# Taras Gerya: Catalogue data in Autumn Semester 2016

Name | Prof. Dr. Taras Gerya |

Field | Geodynamics and analytical and numerical modelling of geological and planetary processes |

Address | Institut für Geophysik ETH Zürich, NO H 9.2 Sonneggstrasse 5 8092 Zürich SWITZERLAND |

Telephone | +41 44 633 66 23 |

Fax | +41 44 633 10 65 |

taras.gerya@erdw.ethz.ch | |

URL | http://jupiter.ethz.ch/~tgerya/ |

Department | Earth Sciences |

Relationship | Adjunct Professor and Privatdozent |

Number | Title | ECTS | Hours | Lecturers | |
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651-1617-00L | Geophysical Fluid Dynamics and Numerical Modelling Seminar | 0 credits | 1S | P. Tackley, M. D. Ballmer, T. Gerya, D. A. May | |

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651-3050-AAL | Fundamentals of GeophysicsEnrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 6 credits | 13R | P. Tackley, T. Gerya | |

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651-3521-AAL | TectonicsEnrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 3 credits | 6R | T. Gerya, E. Kissling | |

Abstract | Comprehensive understanding of role and evolution of oceanic and continental lithosphere in global plate tectonics and evolution of earth. Understanding principles of theoretical and experimental geothermics and fundamentals of mantle and lithosphere rheologies. | ||||

Objective | Comprehensive understanding of role and evolution of oceanic and continental lithosphere in global plate tectonics and evolution of earth. Understanding principles of theoretical and experimental geothermics and fundamentals of mantle and lithosphere rheologies. | ||||

Content | Concept of lithosphere-asthenosphere system in plate tectonics. Physics, chemistry, and rheology of crust and uppermost mantle. Thermal, chemical, and mechanical evolution and destruction/subduction of oceanic lithosphere and evolution of continents. Continental growth, example Europe. Fundamentals of rheology and geothermics of the mantle-lithosphere-crust system. | ||||

Lecture notes | Detailed scriptum in digital form and additional learning moduls (www.lead.ethz.ch) available on intranet. | ||||

Literature | see list in scriptum. | ||||

Prerequisites / Notice | PPT-files of each lecture may be played back for rehearsal on www.lead.ethz.ch. | ||||

651-4007-00L | Continuum Mechanics | 3 credits | 2V | T. Gerya | |

Abstract | In this course, students learn crucial partial differential equations (conservation laws) that are applicable to any continuum including the Earth's mantle, core, atmosphere and ocean. The course will provide step-by-step introduction into the mathematical structure, physical meaning and analytical solutions of the equations. The course has a particular focus on solid Earth applications. | ||||

Objective | The goal of this course is to learn and understand few principal partial differential equations (conservation laws) that are applicable for analysing and modelling of any continuum including the Earth's mantle, core, atmosphere and ocean. By the end of the course, students should be able to write, explain and analyse the equations and apply them for simple analytical cases. Numerical solving of these equations will be discussed in the Numerical Modelling I and II course running in parallel. | ||||

Content | A provisional week-by-week schedule (subject to change) is as follows: Week 1: The continuity equation Theory: Definition of a geological media as a continuum. Field variables used for the representation of a continuum.Methods for definition of the field variables. Eulerian and Lagrangian points of view. Continuity equation in Eulerian and Lagrangian forms and their derivation. Advective transport term. Continuity equation for an incompressible fluid. Exercise: Computing the divergence of velocity field. Week 2: Density and gravity Theory: Density of rocks and minerals. Thermal expansion and compressibility. Dependence of density on pressure and temperature. Equations of state. Poisson equation for gravitational potential and its derivation. Exercise: Computing density, thermal expansion and compressibility from an equation of state. Week 3: Stress and strain Theory: Deformation and stresses. Definition of stress, strain and strain-rate tensors. Deviatoric stresses. Mean stress as a dynamic (nonlithostatic) pressure. Stress and strain rate invariants. Exercise: Analysing strain rate tensor for solid body rotation. Week 4: The momentum equation Theory: Momentum equation. Viscosity and Newtonian law of viscous friction. Navier-–Stokes equation for the motion of a viscous fluid. Stokes equation of slow laminar flow of highly viscous incompressible fluid and its application to geodynamics. Simplification of the Stokes equation in case of constant viscosity and its relation to the Poisson equation. Exercises: Computing velocity for magma flow in a channel. Week 5: Viscous rheology of rocks Theory: Solid-state creep of minerals and rocks as themajor mechanism of deformation of the Earth’s interior. Dislocation and diffusion creep mechanisms. Rheological equations for minerals and rocks. Effective viscosity and its dependence on temperature, pressure and strain rate. Formulation of the effective viscosity from empirical flow laws. Exercise: Deriving viscous rheological equations for computing effective viscosities from empirical flow laws. Week 6: The heat conservation equation Theory: Fourier’s law of heat conduction. Heat conservation equation and its derivation. Radioactive, viscous and adiabatic heating and their relative importance. Heat conservation equation for the case of a constant thermal conductivity and its relation to the Poisson equation. Exercise: steady temperature profile in case of channel flow. Week 7: Elasticity and plasticity Theory: Elastic rheology. Maxwell viscoelastic rheology. Plastic rheology. Plastic yielding criterion. Plastic flow potential. Plastic flow rule. GRADING will be based on honeworks (30%) and oral exams (70%). Exam questions: http://www.erdw.ethz.ch/people/geophysics/tgerya/EXAM_QUESTIONS | ||||

