Guidelines for Distinguished Lecturer

The IAMG council voted in 2000 to establish a Distinguished Lecture series and has recently approved a committee charged with implementing the recommendations contained in the report of the IAMG Lecture Series Commission (July 2000).

The purpose of the IAMG Distinguished Lecture series is to demonstrate to the broader geological community the power of mathematical geology to address routine geological interpretation and to deliver this knowledge to audiences in selected parts the world. Therefore, the IAMG Distinguished Lecture Series Committee is seeking nominations for outstanding individuals who meet the following criteria:

* A demonstrated ability to communicate mathematical concepts to a general geological audience.

* A clear enthusiasm for mathematical geology.

* Recognition for work in their field.

* Established skill in working with individuals and in group discussions on geological problems.

The Distinguished Lecturer must be ready to travel and to perform the following duties:

* Prepare and present a lecture suitable for a general geological audience.

* Prepare and present one or two lectures on a more specialized topic.

* Interact and hold discussions with individuals, both professionals and students, on applications of mathematical geology to local problems of interest.

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DONALD E. MYERS

2008 IAMG DISTINGUISHED LECTURER

*I am prepared to present the following one hour lectures, each can be tailored somewhat to
specific audiences*. *There will be a strong emphasis on the use of software and actual data in
each of the lectures*

I. For a general audience with little prior knowledge of geostatistics

HISTORY OF GEOSTATISTICS- PAST, PRESENT AND FUTURE

Geostatistics as we know it now is only about 45 years old although clearly it is based on earlier ideas. Initially and even yet to a considerable extent it has developed outside of the statistical community, its development being heavily influenced by applications. While similar ideas were being put forward by Gandin in the USSR and Matérn at about the same time, it was the work of G. Matheron and his students at the Centre de Geostatistiques that prompted the spread of geostatistics in mining, hydrology, petroleum in the early years. Geostatistics might also be viewed as a special case of spatial statistics which also is a relatively recent development. Geostatistics and more generally spatial statistics have been greatly influenced by the development of fast, inexpensive computing. The development and availability of software for geostatistics has also been a critical factor.

II.. CONNECTIONS- GEOSTATISTICS, RADIAL BASIS FUNCTIONS AND OBJECTIVE ANALYSIS

Objective Analysis was the name given to the work of Gandin and it was primarily known in the atmospheric sciences. It has largely been absorbed and merged with the results and ideas of geostatistics. In contrast the work of R. Hardy in the early 1970's on interpolation of gravity data was and is best known in the numerical analysis literature. The equivalence between the RBF interpolating function and the kriging estimator as well as between the equations determining the coefficients requires only basic linear algebra. However the thrust in terms of applications has remained quite different. Moreover the emphasis is almost entirely on radial, i.e., isotropic basis functions in the Radial Basis Function literature. The direct derivations for Radial Basis functions appear to depend on deterministic assumptions rather than statistical assumptions but this is more a difference in interpretation.

III. NON-GEOMETRIC ANISOTROPIES AND SPACE- TIME MODELING

Continuity is a basic function property in analysis but it is deterministic and generally is taken to be non-directional. The variogram and (auto) covariance function are statistical measures of the degree of continuity when it is not deterministic and they might be directionally dependent. The practical problem is constructing valid variograms or covariance functions incorporating directional dependence in the right way.. Models where only the range of dependence is directionally dependent can be obtained by a stretching and a rotation on the underlying space. More complicated models are necessary if the sill or other parameters change with direction. Space-time models are a special case of this latter problem and various authors have used different constructions. The work of Cressie-Huang, De Cesare-Myers-De Iaco and Posa, Ma, Fuentes, Gneiting, Stein and others will be reviewed.

IV. MULTIVARIATE SPATIAL STATISTICS

Some authors have used the term “multivariate statistics” to mean spatial problems in higher dimensional space. But more commonly it means that there are several variables of interest in which case the key question is whether there is some form of dependence between the variables. The dependence may be deterministic, e.g., the differential equation linking head and hydraulic conductivity, or it may be statistical. The difference between variables may be one of the scale of observation, e.g., ground based observation vs satellite mounted sensor observations or core assays vs “block” assays. Sometimes the relationship is assumed to be one of “cause and effect” but does not give rise to an analytic expression. Linear models (including Linear Mixed models and Generalized Linear Mixed Models) is one method for obtaining empirical relationships. Cokriging in its various forms is a generalization of kriging from the univariate form. Various problems arise in applying each of these techniques and they overlap to some extent. Cokriging is often used to utilize the redundancy in multivariate data to compensate for a lack of data for some variables by using spatial cross-correlations between pairs of variables as well as the spatial correlations for each variable separately. There are both practical and theoretical problems with applying these techniques. Their development have been strongly driven by applications.

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