Mathematical and Numerical Methods in solid Earth Physics

• explain the concepts tensor, tension, deformation, external forces, constitutive relationships
• explain fundamental concepts in connection with interpolation, projection, including kriging, simulation, semi-variogram, correlation, area/distance/angle conservation
• solve simple linear and non-linear inverse problems in 1D and 2D
• solve problems regarding static pressure and stress conditions, flow phenomena in the ocean and in the earth
• solve problems regarding plastic flow in ice caps and flow in porous media
• solve problems concerning transformations between geodetic coordinate systems (ITRF, EUREF)
• analyze time series and calculate the corresponding uncertainty
• program in Matlab and compile complex code to solve numerical integration in connection with geophysical problems
• use Matlab to construct animations/videos in connection with the dissemination of geophysical problems.

Introduction to Cartesian tensors, stress, strain, volume forces, deformation, and rotation. Advanced programming in Matlab. Introduction to numerical methods for projection and transformations with distance, area and/or angle conservation. Introduction to linear and non-linear inverse problems in 1D and 2D. Analysis of time series and uncertainty and interpolation in 1D g 2D using kriging. Examples of equations of motion and conservation of mass/flux. Examples of applications: Hydrostatic pressure, elasticity, viscous flow (earth mantle), ice flow, turbulence, and laminar flow. Introduction to geodetic coordination systems and transformation between them by Helmert transformation, including ITRF, EUREF. Introduction to Euler rotation, plate motion, and post-glacial rebound.

01035/30140/30141/30142/30130/30131, Basic programming skills in Matlab are important.

Lectures and exercises.