Lecture notes | Script is available by request to taras.gerya@erdw.ethz.ch Exam questions: http://www.erdw.ethz.ch/people/geophysics/tgerya/EXAM_QUESTIONS | ||||

Literature | Taras Gerya Introduction to Numerical Geodynamic Modelling Cambridge University Press, 2010 | ||||

651-4241-00L | Numerical Modelling I and II: Theory and Applications | 6 credits | 4G | T. Gerya | |

Abstract | In this 13-week sequence, students learn how to write programs from scratch to solve partial differential equations that are useful for Earth science applications. Programming will be done in MATLAB and will use the finite-difference method and marker-in-cell technique. The course will emphasise a hands-on learning approach rather than extensive theory. | ||||

Objective | The goal of this course is for students to learn how to program numerical applications from scratch. By the end of the course, students should be able to write state-of-the-art MATLAB codes that solve systems of partial-differential equations relevant to Earth and Planetary Science applications using finite-difference method and marker-in-cell technique. Applications include Poisson equation, buoyancy driven variable viscosity flow, heat diffusion and advection, and state-of-the-art thermomechanical code programming. The emphasis will be on commonality, i.e., using a similar approach to solve different applications, and modularity, i.e., re-use of code in different programs. The course will emphasise a hands-on learning approach rather than extensive theory, and will begin with an introduction to programming in MATLAB. | ||||

Content | A provisional week-by-week schedule (subject to change) is as follows: Week 1: Introduction to the finite difference approximation to differential equations. Introduction to programming in Matlab. Solving of 1D Poisson equation. Week 2: Direct and iterative methods for obtaining numerical solutions. Solving of 2D Poisson equation with direct method. Solving of 2D Poisson equation with Gauss-Seidel and Jacobi iterative methods. Week 3: Solving momentum and continuity equations in case of constant viscosity with stream function/vorticity formulation. Weeks 4: Staggered grid for formulating momentum and continuity equations. Indexing of unknowns. Solving momentum and continuity equations in case of constant viscosity using pressure-velocity formulation with staggered grid. Weeks 5: Conservative finite differences for the momentum equation. "Free slip" and "no slip" boundary conditions. Solving momentum and continuity equations in case of variable viscosity using pressure-velocity formulation with staggered grid. Week 6: Advection in 1-D. Eulerian methods. Marker-in-cell method. Comparison of different advection methods and their accuracy. Week 7: Advection in 2-D with Marker-in-cell method. Combining flow calculation and advection for buoyancy driven flow. Week 8: "Free surface" boundary condition and "sticky air" approach. Free surface stabilization. Runge-Kutta schemes. Week 9: Solving 2D heat conservation equation in case of constant thermal conductivity with explicit and implicit approaches. Week 10: Solving 2D heat conservation equation in case of variable thermal conductivity with implicit approach. Temperature advection with markers. Creating thermomechanical code by combining mechanical solution for 2D buoyancy driven flow with heat diffusion and advection based on marker-in-cell approach. Week 11: Subgrid diffusion of temperature. Implementing subgrid diffusion to the thermomechanical code. Week 12: Implementation of radioactive, adiabatic and shear heating to the thermomechanical code. Week 13: Implementation of temperature-, pressure- and strain rate-dependent viscosity, temperature- and pressure-dependent density and temperature-dependent thermal conductivity to the thermomechanical code. Final project description. GRADING will be based on weekly programming homeworks (50%) and a term project (50%) to develop an application of their choice to a more advanced level. | ||||

Literature | Taras Gerya, Introduction to Numerical Geodynamic Modelling, Cambridge University Press 2010 |