Stanford ERE/GES-240


aboucher - Posted on 18 June 2009

This class and set of Power Point and Word files cover the theory of geostatistics as developed in the School of Earth Sciences at Stanford since the late 1970’s, as printed in a series of books starting from Mining Geostatistics (1978) to the latest SGeMS Software and Users’ Guide (2008).

Preamble:

Although theoretical this presentation is guided by the practice of geostatistics in modeling earth sciences phenomena. There would be no geostatistics as a specific discipline without that precedence of practice, a practice conditioned by the characteristics of earth sciences distributions which are:

  • data are dependent in space and time

  • that dependence goes much beyond the traditional correlation model and its corollary, the Gaussian model

  • data comes under diverse forms, related to diverse attributes; data can be hard or soft, with various volume supports (resolution) and various accuracies. All are potentially important and they interact altogether calling for their simultaneous integration. . .. Data sing altogether through multiple-point/location and multiple attributes statistics as in an orchestra, not as a set of two-point dialogues which are the covariances. You do not appreciate a symphony by listening at the score of each instrument one at a time.

  • least squared error-type estimates are not enough to build reliable maps, nor do they provide usable assessment of uncertainty

  • there is no inference possible without a prior model linking all data and unknowns altogether. That model could be simplistic such as provided by full or conditional independence hypotheses or a Gaussian-type multivariate distribution, or more complete such as a numerical training image; the latter requires evidently a prior choice or model decision. Preferably, this model should deliver elements of the physics underlying the phenomenon studied (e.g. geology).

Without some prior geological/physical interpretation there cannot be any serious inference possible. It is foolish to think that statistics without some prior data interpretation could allow to go anywhere beyond a listing of the data available. There is neither magic nor objectivity behind any statistical analysis. Modern Geostatistics accepts that limitation and is content at providing tools to integrate data within a prior necessarily subjective model, but one that is clearly stated. Alternative priors can and should be considered; there lies the major source of uncertainty.