Finite Element Models of Elastic Volcano Deformation

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

Finite Element Models of Elastic Earthquake Deformation

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

Did a submarine landslide contribute to the 2011 Tohoku tsunami?

Many studies have modeled the Tohoku tsunami of March 11, 2011 as being due entirely to slip on an earthquake fault, but the following discrepancies suggest that further research is warranted. (1) Published models of tsunami propagation and coastal impact underpredict the observed runup heights of up to 40 m measured along the coast of the Sanriku district in the northeast part of Honshu Island. (2) Published models cannot reproduce the timing and high-frequency content of tsunami waves recorded at three nearshore buoys off Sanriku, nor the timing and dispersion properties of the waveforms at offshore DART buoy #21418. (3) The rupture centroids obtained by tsunami inversions are biased about 60 km NNE of that obtained by the Global CMT Project. Based on an analysis of seismic and geodetic data, together with recorded tsunami waveforms, we propose that, while the primary source of the tsunami was the vertical displacement of the seafloor due to the earthquake, an additional tsunami source is also required. We infer the location of the proposed additional source based on an analysis of the travel times of higher-frequency tsunami waves observed at nearshore buoys. We further propose that the most likely additional tsunami source was a submarine mass failure (SMF—i.e., a submarine landslide). A comparison of pre- and post-tsunami bathymetric surveys reveals tens of meters of vertical seafloor movement at the proposed SMF location, and a slope stability analysis confirms that the horizontal acceleration from the earthquake was sufficient to trigger an SMF. Forward modeling of the tsunami generated by a combination of the earthquake and the SMF reproduces the recorded on-, near- and offshore tsunami observations well, particularly the high-frequency component of the tsunami waves off Sanriku, which were not well simulated by previous models. The conclusion that a significant part of the 2011 Tohoku tsunami was generated by an SMF source has important implications for estimates of tsunami hazard in the Tohoku region as well as in other tectonically similar regions

Finite element models for the deformation of the Askja volcanic complex and rift segment, Iceland

The Askja volcanic complex and rift segment of Iceland's Northern Volcanic Zone has been continuously subsiding at an usually high rate for more than two decades. InSAR data compiled over the last decade reveal two patterns of deformation: (1) a radially symmetric pattern of subsidence local to Askja's caldera and (2) an elongated pattern of subsidence tracking the rift segment. Microgravity data suggest a mass loss from a shallow reservoir and seismicity data reveal a relatively shallow brittle-ductile transition. A simple model combining two vertically-aligned and contracting Mogi sources, one shallow (~3 km) and one deep (~20 km), in an elastic half space generally predicts the observed InSAR deformation. Subsidence along the Askja fissure swarm has also been attributed to effects of plate spreading across rheologically weak fissure swarms. The shallow contracting Mogi source and microgravity data are consistent with magma migration out of the shallow reservoir. Interpretations of the deep contracting source are more uncertain. We present an alternative model that combines magma extraction from a shallow, fluid-filled cavity with a plate spreading model having rheologic partitioning expected for the rift segment. This 3D finite element model (FEM) simulates an elastic upper crust and viscoelastic lower crust. Inspired by a model configuration presented by Pedersen et al. (2009), the simulated brittle-ductile transition shallows beneath the rift, in accord with seismicity data. The FEM is driven by plate spreading at a constant rate and specified mass flux from the shallow cavity. The magnitude of flux is a calibration parameter estimated from InSAR data via inverse methods. Preliminary results suggest this alternative model generally predicts the both deformation patterns. However, the simulated shallow brittle ductile transition, combined with kinematic loading of plate spreading, accounts for much of the regional deformation originally attributed to magma migration out of a deep reservoir. This suggests that the estimated characteristics of magma extraction from the deep reservoir should be re-examined. The FEM accounts for multiple types of observations (both local and regional subsidence patterns, microgravity data, seismicity data, and plate spreading) associated with active deformation of the Askja volcano complex and rift segment. (Published By University of Alabama Libraries

Estimating nonlinear source parameters of volcano deformation: an application of FEM-based inverse methods and InSAR

