ALBERT

Description: 〈span〉〈div〉SUMMARY〈/div〉Knowledge of deformation at plate boundaries has been improved greatly by the development of observational techniques in space geodesy. However, most theoretical and numerical models of coseismic deformation have remained very simple and do not include realistic Earth structure. 3-D material heterogeneity and topography are often neglected because simple models are assumed to be sufficient and available tools cannot easily accommodate complex heterogeneity. In this study, we demonstrate the importance of 3-D heterogeneity using a spectral element method that incorporates topography and 3-D material properties. Using a parabolic hill model and a topographic model of the 2010 Maule earthquake, we show that topographic features can alter the shape of observed surface deformation patterns. We also estimate the coseismic surface deformation due to a model of the slip distribution of the 2015 Gorkha earthquake using realistic topography and 3-D elastic structure, and find that the presence of topography causes changes in the shape of observed surface displacement patterns, while material heterogeneities primarily affect the magnitude of observed displacements. Our results show that the inclusion of topography in particular can affect predictions of coseismic deformation modelling.〈/span〉

Description: 〈span〉〈div〉SUMMARY〈/div〉Although earthquake-induced gravity perturbations are frequently observed, numerical modelling of this phenomenon has remained a challenge. Due to the lack of reliable and versatile numerical tools, induced-gravity data have not been fully exploited to constrain earthquake source parameters. From a numerical perspective, the main challenge stems from the unbounded Poisson/Laplace equation that governs gravity perturbations. Additionally, the Poisson/Laplace equation must be coupled with the equation of conservation of linear momentum that governs particle displacement in the solid. Most existing methods either solve the coupled equations in a fully spherical harmonic representation, which requires models to be (nearly) spherically symmetric, or they solve the Poisson/Laplace equation in the spherical harmonics domain and the momentum equation in a discretized domain, a strategy that compromises accuracy and efficiency. We present a spectral-infinite-element approach that combines the highly accurate and efficient spectral-element method with a mapped-infinite-element method capable of mimicking an infinite domain without adding significant memory or computational costs. We solve the complete coupled momentum-gravitational equations in a fully discretized domain, enabling us to accommodate complex realistic models without compromising accuracy or efficiency. We present several coseismic and post-earthquake examples and benchmark the coseismic examples against the Okubo analytical solutions. Finally, we consider gravity perturbations induced by the 1994 Northridge earthquake in a 3-D model of Southern California. The examples show that our method is very accurate and efficient, and that it is stable for post-earthquake simulations.〈/span〉

Description: 〈span〉〈div〉Summary〈/div〉Knowledge of deformation at plate boundaries has been improved greatly by the development of observational techniques in space geodesy. However, most theoretical and numerical models of coseismic deformation have remained very simple and do not include realistic Earth structure. Three-dimensional material heterogeneity and topography are often neglected because simple models are assumed to be sufficient and available tools cannot easily accommodate complex heterogeneity. In this study, we demonstrate the importance of three-dimensional heterogeneity using a spectral-element method that incorporates topography and 3D material properties. Using a parabolic hill model and a topographic model of the 2010 Maule earthquake, we show that topographic features can alter the shape of observed surface deformation patterns. We also estimate the coseismic surface deformation due to a model of the slip distribution of the 2015 Gorkha earthquake using realistic topography and 3D elastic structure, and find that the presence of topography causes changes in the shape of observed surface displacement patterns while material heterogeneities primarily affect the magnitude of observed displacements. Our results show that the inclusion of topography in particular can affect predictions of coseismic deformation modeling.〈/span〉

Description: 〈span〉〈div〉Summary〈/div〉Although earthquake-induced gravity perturbations are frequently observed, numerical modeling of this phenomenon has remained a challenge. Due to the lack of reliable and versatile numerical tools, induced-gravity data have not been fully exploited to constrain earthquake source parameters. From a numerical perspective, the main challenge stems from the unbounded Poisson/Laplace equation that governs gravity perturbations. Additionally, the Poisson/Laplace equation must be coupled with the equation of conservation of linear momentum that governs particle displacement in the solid. Most existing methods either solve the coupled equations in a fully spherical harmonic representation, which requires models to be (nearly) spherically symmetric, or they solve the Poisson/Laplace equation in the spherical harmonics domain and the momentum equation in a discretized domain, a strategy that compromises accuracy and efficiency. We present a spectral-infinite-element approach that combines the highly accurate and efficient spectral-element method with a mapped-infinite-element method capable of mimicking an infinite domain without adding significant memory or computational costs. We solve the complete coupled momentum-gravitational equations in a fully discretized domain, enabling us to accommodate complex realistic models without compromising accuracy or efficiency. We present several coseismic and postearthquake examples and benchmark the coseismic examples against the Okubo analytical solutions. Finally, we consider gravity perturbations induced by the 1994 Northridge earthquake in a 3D model of Southern California. The examples show that our method is very accurate and efficient, and that it is stable for postearthquake simulations.〈/span〉

Description: 〈span〉〈div〉Summary〈/div〉Accurate and efficient simulations of coseismic and postearthquake deformation are important for proper inferences of earthquake source parameters and subsurface structure. These simulations are often performed using a truncated halfspace model with approximate boundary conditions. The use of such boundary conditions introduces inaccuracies unless a sufficiently large model is used, which greatly increases the computational cost. To solve this problem, we develop a new approach by combining the spectral-element method with the mapped infinite-element method. In this approach, we still use a truncated model domain, but add a single outer layer of infinite elements. While the spectral elements capture the domain, the infinite elements capture the far-field boundary conditions. The additional computational cost due to the extra layer of infinite elements is insignificant. Numerical integration is performed via Gauss-Legendre-Lobatto and Gauss-Radau quadrature in the spectral and infinite elements, respectively. We implement an equivalent moment-density tensor approach and a split-node approach for the earthquake source, and discuss the advantages of each method. For postearthquake deformation, we implement a general Maxwell rheology using a second-order accurate and unconditionally stable recurrence algorithm. We benchmark our results with the Okada analytical solutions for coseismic deformation, and with the Savage & Prescott analytical solution and the PyLith finite-element code for postearthquake deformation.〈/span〉