Geodynamical simulations over the past decades have widely been built on quadrilateral and hexahedral finite elements. For the discretization of the key Stokes equation describing slow, viscous flow, ...most codes use either the unstable Q.sub.1 xP.sub.0 element, a stabilized version of the equal-order Q.sub.1 xQ.sub.1 element, or more recently the stable Taylor-Hood element with continuous (Q.sub.2 xQ.sub.1) or discontinuous (Q2xP-1) pressure. However, it is not clear which of these choices is actually the best at accurately simulating "typical" geodynamic situations.
ASPECT (Advanced Solver for Problems in Earth's ConvecTion) is a massively parallel finite element code originally designed for modeling thermal convection in the mantle with a Newtonian rheology. ...The code is characterized by modern numerical methods, high-performance parallelism and extensibility. This last characteristic is illustrated in this work: we have extended the use of ASPECT from global thermal convection modeling to upper-mantle-scale applications of subduction.Subduction modeling generally requires the tracking of multiple materials with different properties and with nonlinear viscous and viscoplastic rheologies. To this end, we implemented a frictional plasticity criterion that is combined with a viscous diffusion and dislocation creep rheology. Because ASPECT uses compositional fields to represent different materials, all material parameters are made dependent on a user-specified number of fields.The goal of this paper is primarily to describe and verify our implementations of complex, multi-material rheology by reproducing the results of four well-known two-dimensional benchmarks: the indentor benchmark, the brick experiment, the sandbox experiment and the slab detachment benchmark. Furthermore, we aim to provide hands-on examples for prospective users by demonstrating the use of multi-material viscoplasticity with three-dimensional, thermomechanical models of oceanic subduction, putting ASPECT on the map as a community code for high-resolution, nonlinear rheology subduction modeling.
Numerical models are a powerful tool for investigating the dynamic processes in the interior of the Earth and other planets, but the reliability and predictive power of these discretized models ...depends on the numerical method as well as an accurate representation of material properties in space and time. In the specific context of geodynamic models, particle methods have been applied extensively because of their suitability for advection-dominated processes and have been used in applications such as tracking the composition of solid rock and melt in the Earth's mantle, fluids in lithospheric- and crustal-scale models, light elements in the liquid core, and deformation properties like accumulated finite strain or mineral grain size, along with many applications outside the Earth sciences. There have been significant benchmarking efforts to measure the accuracy and convergence behavior of particle methods, but these efforts have largely been limited to instantaneous solutions, or time-dependent models without analytical solutions. As a consequence, there is little understanding about the interplay of particle advection errors and errors introduced in the solution of the underlying transient, nonlinear flow equations. To address these limitations, we present two new dynamic benchmarks for transient Stokes flow with analytical solutions that allow us to quantify the accuracy of various advection methods in nonlinear flow. We use these benchmarks to measure the accuracy of our particle algorithm as implemented in the ASPECT geodynamic modeling software against commonly employed field methods and analytical solutions. In particular, we quantify if an algorithm that is higher-order accurate in time will allow for better overall model accuracy and verify that our algorithm reaches its intended optimal convergence rate. We then document that the observed increased accuracy of higher-order algorithms matters for geodynamic applications with an example of modeling small-scale convection underneath an oceanic plate and show that the predicted place and time of onset of small-scale convection depends significantly on the chosen particle advection method. Descriptions and implementations of our benchmarks are openly available and can be used to verify other advection algorithms. The availability of accurate, scalable, and efficient particle methods as part of the widely used open-source code ASPECT will allow geodynamicists to investigate complex time-dependent geodynamic processes such as elastic deformation, anisotropic fabric development, melt generation and migration, and grain damage.
Geodynamic modelling provides a powerful tool to investigate processes in the Earth's crust, mantle, and core that are not directly observable. However, numerical models are inherently subject to the ...assumptions and simplifications on which they are based. In order to use and review numerical modelling studies appropriately, one needs to be aware of the limitations of geodynamic modelling as well as its advantages. Here, we present a comprehensive yet concise overview of the geodynamic modelling process applied to the solid Earth from the choice of governing equations to numerical methods, model setup, model interpretation, and the eventual communication of the model results. We highlight best practices and discuss their implementations including code verification, model validation, internal consistency checks, and software and data management. Thus, with this perspective, we encourage high-quality modelling studies, fair external interpretation, and sensible use of published work. We provide ample examples, from lithosphere and mantle dynamics specifically, and point out synergies with related fields such as seismology, tectonophysics, geology, mineral physics, planetary science, and geodesy. We clarify and consolidate terminology across geodynamics and numerical modelling to set a standard for clear communication of modelling studies. All in all, this paper presents the basics of geodynamic modelling for first-time and experienced modellers, collaborators, and reviewers from diverse backgrounds to (re)gain a solid understanding of geodynamic modelling as a whole.
