Summer Semester -

Recent advances in imaging Earth -

2014-12-07T19:17:53+00:00

The fundamental components of inverse theory in the solid earth are (i) spectral perturbation, (ii) the geodesic $X$-ray transform, (iii)the generalized Radon transform - tied to reflection tomography, and (iv) the wave-equation analogues of (ii)-(iii). Inverse surface-wave scattering yields a modification of (iii)-to-(iv). Receiver functions can be derived from (iii) & (iv). Surface-wave tomography can be derived from (i).

The goal of this course is to provide an overview of approaches -associated with time reversal - to imaging the materials properties and processes (under (iii)-(iv)). We focus on reverse-time migration
(RTM), the new notion of array receiver functions, and finite-frequency reflection tomography. Applications pertain to the crust, the transition zone and the lowermost mantle. The course will consist of 15 hours of lectures and an oral exam, in 6 days.

course material: www.math.purdue.edu/~mdehoop/10_topics

day 1

SESSION 1: introduction to imaging and inverse scattering
- an incident plane wave [ 3 hours]

day 2

SESSION 2: reciprocity, time reversal [ 2 hours]

backpropagation

day 2/3

SESSION 3: RTM acoustic [ 4 hours]

adjoint state method and waveform inversion

introduction to fast wave-packet/curvelet migration

day 4

SESSION 4: extended imaging, reflection tomography [ 3 hours]

artifacts and resolution

day 5

SESSION 5: RTM elastic, anisotropy [ 3 hours]

array receiver functions

day 6

SESSION 6: imaging via noise blending [ 1 hour ]

ORAL EXAM (material: SESSIONS 1-5) [ 2 hours]

Maarten V. de Hoop
Geo-Mathematical Imaging Group
Purdue University, West Lafayette IN 47907, USA

Computational Seismology: Theory and Practice

2014-12-07T19:17:53+00:00

1st day:
Introduction to geomechanical boundary value problems (3 hrs.)
2nd day:
The dislocation model and quantitative seismology (3 hrs.)
3rd day:
Computation of earthquake’s elastic deformation (2 hrs.)
Introduction to the software EDCMP for interpreting coseismic
surface deformation derived from GPS and InSAR data (1 hr.)
4th day:
Computation of viscoelastic deformation (2 hrs.)
Introduction to the software PSGRN/PSCMP with application
to the 2004 Mw = 9.3 Sumatra-Andaman earthquake (1 hr.)
5th day:
Seismic wave propagation and synthetic seismograms (2 hrs.)
Introduction to the software QSEIS (1 hr.)
6th day:
Exercises with any above tools selected by students themself (3 hrs.)
7th day:
Student reports (2 hrs.)

Modern Topics in Computational Geodynamics

2014-12-07T19:17:53+00:00

First day
Overview of Geodynamics today ( one hour )
Global Earth Structure ( 1.5 hour )
Second day
Mantle Viscosity Structures ( from geophysical inferences) ( one hour )
Mantle Rheology ( different creep mechanisms ) ( 1.5 hour )
Third day
Thermal Conductivity ( one hour )
Equation of state and mantle phase transitions ( 1.5 hour )
Fourth day
Introduction to nonlinear systems ( one hour )
Nonlinear Systems and Feedback ( two hours )
Fifth Day
Introduction to equations of ( one hour )
Mantle convection: various levels of approximation ( two hours )
Sixth Day
Numerical methods in mantle ( one hour )
Numerical Results in mantle convection ( slabs upper-mantle plumes, superplumes ) ( two hours )
seventh day
visualization and post-processing ( one hour )
large-scale computing in geophysics ( two hours )
eighth day
student oral exams ( three hours )

Reference
Karato, S., The Dynamic Structure of the Deep Earth, Princeton
University Press, 2003.
Schubert, G., Turcotte, D.L. and P. L. Olson, Mantle Convection,
Cambridge Univ. Press, 2001.
Cohen R., E., Ed., High-Performance Computing Requirements for
the Computational Solid Earth Sciences, 96 pp, 2005
http://www.geo-prose.com/computational_SES.html
Hansen C.D. and C.R. Johnson ( Eds )., The Visualization Handbook,
962 pp., Elsevier Press, Amsterdam , Holland, 2005.
Yuen, D.A., Maruyama, S., Karato, S.-I. and B.J. Windley, Superplumes: Beyond Plate Tectonics, Springer Verlag, 2007.

