with finite element models (FEMs) in the framework of a deformation modeling protocol. This chapter will (1) address the design and execution of FEMs that can account for the geophysical complexity of a volcano deformational system and (2) define techniques for including FEMs in both linear and nonlinear inverse methods to characterize a magmatic system based on observed geodetic data. With these techniques, researchers can estimate magmatic migration within active volcanoes and understand how uncertainties in the data propagate into predictions. These estimates comprise some measure of central tendency, a sense of uncertainty, and a quantification of biases.
Part of the book: Volcanoes
The Earth’s surface deforms in response to earthquake fault dislocations at depth. Deformation models are constructed to interpret the corresponding ground movements recorded by geodetic data such GPS and InSAR, and ultimately characterize the seismic ruptures. Conventional analytical and latest numerical solutions serve similar purpose but with different technical constraints. The former cannot simulate the heterogeneous rock properties and structural complexity, while the latter directly tackles these challenges but requires more computational resources. As demonstrated in the 2015 M7.8 Gorkha, Nepal earthquake and the 2016 M6.2 Amatrice, Italy earthquake, we develop state-of-art finite element models (FEMs) to efficiently accommodate both the material and tectonic complexity of a seismic deformational system in a seamless model environment. The FEM predictions are significantly more accurate than the analytical models embedded in a homogeneous half-space at the 95% confidence level. The primary goal of this chapter is describe a systematic approach to design, construct, execute and calibrate FEMs of elastic earthquake deformation. As constrained by coseismic displacements, FEM-based inverse analyses are employed to resolve linear and nonlinear fault-slip parameters. With such numerical techniques and modeling framework, researchers can explicitly investigate the spatial distribution of seismic fault slip and probe other in-depth rheological processes.
Part of the book: Earthquakes