Lutz Gross

Analysis of slip-weakening frictional laws with static restrengthening and their implications on the scaling, asymmetry, and mode of dynamic rupture on homogeneous and bimaterial interfaces

Dynamic simulations of homogeneous, heterogeneous and bimaterial fault rupture using modified slip-weakening frictional laws with static restrengthening are presented giving rise to both crack-like and pulse-like rupture. We demonstrate that pulse-like rupture is possible by making a modification of classical slip-weakening friction to include static restrengthening. We employ various slip-weakening frictional laws to examine their effect on the resulting earthquake rupture speed, size and mode. More complex rupture characteristics were produced with more strongly slip-weakening frictional laws, and the degree of slip-weakening had to be finely tuned to reproduce realistic earthquake rupture characteristics. Rupture propagation on a fault is controlled by the constitutive properties of the fault. We provide benchmark tests of our method against other reported solutions in the literature. We demonstrate the applicability of our elastoplastic fault model for modeling dynamic rupture and wave propagation in fault systems, and the rich array of dynamic properties produced by our elastoplastic finite element fault model. These are governed by a number of model parameters including: the spatial heterogeneity and material contrast across the fault, the fault strength, and not least of all the frictional law employed. Asymmetric bilateral fault rupture was produced for the bimaterial case, where the degree of material contrast influenced the rupture speed in the different propagation directions.

PDE-based geophysical modelling using finite elements: examples from 3D resistivity and 2D magnetotellurics

We present a general finite-element solver, escript, tailored to solve geophysical forward and inverse modeling problems in terms of partial differential equations (PDEs) with suitable boundary conditions. Escripts abstract interface allows geoscientists to focus on solving the actual problem without being experts in numerical modeling. General-purpose finite element solvers have found wide use especially in engineering fields and find increasing application in the geophysical disciplines as these offer a single interface to tackle different geophysical problems. These solvers are useful for data interpretation and for research, but can also be a useful tool in educational settings. This paper serves as an introduction into PDE-based modeling with escript where we demonstrate in detail how escript is used to solve two different forward modeling problems from applied geophysics (3D DC resistivity and 2D magnetotellurics). Based on these two different cases, other geophysical modeling work can easily be realized. The escript package is implemented as a Python library and allows the solution of coupled, linear or non-linear, time-dependent PDEs. Parallel execution for both shared and distributed memory architectures is supported and can be used without modifications to the scripts.

A python module for PDE-Based numerical modelling

The escript package is an extension of python. It provides an easy-to-use programming environment for numerical simulations based on the solution of partial differential equations (PDEs), while at the same time providing for fast solution of large models by performing time-intensive calculations in C++ and C. The escript functionality allows the user to implement high-level numerical schemes to reduce coupled, nonlinear, time-dependent PDEs to linear, steady PDEs that have to be solved in each time and/or iteration step. The PDEs are then solved by our finley PDE solver library. The layer of abstraction provided by escript allows an implementation which is independent from particular discretization schemes, PDE solver libraries, their data structures, and the computing platform itself. In the paper we will briefly outline the basic concepts of escript, illustrate its usage for modelling seismic wave propagation and discuss some parallelization issues with OpenMP and MPI.

Numerical investigations on mapping permeability heterogeneity in coal seam gas reservoirs using seismo-electric methods

Mapping the horizontal distribution of permeability is a key problem for the coal seam gas industry. Poststack seismic data with anisotropy attributes provide estimates for fracture density and orientation which are then interpreted in terms of permeability. This approach delivers an indirect measure of permeability and can fail if other sources of anisotropy (for instance stress) come into play. Seismo-electric methods, based on recording the electric signal from pore fluid movements stimulated through a seismic wave, measure permeability directly. In this paper we use numerical simulations to demonstrate that the seismo-electric method is potentially suitable to map the horizontal distribution of permeability changes across coal seams. We propose the use of an amplitude to offset (AVO) analysis of the electrical signal in combination with poststack seismic data collected during the exploration phase. Recording of electrical signals from a simple seismic source can be closer to production planning and operations. The numerical model is based on a sonic wave propagation model under the low frequency, saturated media assumption and uses a coupled high order spectral element and low order finite element solver. We investigate the impact of seam thickness, coal seam layering, layering in the overburden and horizontal heterogeneity of permeability.

A progressive analysis of matrix cracking-induced delamination in composite laminates using an advanced phantom node method

Matrix cracking-induced delamination in composite laminates is qualitatively and quantitatively investigated in a finite element framework. The phantom node method is extended to incorporate breakable interfaces at transverse matrix crack tips. New user-defined element types in Abaqus improve the numerical stability in a geometrically nonlinear analysis. The new formulation allows for accurate prediction of matrix crack density and stiffness reduction in a number of composite laminates. Furthermore, the advanced phantom node method is able to simulate progressive matrix cracking-induced delamination with good accuracy.