David A. Yuen

Rock Mechanics Applied to Earthquake and Reservoir

2014-12-07T19:17:53+00:00

This course will present a comprehensive review of recent advances in the laboratory investigation of brittle fracture, frictional strength and stick-slip instability, brittle-ductile transition, and permeability evolution in crustal rocks. Fundamentals of theoretical concepts in elastic fracture mechanics, poroelasticity, critical state and cap models of rock plasticity, bifurcation analysis of strain localization, as well as rate- and state-dependent friction constitutive models will be introduced. These concepts provide the overall framework for the phenomenological interpretation and micromechanical analysis of the rock physics data. The tectonic and reservoir applications of these concepts and data are illustrated by selected applications, including the representation of seismic source, mechanics of earthquake rupture, borehole instability, reservoir compaction, and geologic sequestration of carbon dioxide.

Teng-fong WONG
Present Position: Professor of Geophysics
Department of Geosciences
State University of New York at Stony Brook
Stony Brook, N.Y. 11794-2100

Solving partial differential equations with PGI CUDA Fortran

2014-12-07T19:17:53+00:00

(1) Introduction to NVIDIA hardware and CUDA architecture

Multiprocessors and memory hierarchy. Kernel, threads, blocks and grids, warps. Compute-capability features and limits, floating-point arithmetic, memory coalescing. Stream management.

(2) Introduction to PGI CUDA Fortran and PGI accelerator

Why Fortran, why CUDA Fortran. Hierarchy of CUDA Fortran, CUDA C and CUDA Runtime API. A CUDA Fortran source-code template. Kernel and device subroutines. Configuring kernel calls. Device, shared, constant and pinned memory declaration. Synchronization of threads. An alternative to CUDA Fortran: PGI accelerator directives.

(3) Linear algebra and interpolation

Compute- and memory-bound kernels. Simple linear algebra with CUDA Fortran and CULA library. Direct and iterative methods for linear algebraic equations. Linear and spline interpolation in one and more dimensions.

(4) Initial-value problems for ordinary differential equations

Runge-Kutta methods. Predictor-corrector methods. Implicit methods. Example of Lorenz-attractor solutions.

(5) Explicit methods for evolutionary partial differential equations

Heat equation in one, two and three dimensions. Spatial discretization: stencils of 2nd- and higher-order finite differences. Block and tiling implementations. Speedups for various compute capabilities.

(6) More methods for more partial differential equations

Fully implicit and Crank-Nicolson schemes. Method od lines. Alternating direction implicit method. Multigrid methods. Wave equation in one and more dimensions.

(7) Technical issues

CUDA-runtime API calls. Asynchronous streams and memory transfers. Pitfalls of inter-block synchronization. Interoperability of Fortran with C and CUDA C kernels. Running on GPU clusters with MPI calls.

Ladislav ( Larry ) Hanyk

Charles University Prague
Faculty of Mathematics and Physics
Department of Geophysics

Normal Mode Relaxation Theory in Solid Earth and Planetary

2014-12-07T19:17:53+00:00

1 Normal mode theory in viscoelasticity.
Rheological models. Momentum an Poisson equation for a spherical, stratified and elastic
Earth’s model. Background density stratification for a self-compressed Earth.
Compressible and incompressible models, generalized Williamson-Adams equation.

2- Momentum and Poisson equations in spherical coordinates. Expansion in spherical harmonics. Spheroidal and toroidal parts.

3 -Development of the radial and tangential components of the differential equations in the radial variable describing the conservation of momentum, for the compressible and incompressible self-gravitating spherical stratified Earth.

