Resources / Software:  
Technical Background Documents

Technical information about the mathematics and methodologies developed at the UBC-GIF can be found in peer reviewed scientific literature (see publications) and in manuals for the modelling and inversion software. The following list is a subset of the complete documentation list to be found the menu for this website. These are not tutorials - they are technical descriptions of methodology and theory.

Topic Source - all are in PDF format
2D DC resistivity and Induced Polarization Chapter 1 of the DCIP2D manual:
  a. Introduction
  b. Forward Modelling
  c. General Methodology for inverting DC and IP data
  d. Inversion of DC Resistivity Data
  e. Inversion of IP Data
  f. References
3D DC resistivity and Induced Polarization Chapter 1 of the DCIP3D manual:
    1.2. Forward Modelling
    1.3. General Methodology for inverting DC & IP data
    1.4. Inversion of DC Resistivity Data
    1.5. Inversion of IP Data
    1.6. Compression of Sensitivity Matrix
    1.7. References
3D magnetics Chapter 1 of the MAG3D manual:
   b. Forward Modelling
   c. Inversion Methodology
   d. Depth Weighting
   e. Wavelet Compression of Sensitivity
   f. Choice of Tradeoff Parameter
   g. Example of Inversion
   h. References
3D gravity Chapter 1 of the GRAV3D manual:
  1.2 Forward Modelling
  1.3 Inversion Methodology
  1.4 Depth Weighting
  1.5 Wavelet Compression of Sensitivity Matrix
  1.6 Choice of Regularization Parameter
  1.7 Example Inversion
  1.8 References
1D frequency domain electromagnetics EM1DFM technical background (PDF):
1. Program EM1DFM: An Overview
2. Theoretical Background
  2.1 Electromagnetic loop-loop data
  2.2 The Earth model
  2.3 Forward modelling
  2.4 Computing the sensitivities
  2.5 The inversion algorithms
    2.5.1 General formulation
    2.5.2 Algorithm 1: fixed trade-off parameter
    2.5.3 Algorithm 2: discrepancy principle
    2.5.4 Algorithm 3: GCV criterion
    2.5.5 Algorithm 4: L-curve criterion
    2.5.6 Relative weighting within the model norm
    2.5.7 Positivity of susceptibility
    2.5.8 Convergence criteria
3. References
1D time domain
electromagnetics
EM1DTM technical background (PDF):
1. Program EM1DTM: An Overview
2. Theoretical Background
  2.1 The observations
  2.2 The Earth model
  2.3 Forward modelling
  2.4 Frequency- to time-domain transformation
  2.5 Computing the sensitivities
  2.6 The inversion algorithms
    2.6.1 General formulation
    2.6.2 General measures
    2.6.3 General algorithm
    2.6.4 Algorithm 1: fixed trade-off parameter
    2.6.5 Algorithm 2: discrepancy principle
    2.6.6 Algorithm 3: GCV criterion
    2.6.7 Algorithm 4: L-curve criterion
    2.6.8 Convergence criteria
  3. References
 

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