Survey and Experimental Design
Experimental Design theory (a field of Statistics) spans the set of techniques that allow data sets to be designed that will provide some optimal constraints on a model of interest. The appropriate meaning of 'optimal' depends on the situation, and can include: most robust, minimum variance, minimum bias, etc.
Such techniques have been applied to design laboratory experiments and field-based surveys in the Geosciences. This page contains links to some of the recent work in this field in which I have participated. It contains much work from other co-authors, to all of whome I am indebted.
For those that would like to know more about this field but who have little background other than basic mathematics and geophysics, I have written the following tutorial on Geophysical Survey and Experimental Design (published in The Leading Edge). It also includes examples of most of the advances in theory and applications to which I have contributed.
It is divided into two parts:
- Part A deals with cases where there is an approximately linear relationship between the model to be constrained and the data to be recorded, and
- Part B deals with cases where this relationship is significantly nonlinear.
I recommend reading that tutorial (or the Leading Edge version below) before going on to the other publications listed below, unless you are already familiar with the field.
- Hansruedi Maurer's page: Keep an eye out - Hansruedi and co-workers are always working on something new!
- Partha Routh's page: Again, keep an eye out - Partha and colleagues are developing some neat advances using features of Backus Gilbert averaging kernels as design criteria.
- Anthony Lomax's pages: Anthony has a JAVA applet version of one design algorithm that you can use on-line, in particular to design your own optimal networks for sub-surface event (e.g., earthquake) monitoring. He also has references to the related papers.
- Gijs Vermeer's 3DSymSam pages: Gijs has written a book on methods of industrial seismic survey design, and maintains references to related articles at this page.
If you have, or know of a page that is actively updated with new research or applications in this field, please let me know and I will add it above.
Related papers from the Edinburgh research group:
- D. Polson and A. Curtis, 2010. Dynamics of uncertainty in geological interpretation. Journal of the Geological Society, London, Vol. 167, pp. 5-10. doi: 10.1144/0016-76492009-055. (PDF)
- T. Guest and A. Curtis, 2009. Iteratively constructive sequential design of experiments and surveys with nonlinear parameter-data relationships, J. Geophys. Res., 114, B04307, doi:10.1029/2008JB005948 (PDF)
- Anthony Lomax, Alberto Michelini, Andrew Curtis 2009. Earthquake location, Direct, Global-Search Methods. in Meyers, R. A. (ed. in chief), Encyclopedia of Complexity and System Science. Springer. (PDF)
- Emanuel Winterfors and Andrew Curtis 2008. Numerical detection and reduction of non-uniqueness in nonlinear inverse problems. Inverse Problems, Vol. 24, No. 2, 025016. doi:10.1088/0266-5611/24/2/025016 (14pp). (PDF)
- A. Curtis 2004a. Theory of model-based geophysical survey and experimental design Part A - Linear Problems. The Leading Edge, Vol. 23, No. 10, pp. 997-1004 (Invited Paper). (PDF)
- A. Curtis 2004b. Theory of model-based geophysical survey and experimental design Part B - Nonlinear Problems. The Leading Edge, Vol. 23, No. 10, pp. 1112-1117 (Invited Paper). (PDF)
- A. Curtis and R. Wood 2004. 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)
- M. Baddeley, A. Curtis and R. Wood 2004. An introduction to prior information derived from probabilistic judgements: elicitation of knowledge, cognitive bias and herding. In, Geological Prior Information, A. Curtis and R. Wood ed's. Geol. Soc. Lond. Special Publication 239. (PDF)
- A. Curtis, A Michelini, D. Leslie and A. Lomax, 2004, Deterministic design of geophysical surveys by linear-dependence reduction. Geophys. J. Int., 157, 595-606. (PDF)
- J. van den Berg, A. Curtis and J. Trampert 2003. Bayesian, nonlinear experimental design applied to simple, geophysical examples. Geophys. J. Int., 55, No. 2, 411-421. (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)
- H. Maurer, D. Boerner and A. Curtis 2000. Design strategies for electromagnetic geophysical surveys. Inverse Problems, 16, No 5, 1097-1117. (PDF)
- A. Curtis and A. Lomax, 2001. Prior information, sampling distributions and the curse of dimensionality. Geophysics, 66, 372-378, 2001. (PDF)
- A. Curtis and H. Maurer 2000. Optimising designs of geophysical experiments and surveys - is it worthwhile? EOS, Trans., Amer. Geophys. Union, 81, no. 20, 224-225. Reprinted in The Leading Edge, October 2000. (PDF)
- A. Curtis and Spencer, C., 1999, Survey design strategies for linearized nonlinear inversion, 69th Ann. Internat. Mtg: Soc. of Expl. Geophys., 1775-1778.
- A. Curtis, 1999. Optimal experiment design: Cross-borehole tomographic examples. Geophys. J. Int., 136, 637-650. (PDF)
- A. Curtis, 1999. Optimal design of focussed experiments and surveys. Geophys J. Int., 139, 205-215. (PDF)
- A. Girard and A. Curtis, 1999. Assessing the complexity of multi-dimensional misfit functions. Schlumberger Scientific Report (public).
- 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)