4- Solution of the differential momentum and Poisson equations in closed analytical form for the incompressible self-gravitating Earth.

5 - Boundary conditions for the outer surface, for the inner CMB (Core Mantle Boundary), for internal and surface loads and for tidal loading.

5 Implementation of the fundamental matrix in closed analytical form for the incompressible stratified Earth. Propagator technique, from the CMB to the Earth’s surface. Correspondence Principle. Solution in the time domain for the linear viscoelastic Maxwell rheology.

6 Normal modes from Earth’s radial discontinuities in the elastic parameters and density.
Spectrum from compressible versus incompressible models and normal mode classification.

7- MacCullagh formula, perturbation of the moment of inertia from surface and internal loads, Liouville rotational equations.

8 Modelling of present-day J2 changes due to Post Glacial Rebound for a viscoelastic, incompressible Earth, based on analytical solutions and realistic loading history.

9 Polar Wandering on viscoelastic planets

10 Application of viscoelaticity for the modelling of present-day changes of radial and horizontal displacements and gravity perturbation from surface and internal mass redistribution, from earthquakes and comparison with GPS, DInSAR, GRACE and GOCE data.

Prof. Roberto Sabadini
Full Professor
of Solid Earth Geophysics
University of Milano

Parallel scalable scientific computing with PETSc

2014-12-07T19:17:53+00:00

Lecture 1: Introduction to parallel scientific computing
- typical scientific and engineering problems: PDEs & ODEs
- Newton’s method, discretizations and how they lead to large-scale (sparse) linear algebra
- Need for parallelization and different programming models: MPI, shared memory, CUDA
- Different types of hardware and their limitations: memory hierarchy, memory bandwidth
- Parallelization strategies: domain-decomposition (MPI), vectorization (CUDA)

Lecture 2: Introduction to PETSc
- Parallel scalable sparse linear algebra
- Direct methods vs iterative methods
- Linear algebra abstractions and their implementation in PETSc
- Installing PETSc, running examples, getting help
- Who uses PETSc (government research, universities, industry)?
- What machines does PETSc run on (from laptop to largest scalability on ~100K nodes)?

Lecture 3: PETSc design and structure
- PETSc is a platform for experimentation
- Krylov subspace methods (CG, GMRES), need for preconditioning
- Linear and nonlinear PDEs in PETSc
- Time-dependent problems in PETSc
- PETSc interface to other packages (HYPRE, MUMPS,SUNDIALS, BoomerAMG, ...)

Lecture 4. Mesh support in PETSc
- structured and unstructured grids
- mesh partitioning, distribution, load-balancing
- finite-difference and finite-element methods in PETSc
- ghosting, stencils and boundary condition handling

Lectures 5-6. Preconditioning
- Domain-decomposition preconditioners
- Geometric multigrid preconditioners, numerical homogenization
- Matrix-free problems and their preconditioning
- Multiphysics problems, ”physics-based” preconditioning
- JFNK(S) paradigm [Jacobian-free Newton-Krylov (Schwarz)]
- Grid sequencing, ”preconditioning” nonlinear problems
- Nonlinear hydrostatic ice model (due to Jed Brown): achieving textbook MG scaling

Lecture 7. Advanced topics
- GPU support in PETSc: CUDA, CUSP&THRUST
- Advanced time-stepping algorithms
- Symplectic and multi-symplectic integrators in PETSc

Dmitry Karpeev
September 2010
Mathematics and Computer Science Division Argonne National Laboratory

Thermal Processes in the Solid Earth

2014-12-07T19:17:53+00:00

Heat transfer plays a major role in most geological processes. This course introduces 1) The basic theory of heat transfer, 2) Thermal structures of the Earth, and 3) heat transfer in selected geological process. The first two parts are lectures with home works. The last part involves both lectures and discussion of papers.
PART I. BASICS OF HEAT TRANSFER
(15 hrs)

1. Introduction
• Overview: heat transfer in geological processes
• Basic concepts: temperature, heat, energy
• Heat transfer and thermodynamics
• Mechanism of heat transfer: conduction, convection, and radiation
• Heat flu and heat flux
• Conservation of mass, momentum, and energy
• Methods of studying heat transfer

