Tutorial Contents

[lheagy]

Tentative outline

• [ ] pre-requisites : installing python (anaconda), git, using the jupyter notebook
• [ ] quick overview of python, numpy, scipy
• [ ] overview of SimPEG framework and gradient based inversions - using a linear problem
• [ ] SimPEG framework (DC resistivity, EM examples throughout)
  • [ ] Mesh class -> how do we construct differential operators
  • [ ] Solving a forward simulation
  • [ ] how do we solve the PDE's to create data
  • [ ] abstracting this into the problem and survey classes
  • [ ] sensitivities (motivated by the inverse problem) - overview of organization of sensitivities (light, based on EM paper)
  • [ ] mappings and chain rule --> What is your model?
  • [ ] stating the inverse problem
  • [ ] data misfit
  • [ ] regularization
  • [ ] statement of the inverse problem
  • [ ] solving the inverse problem
  • [ ] optimization
  • [ ] inversion directives (ie. beta-cooling)
  • [ ] bringing it all together to solve an inverse problem

[lheagy]

Outline

Intro and Purpose

• See readme
• Brief Introduction to Inversions and SimPEG
• Why
  • How do we estimate models from data? and motivation for SimPEG!: including - reproducible inversions
• Framework
• Resources
  • SimPEG
  • Software carpentry
  • Jupyter
  • Microsoft Azure
  • …

There and back again

• A once over forward simulation and inversion
  • Linear problem: tomography?
• Introduces each element of the framework
  • Mesh
  • Defining a problem and survey
  • Data misfit
  • Regularization
  • Tradeoff parameter
  • Optimization
  • Bringing it all together

Pixels and their neighbors

• Overview of finite volume discretization (As per what is already there)

Fields, Fluxes, Physics

• Model to physical properties
• Mappings, eg log conductivity
• Physics and sources
• Solutions to fields
• Fields to data
• Forward simulation sampler

Guess, but first tell me what you know

Defining the inverse problem

• I know the data
  • Plus or minus some noise?
  • Plus or minus the source locations?
• I know the model should be → Mappings
  • Smooth?
  • Compact?
  • A circle?
• Write it down
• Sometimes we have to compromise
  • Choosing beta
• stating the inverse problem
  • data misfit
  • regularization
  • statement of the inverse problem

Stroll - Preferably downhill

• solving the inverse problem
  • optimization
  • inversion directives (ie. beta-cooling)
• bringing it all together to solve an inverse problem
• When do I stop?
• Converging quadratically - use second order methods

Which way is down?

• Need derivatives … of everything
• Chain rules
• How do I know?
  • Magical 2
• Organization → EM picture
• Adjoint

Spices - Embedding knowledge

• Directives,
• Mappings,
• Regularization

Examples

Self contained examples that walk through a problem Each example contains:

• Purpose - what will we accomplish in this walk-through
• Highlights - what are some of the interesting aspects or reasons to work through the example
• Walk through of the example, in particular using headings that align with the SimPEG framework where applicable
• Questions and Extensions - questions for readers to explore, ideas for how this work can be extended.