School of GeoSciences

School of GeoSciences

Inverse Theory

Inverse theory is a field of mathematics that aims to solve problems in which we wish to use data to constrain a model when we only know how to predict data given the model. There are many examples of such Inverse Problems, and my research has focused around:

  • Neural network methods to perform probabilistic, Bayesian inversions (Devilee et al., 1999; current work with Ueli Meier)
  • Optimal model parameterisations given a particular data set (Curtis and Snieder, 1997)
  • New types of a priori information and new methods to analyse such (Curtis and Lomax, 2001; Curtis and Wood, 2004a,b; Wood and Curtis, 2004)
  • Nonlinear inverse problems (Girard and Curtis, 1999; Curtis and Lomax, 2001; Curtis and Snieder, 2002; current work with Philip Stark)
  • Applying inverse theory to industrial seismic or earthquake seismological problems in order to infer the structure and properties of the Earth's subsurface (references on my main web page)

Below I list some relevant references from my work in this area. I have also developed new survey and experimental design methods that are all based on inverse theory. Finally, I have made a first step to introduce Elicitation Theory to Geoscience (the theory of how best to ask experts for information that will be used as prior information to condition inversions - a field that lies between statistics and cognitive psychology).

Relevant References

Books: Papers in refereed journals:
  • A. Curtis and R. Wood 2004b. Optimal elicitation of prior information from experts. In, Geological Prior Information, A. Curtis and R. Wood ed's. Geol. Soc. Lond. Special Publication 239. (PDF)
  • R. Wood and A. Curtis 2004. Geological prior information, and its applications to solving geoscientific problems. In, Geological Prior Information, A. Curtis and R. Wood ed's. Geol. Soc. Lond. Special Publication 239, 1-14. (PDF)
  • A. Curtis and R. Snieder 2002. Probing the Earth's interior with seismic tomography. Chapter 52 , International Handbook of Earthquake and Engineering Seismology, Part A. William H. K. Lee, Hiroo Kanamori, Paul C. Jennings and Carl Kisslinger, edís. Academic Press pub. Vol. 81A in Int. Geophys. Series, pp. 861-874. (Paper_PDF, Colour_Plate_1_PDF, Colour_Plate_2_PDF)
  • A. Curtis and A. Lomax, 2001. Prior information, sampling distributions and the curse of dimensionality. Geophysics, 66, 372-378, 2001. (PDF)
  • A. Girard and A. Curtis, 1999. Assessing the complexity of multi-dimensional misfit functions. Schlumberger Scientific Report (public).
  • R. Devilee, A. Curtis and K. Roy-Chowdhurry, 1999. An efficient, probabilistic, neural network approach to solving inverse problems: Inverting surface wave velocities for eurasian crustal thickness. J. Geophys. Res., 104 No. B12, pp. 28,841-28,856. (PDF)
  • A. Curtis and R. Snieder, 1997. Reconditioning inverse problems using the genetic algorithm and revised parameterisation. Geophysics, 62, No. 5, pp. 1,524-1,532. (PDF)