2. Heat Conduction
• Fourier’s law and rate equation
• The heat diffusion equation
• Boundary and initial conditions
• One-Dimensional, steady-state conduction
• Two-Dimensional, steady-state conduction
• Transient conduction

3. Heat Advection and Convection:
• Advection, convection, and boundary layers
• The convection transfer equations
• Boundary layer similarity and dimensionless numbers

PART II. THERMAL STATE OF THE EARTH
(15 hrs)

4. Earth as a heat engine
• Earth’s thermal history and internal heat sources
• Heat flux measurements and energy budget of Earth
• Earth’s internal thermal structure
• Heat transfer and plate tectonics

5. Oceanic Lithosphere
• Thermal evolution of oceanic plates
• Ocean floor topography
• Hotspot and other thermal perturbations

6. Continental Lithosphere:
• Heat flow and heat sources
• Steady-state geotherms
• Thermal effects of tectonic processes
o crustal thickening
o underplating
o delamination
o lithospheric extension

7. Mantle Convection
• Driving mechanisms and convection patterns
• Mantle convection and plate tectonics
• Approaches of studying mantle convection
• Numerical simulations
• Geophysical observational constraints

PART III. APPLICATIONS
(11 hrs)

8. Magmatic intrusions
• Cooling of lava flow
• Thermal consequences of magma intrusion
• Contact metamorphism
• Analytical and numerical solutions

9. Thrusting belts
• Thermal processes associated with crustal thickening and thinning
• Mantle thermal perturbations
• PTt paths
• Heat sources for anatexis

10. Extension and basin formation
• Tectonic models and thermal consequences of basin formation,
• Lateral heat transfer in basins
• Thermal advection by fluid flow

11. Environmental problems
• Record of climate change in temperature profiles
• Ice sheet and glaciers

Other topics can be added if there are enough interests.

PART I. BASICS OF HEAT TRANSFER
(15 hrs)

1. Introduction
• Overview: heat transfer in geological processes
• Basic concepts: temperature, heat, energy
• Heat transfer and thermodynamics
• Mechanism of heat transfer: conduction, convection, and radiation
• Heat flu and heat flux
• Conservation of mass, momentum, and energy
• Methods of studying heat transfer

2. Heat Conduction
• Fourier’s law and rate equation
• The heat diffusion equation
• Boundary and initial conditions
• One-Dimensional, steady-state conduction
• Two-Dimensional, steady-state conduction
• Transient conduction

3. Heat Advection and Convection:
• Advection, convection, and boundary layers
• The convection transfer equations
• Boundary layer similarity and dimensionless numbers

PART II. THERMAL STATE OF THE EARTH
(15 hrs)

4. Earth as a heat engine
• Earth’s thermal history and internal heat sources
• Heat flux measurements and energy budget of Earth
• Earth’s internal thermal structure
• Heat transfer and plate tectonics

5. Oceanic Lithosphere
• Thermal evolution of oceanic plates
• Ocean floor topography
• Hotspot and other thermal perturbations

6. Continental Lithosphere:
• Heat flow and heat sources
• Steady-state geotherms
• Thermal effects of tectonic processes
o crustal thickening
o underplating
o delamination
o lithospheric extension

7. Mantle Convection
• Driving mechanisms and convection patterns
• Mantle convection and plate tectonics
• Approaches of studying mantle convection
• Numerical simulations
• Geophysical observational constraints

PART III. APPLICATIONS
(11 hrs)

8. Magmatic intrusions
• Cooling of lava flow
• Thermal consequences of magma intrusion
• Contact metamorphism
• Analytical and numerical solutions

9. Thrusting belts
• Thermal processes associated with crustal thickening and thinning
• Mantle thermal perturbations
• PTt paths
• Heat sources for anatexis

10. Extension and basin formation
• Tectonic models and thermal consequences of basin formation,
• Lateral heat transfer in basins
• Thermal advection by fluid flow

11. Environmental problems
• Record of climate change in temperature profiles
• Ice sheet and glaciers

Other topics can be added if there are enough interests.