Migration of magma within an active volcano produces a deformation signature at the Earth's surface. The internal structure of a volcano and specific movements of the magma control the actual deformation that is observed. Relatively simple models that simulate magma injection as a pressurized body embedded in a homogeneous elastic half-space (e.g., Mogi) can predict the characteristic radially-symmetric deformation patterns that are commonly observed for episodes of volcano inflation or deflation. Inverse methods, based on half-space models, can precisely and efficiently estimate the non-linear parameters that describe the geometry (position and shape) of the deformation source, as well as the linear parameter that describes the strength (pressure) of the deformation source. However, although such models can accurately predict the observed deformation, actual volcanoes have internal structures that are not compatible with the elastic half-space assumptions inherent to Mogi-type models. This incompatibility translates to errors in source parameter estimations. Alternatively, Finite Element Models (FEMs) can simulate a pressurized body embedded in a problem domain having an arbitrary distribution of material properties that better corresponds to the internal structure of an active volcano. FEMs can be used in inverse methods for estimating linear deformation source parameters, such as the source pressure. However, perturbations of the non-linear parameters that describe the geometry of the source require automated re-meshing of the problem domain - a significant obstacle to implementing FEM-based nonlinear inverse methods in volcano deformation studies. I present a parametric executable (C++ source code), which automatically generates FEMs that simulate a pressurized ellipsoid embedded in an axisymmetric problem domain, having an a priori distribution of material properties. I demonstrate this executable by analyzing Interferometric Synthetic Aperture Radar (InSAR) deformation data of the 1997 eruption of Okmok Volcano, Alaska as an example. This executable facilitates an inverse analysis that estimates the non-linear parameters that describe the depth and radius of the spherical source, as well as the linear strength parameter that best accounts for the InSAR data. The strong radial symmetry and high signal-to-noise ratio of the InSAR data, along with known seismic tomography data, provide robust constraints for estimated parameters and sensitivity analyses. (Published By University of Alabama Libraries

Numerical simulation of the 2011 Tohoku tsunami: Comparison with field observations and sensitivity to model parameters

The March 11, 2011 M9 Tohoku-Oki Earthquake, which is believed to be the largest event recorded in Japanese history, created a major tsunami that caused numerous deaths and enormous destruction on the nearby Honshu coast. Various tsunami sources were developed for this event, based on inverting seismic or GPS data, often using very simple underlying fault models (e.g., Okada, 1985). Tsunami simulations with such sources can predict deep water and far-field observations quite well, but coastal impact is not as well predicted, being over- or under-estimated at many locations. In this work, we developed a new tsunami source, similarly based on inverting onshore and offshore geodetic (GPS) data, but using 3D Finite Element Models (FEM) that simulate elastic dislocations along the plate boundary interface separating the stiff subducting Pacific Plate, and relatively weak forearc and volcanic arc of the overriding Eurasian plate. Due in part to the simulated weak forearc materials, such sources produce significant shallow slip along the updip portion of the rupture near the trench (several tens of meters). We assess the accuracy of the new approach by comparing numerical simulations to observations of the tsunami far- and near-field coastal impact using: (i) one of the standard seismic inversion sources, which we found provided the best prediction of tsunami near-field impact in our model (UCSB; Shao et al., 2011); and (ii) the new FEM source. Specifically, we compare numerical results to DART buoy, GPS tide gage, and inundation/runup measurements. Numerical simulations are performed using the fully nonlinear and dispersive Boussinesq wave model FUNWAVE-TVD, which is parallelized and available in Cartesian or spherical coordinates. We use a series of nested model grids, with varying resolution (down to 250 m nearshore) and size, and assess effects on results of the latter and of model physics (such as when including dispersion or not). We also assess effects of triggering the various tsunami sources in the propagation model: (i) either at once as a hot start, or with the spatio-temporal sequence derived from seismic inversion; and (ii) as a specified surface elevation or as a more realistic time and spacevarying bottom boundary condition (in the latter case, we compute the initial tsunami generation up to 300 s using the non-hydrostatic model NHWAVE). Although additional refinements are expected in the near future, results based on the current FEM sources better explain near field observations at DART and GPS buoys near Japan, and measured tsunami inundation, while they simulate observations at distant DART buoys as well or better than the UCSB source. Copyright © 2012 by the International Society of Offshore and Polar Engineers (ISOPE)

Numerical simulation of the 2011 Tohoku tsunami: Comparison with field observations and sensitivity to model parameters