Conforming Finite-Element Methods for Modeling Convection in an Incompressible Rock Matrix

Coupled heat transport and fluid flow in porous rocks play a role in many geological phenomena, including the formation of hydrothermal mineral deposits, the productivity of geothermal reservoirs and the reliability of geo-sequestration. Due to the low compressibility of the fluid and rock matrix and the long-time scales the fluid can be treated as incompressible. The solution of the incompressible Darcy flux problem and the advection-dominated heat transport both provide numerically challenging problems typically addressed using methods specialized for the individual equations. In order to avoid the usage of two different meshes and solution approximations for pressure, flux, and temperature we propose to use standard conforming finite-element methods on the same mesh for both problems. The heat transport equation is solved using a linearized finite-element flux corrected transport scheme which introduces minimum artificial diffusion based on the discretized transport problem. The Darcy flux calculation from pressure uses a global post-processing strategy which at the cost of an extra partial differential equation leads to highly accurate flux approximation. In the limit of zero element size the flux is in fact incompressible. We investigate the numerical performance of our proposed method on a test problem using the parallelized modeling environment escript. We also test the approach to simulate convection in geologically relevant scenarios.

High-Performance Scientific Computing for the Masses: Developing Secure Grid Portals for Scientific Workflows

We present a web-based Grid job submission system which combines open-source software components and available system services freeing developers from having to deal with Grid middleware, credential management and user authentication. Instead, a Short Lived Credential Service provides the necessary user certificates, while Grisu libraries, developed by the Australian Research Collaboration Service, handle Grid-related tasks such as job submission and remote file operations. Thus portal developers can focus on modeling domain-specific workflows and create high-level and easy to use interfaces for scientists who want to run and monitor large simulations. This paper explains the components and demonstrates how we use the system in two submission portals for separate applications.

Orientation of shear bands for a rigid plastic frictional material in simple shear

The orientation of shear bands is investigated analytically and numerically for a rigid plastic frictional material in simple shear. The model is based on co-axial flow rule, incompressible deformations and a friction factor which depends on the strain history. Since we are focussing on geological timescales, the influence of elasticity is neglected. Firstly, a linear stability analysis is performed confirming Rices 1976 assertion [The localization of plastic deformation, in Proceedings of the 14th International Congress on Theoretical and Applied Mechanics, W.T. Koiter, ed., North Holland, Amsterdam, 1976, p.207] that, in the hardening regime, bifurcation is possible at every stage. Orientation of shear bands against the less compressive principal axis lies anywhere between the Roscoe and Coulomb angles, namely between π/4+ψ/2 and π/4 + ϕ/2, where ϕ and ψ are the mobilised angles of friction and dilatancy, respectively (in our study, we assume ψ = 0). The linear stability analysis leaves open the question of which orientation will actually emerge in a boundary value problem that consider all nonlinearities. This question is addressed in a finite element study of simple shear with periodic boundary conditions in the shear direction. Our simulations show temporary inclined shear bands in the hardening regime followed by a persistent horizontal shear band. A sensitivity study with respect to geometric and constitutive parameters indicates that the height of the sample controls the orientation of the inclined shear bands. Finally, we extend our analytical and numerical studies to Cosserat plasticity. It turns out that inclined shear bands are suppressed for large values of the internal length R (narrow bands). The case of a standard continuum is gradually recovered for small R (wide bands).

Numerical Investigation of Melt Segregation Using FEM Coding Environment Escript

Understanding of melt segregation and extraction is one of the major outstanding problems of melting processes in Earths mantle. The volcanoes that lie along the Earths tectonic boundaries are fed by melt that is generated in the mantle. However, it still remains unclear how this melt is extracted and finds its way towards the volcanoes. Two important mechanisms in melt segregation and migration are reactive fluid flow and mechanical shear. Reactive fluid flow describes the formation and segregation/migration of melt significantly affected by chemical interaction between melt and rock. This reactive-infiltration instability results in melt fingering which eases the transition from porous to channelized flow and provides a key element in some of the geological phenomena on earth. The second important mechanism in melt migration is localization due to mechanical shear. Recent studies have shown that when partially molten rock is subjected to simple shear, bands of high and low porosity are formed at a particular angle to the direction of maximum extension. Thus melt distribution is also influenced by stresses in partially molten rock [2,3]. The main aim of this paper is to identify the main mechanisms inducing melt segregation and effective flow. More specifically we investigate the melt reaction instability and melt band formation in this study. Here, in addition to providing a better understanding of melting phenomena in the mantle, we also develop a numerically validated model which can be used as an active and open source for future more complicated studies. For the melt bands problem, we employ the equations of magma migration in viscous materials which was originally derived by McKenzie (1984), and for the fingering instability problem we refer to the well known equations of reactive transport [4]. We write two different numerical codes using the FEM environment “escript”. We test the codes for a set of well-understood case problems which have been studied previously by other researchers.

Coupled Mechanical-Hydrological-Chemical Problems in Elasto-plastic Saturated Soils and Soft Rocks Using escript

The understanding of chemical effects on mechanical behavior of porous media is a key element in the solution of problems in geology, mining, soil, rock and environmental engineering. In order to develop this understanding, the current work employs a new set of equations to numerically investigate the coupled mechanical-hydrological-chemical (MHC) problem for soils and soft rocks. The objectives of this research are to observe the soil and soft rock behavior under mechanical loading and chemical erosion and also to validate the application of our solver algorithm written in a finite element programming environment “escript”.