Environmental and Applied Geophysics

2014-12-07T19:17:53+00:00

Lecture 1: Introduction: An overview of field geophysics
1. Site characterization
2. Types of field geophysical targets: fixed and mobile
2.1. landfills contaminant plumes
2.2. conduits, fractures and voids
2.3. groundwater, aquifer characterization
2.4. buried objects, utility lines, unexploded ordnance (UXO)
2.5. soil stratigraphy, earthquake liquefaction features
2.6. petroleum exploration

Lecture 2: Physical properties of near-surface geological materials
1. Magnetic properties
2. Low frequency electrical properties
3. Archie’s law, Waxman-Smits equation
4. Electrical conductivity and hydraulic conductivity
5. Kozeny-Carman relationship
6. Electrical properties of organically contaminated soils

Lecture 3: 1. Derivation of Maxwell equations from basic physic laws
2. Helmholtz equation
3. Boundary conditions
4. Electromagnetic parameters

Lecture 4: Direct current (DC) Resistivity I
1. Introduction
2. Current flow in inhomogeneous ground
3. Current flow in layered media
4. Schlumberger, Wenner, dipole-dipole, pole-dipole arrays

Lecture 5: Direct current (DC) Resistivity II
1. Field methods: profiling, sounding, instrumentation
2. Data interpretation with examples
3. Case histories: landfill site characterization, fracture mapping

Lecture 6: Geomagnetic Methods
1. Fundamentals of geomagnetic field
2. Soil and rock magnetism
3. Magnetization and buried magnetic targets
4. Magnetic prospecting
5. Field example: buried metals detection

Lecture 7: Electromagnetic Induction I
1. Introduction
2. Basic Theory: laws of Ohm, Ampere and Faraday
3. Direct vs. inductive coupling
4. Frequency domain vs. time domain systems
5. Smoke-ring diffusion
6. Mutual coupling of coils: LR circuit analogy of an EM system
7. Case histories: landfill characterization, brine migration

Lecture 8: Seismic Exploration and Microtremors
1. Principles of seismic exploration
2. Refraction
3. Reflection
4. Surface wave
5. Microtremor

Lecture 9: Ground-penetrating Radar I
1. Introduction
2. EM wave propagation: velocity, attenuation
3. Dielectric properties
4. Loss mechanisms
5. GPR systems
6. Noise, including clutter, ringing, and scattering from inhomogeneities
7. Case histories: soil stratigraphy

Lecture:10 Borehole Geophysics
1. Geophysical well logging
2. Electrical resistance tomography
3. Borehole radar tomography
4. Case history: Borehole radar monitoring saline water transport

The Series of Lectures of Professors of University of Tokyo

2014-12-07T19:17:53+00:00

Structure and Dynamics of the Global Earth and East Asia

Earthquakes and volcanic eruptions are part of the processes of the energy release by the global Earth. To understand the geodynamics, both global and regional scope is indispensable.
In this course, we introduce the most recent knowledge about structure and dynamics of the global Earth and East Asia.
We especially highlight exciting results obtained by dense and advanced observations. Both seismological and geodetic results will be introduced.

Name Nozomu Takeuchi
Sex Male
Date of Birth 7th July, 1969
Nationality Japan
Contact Address Earthquake Research Institute, Univ of Tokyo

Yosuke Aoki
Earthquake Research Institute, University of Tokyo
BIRTH: 1 December, 1973, Yokohama, Japan; Male
NATIONALITY: Japanese citizen
MARITAL STATUS: Married, two daughters (born in 2003 and 2005) and one son (born in 2007)
PRESENT POSITION: Assistant Professor
EDUCATION:
University of Tokyo (Ph.D., 2001; M.S., 1998; B.S., 1996, in Geophysics)
RESEARCH APPOINTMENTS:
Earthquake Research Institute, University of Tokyo