eciraci / menke-geophysical_data_analysis-1

iPython notebook transcription/translation(s) by chapter of William Menke's "Geophysical Data Analysis: Discrete Inverse Theory"

Geophysical Data Analysis: Discrete Inverse Theory

William Menke

Third Edition
Transcribed and translated (from Matlab to Python) by Joshua Poirier

Purpose

The purpose of this repository is solely for personal development and is intended strictly as a remote copy of the version controlled repository. All material is credited to William Menke's 2012 Third Edition of "Geophysical Data Analysis: Discrete Inverse Theory (Matlab Edition)" and its publisher Academic Press. The data contained in this repository was originally downloaded from the books companion website here, along with PowerPoint presentations of related lecture material, and Matlab code.

NOTE: Much of the LaTeX is not properly rendered/formatted by GitHub. Locally, it all looks good for me.

Repository Description

This repository differs from the book in that the Matlab code has been translated to Python, intermingling with a subset of the books text via iPython Notebooks.

• \data

  • These are the related data files used by the notebooks

• \nb

  • ch00.ipynb Introduction

    • I.3 A very quick Python tutorial
    • I.4 Review of vectors and matrices and their representation
    • I.5 Useful Python operations

  • ch01.ipynb Describing inverse problems

    • 1.1 Formulating inverse problems
    • 1.2 The linear inverse problem
    • 1.3 Examples of formulating inverse problems

  • ch02.ipynb Some comments on probability theory

    • 2.1 Noise and random variables
    • 2.2 Correlated data
    • 2.3 Functions of random variables
    • 2.4 Gaussian probability density functions
    • 2.5 Testing the assumption of Gaussian statistics
    • 2.6 Conditional probability density functions
    • 2.7 Confidence intervals
    • 2.8 Computing realizations of random variables

  • ch03.ipynb Solution of the linear, Gaussian inverse problem, Viewpoint 1: The length method

    • 3.1 The lengths of estimates
    • 3.2 Measures of length
    • 3.3 Least squares for a straight line
    • 3.4 The least squares solution of the linear inverse problem
    • 3.5 Some examples
      • 3.5.1 The straight line problem
        • Using simulated data
      • 3.5.2 Fitting a parabola
        • Kepler's Third Law - The cube of the orbital radius of a planet equals the square of its orbital period
      • 3.5.3 Fitting a plane surface
        • Fitting a geologic fault planar surface using earthquake's along Kurile subduction zone
    • 3.6 The existence of the least squares solution
      • 3.6.1 Underdetermined problems
      • 3.6.2 Even-determined problems
      • 3.6.3 Overdetermined problems
    • 3.7 The purely underdetermined problem
    • 3.8 Mixed-determined problems
    • 3.9 Weighted measures of length as a type of a priori information
      • 3.9.1 Weighted least squares
      • 3.9.2 Weighted minimum length
      • 3.9.3 Weighted damped least squares
    • 3.10 Other types of a priori information
      • 3.10.1 Example: Constrained fitting of a straight line
    • 3.11 The variance of the model parameter estimates
    • 3.12 Variance and prediction error of the least squares solution

  • ch04.ipynb Solution of the linear, Gaussian inverse problem, Viewpoint 2: Generalized inverses

    • 4.1 Solutions versus operators
    • 4.2 The data resolution matrix
    • 4.3 The model resolution matrix
    • 4.4 The unit covariance matrix
    • 4.5 Resolution and covariance of some generalized inverses
    • 4.6 Measures of goodness of resolution and covariance
    • 4.7 Generalized inverses with good resolution and covariance
      • 4.7.1 Overdetermined case
      • 4.7.2 Underdetermined case
      • 4.7.3 The general case with Dirichlet spread functions
    • 4.8 Sidelobes and the Backus-Gilbert spread function
    • 4.9 The Backus-Gilbert generalized inverse for the underdetermined problem
    • 4.10 Including the covariance size
    • 4.11 The trade-off of resolution and variance
    • 4.12 Techniques for computing resolution

  • ch05.ipynb Solution of the linear, Gaussian inverse problem, Viewpoint 3: Maximum likelihood methods

    • 5.1 The mean of a group of measurements