The March 11, 2011 M9 Tohoku-Oki Earthquake, which is believed to be the largest event recorded in Japanese history, created a major tsunami that caused numerous deaths and enormous destruction on the nearby Honshu coast. Various tsunami sources were developed for this event, based on inverting seismic or GPS data, often using very simple underlying fault models (e.g., Okada, 1985). Tsunami simulations with such sources can predict deep water and far-field observations quite well, but coastal impact is not as well predicted, being over- or under-estimated at many locations. In this work, we developed a new tsunami source, similarly based on inverting onshore and offshore geodetic (GPS) data, but using 3D Finite Element Models (FEM) that simulate elastic dislocations along the plate boundary interface separating the stiff subducting Pacific Plate, and relatively weak forearc and volcanic arc of the overriding Eurasian plate. Due in part to the simulated weak forearc materials, such sources produce significant shallow slip along the updip portion of the rupture near the trench (several tens of meters). We assess the accuracy of the new approach by comparing numerical simulations to observations of the tsunami far- and near-field coastal impact using: (i) one of the standard seismic inversion sources, which we found provided the best prediction of tsunami near-field impact in our model (UCSB; Shao et al., 2011); and (ii) the new FEM source. Specifically, we compare numerical results to DART buoy, GPS tide gage, and inundation/runup measurements. Numerical simulations are performed using the fully nonlinear and dispersive Boussinesq wave model FUNWAVE-TVD, which is parallelized and available in Cartesian or spherical coordinates. We use a series of nested model grids, with varying resolution (down to 250 m nearshore) and size, and assess effects on results of the latter and of model physics (such as when including dispersion or not). We also assess effects of triggering the various tsunami sources in the propagation model: (i) either at once as a hot start, or with the spatio-temporal sequence derived from seismic inversion; and (ii) as a specified surface elevation or as a more realistic time and spacevarying bottom boundary condition (in the latter case, we compute the initial tsunami generation up to 300 s using the non-hydrostatic model NHWAVE). Although additional refinements are expected in the near future, results based on the current FEM sources better explain near field observations at DART and GPS buoys near Japan, and measured tsunami inundation, while they simulate observations at distant DART buoys as well or better than the UCSB source. Copyright © 2012 by the International Society of Offshore and Polar Engineers (ISOPE)

Numerical Simulation of the 2011 Tohoku Tsunami Based on a New Transient FEM Co-seismic Source: Comparison to Far- and Near-Field Observations

In this work, we simulate the 2011 M9 Tohoku-Oki tsunami using new coseismic tsunami sources based on inverting onshore and offshore geodetic data, using 3D Finite Element Models (FEM). Such FEMs simulate elastic dislocations along the plate boundary interface separating the stiff subducting Pacific Plate from the relatively weak forearc and volcanic arc of the overriding Eurasian plate. Due in part to the simulated weak forearc materials, such sources produce significant shallow slip (several tens of meters) along the updip portion of the rupture near the trench. To assess the accuracy of the new approach, we compare observations and numerical simulations of the tsunami\u27s far- and near-field coastal impact for: (i) one of the standard seismic inversion sources (UCSB; Shao et al. 2011); and (ii) the new FEM sources. Specifically, results of numerical simulations for both sources, performed using the fully nonlinear and dispersive Boussinesq wave model FUNWAVE-TVD, are compared to DART buoy, GPS tide gauge, and inundation/runup measurements. We use a series of nested model grids with varying resolution (down to 250 m nearshore) and size, and assess effects on model results of the latter and of model physics (such as when including dispersion or not). We also assess the effects of triggering the tsunami sources in the propagation model: (i) either at once as a hot start, or with the spatiotemporal sequence derived from seismic inversion; and (ii) as a specified surface elevation or as a more realistic time and space-varying bottom boundary condition (in the latter case, we compute the initial tsunami generation up to 300 s using the non-hydrostatic model NHWAVE). Although additional refinements are expected in the near future, results based on the current FEM sources better explain long wave near-field observations at DART and GPS buoys near Japan, and measured tsunami inundation, while they simulate observations at distant DART buoys as well or better than the UCSB source. None of the sources, however, are able to explain the largest runup and inundation measured between 39.5° and 40.25°N, which could be due to insufficient model resolution in this region (Sanriku/Ria) of complex bathymetry/topography, and/or to additional tsunami generation mechanisms not represented in the coseismic sources (e.g., splay faults, submarine mass failure). This will be the object of future work. © 2012 Springer Basel AG