Structural restoration is commonly used to assess the deformation of geological structures and to reconstruct past basin geometries. For this, geomechanical restoration considers faults as ...frictionless contact surfaces. To bring more physical behavior and better handle large deformations, we build on a reverse-time Stokes-based method, previously applied to restore salt structures with negative time step advection. We test the applicability of the method to structures including sediments of variable viscosity, faults and non-flat topography. We present a simulation code that uses a combination of arbitrary Lagrangian–Eulerian methods and particle-in-cell methods, and is coupled with adaptive mesh refinement. It is used to apply the reverse-time Stokes-based method on simple two-dimensional geological cross-sections and shows that reasonable restored geometries can be obtained.
The Geodynamic World Builder is an open-source code library intended to set up initial conditions for computational geodynamic models in both Cartesian and spherical geometries. The inputs for the ...JavaScript Object Notation (JSON)-style parameter file are not mathematical but rather a structured nested list describing tectonic features, e.g., a continental, an oceanic or a subducting plate. Each of these tectonic features can be assigned a specific temperature profile (e.g., plate model) or composition label (e.g., uniform). For each point in space, the Geodynamic World Builder can return the composition and/or temperature. It is written in C++ but can be used in almost any language through its C and Fortran wrappers. Various examples of 2-D and 3-D subduction settings are presented. The Geodynamic World Builder comes with an extensive online user manual.
The geotherm in subduction zones is thought to vary as a function of the subduction rate and the age of the subducting lithosphere. Along a single subduction zone the rate of subduction may strongly ...vary due to changes in the angle between the trench and the plate convergence vector, i.e., the subduction obliquity, due to trench curvature. We currently observe such curvature in, e.g., the Marianas, Chile and Aleutian trenches. Recently, strong along-strike variations in subduction obliquity were proposed to have caused a major temperature contrast between Cretaceous geological records of western and central Turkey. We test here whether first-order temperature variation in a subduction zone may be caused by variation in the trench geometry using simple thermo-kinematic finite-element 3-D numerical models. We prescribe the trench geometry by means of a simple mathematical function and compute the mantle flow in the mantle wedge by solving the equation of mass and momentum conservation. We then solve the energy conservation equation until steady state is reached. We analyze the results (i) in terms of mantle wedge flow with emphasis on the trench-parallel component and (ii) in terms of temperature along the plate interface by means of maps and the depth–temperature path at the interface. In our experiments, the effect of the trench curvature on the geotherm is substantial. A small obliquity yields a small but not negligible trench-parallel mantle flow, leading to differences of 30 °C along-strike of the model. Advected heat causes such temperature variations (linked to the magnitude of the trench-parallel component of velocity). With increasing obliquity, the trench-parallel component of the velocity consequently increases and the temperature variation reaches 200 °C along-strike. Finally, we discuss the implication of our simulations for the ubiquitous oblique systems that are observed on Earth and the limitations of our modeling approach. Lateral variations in plate sinking rate associated with curvature will further enhance this temperature contrast. We conclude that the synchronous metamorphic temperature contrast between central and western Turkey may well have resulted from reconstructed major variations in subduction obliquity.
Several alternative gravity forward modelling methodologies and associated numerical codes with their own advantages and limitations are available for the solid Earth community. With upcoming ...state-of-the-art lithosphere density models and accurate global gravity field data sets, it is vital to understand the opportunities and limitations of the various approaches. In this paper, we discuss the four widely used techniques: global spherical harmonics (GSH), tesseroid integration (TESS), triangle integration (TRI), and hexahedral integration (HEX). A constant density shell benchmark shows that all four codes can produce similar precise gravitational potential fields. Two additional shell tests were conducted with more complicated density structures: laterally varying density structures and a crust-mantle interface density. The differences between the four codes were all below 1.5 % of the modelled gravity signal suitable for reproducing satellite-acquired gravity data. TESS and GSH produced the most similar potential fields (<0.3 %).
PDF
