Approximately 60 students attended the first GRA course offering "Geostatistics for Hydrogeological and Environmental Applications" on July 31 and August 1, 2001. The course, conducted at San Jose State University, was co-sponsored by the SJSU Geology Department and was also held in cooperation with the International Association of Hydrogeologists and the Association of Engineering Geologists. The course presented students with both the theory and applications of geostatistics. Dr. Steve Carle's (the instructor) goals for the course included the following:

• Improve awareness for potential applications - estimation, quantification of spatial variability and uncertainty, upscaling, and simulation.
• Develop students appreciation for theoretical concepts, including equations and derivations that are useful for explaining the origin of the methods.
• Acquire an ability to interpret geostatistical parameters, so that geologic insight can be infused and plausibility can be checked.
• Gain conceptual understanding that is more lasting than memorization.
• Inspire interest in confronting subjects involving heterogeneity and uncertainty.
• Encourage integration of geologic and quantitative approaches to modeling.

For this course, Dr. Carle prepared a very detailed set of course notes with chapters devoted to the subjects of Bivariate Statistics, Measuring Spatial Variability, Modeling Spatial Variability, Kriging, Discrete Random Variables, Conditional Simulation, and Advanced Hydrogeological Applications. Participants were also presented with the theory underlying Dr. Carle's groundbreaking work on transition probability simulation, which allows the constraint of facies sequence modeling with geologic rules for fining-upward sequences such as Walter's law.

The comprehensive set of course notes provides the central functions and equations needed to employ geostatistical methods, and narrative explanations of their application. The notes provide fundamental geostatistical training concepts in a textbook-style presentation, with thorough explanations. Dr. Carle is considering requests by several participants to enhance the notes and lectures with worked examples, using input/output screen shots and in-course software walk-throughs, such as those presented in the GSLIB book by Deutsch and Journel. The first offering of this course did not include software examples, as these are readily available off the web at no cost (e.g. http://www.gslib.com).

Dealing with the inherent heterogeneity of earth science is obviously challenging. We are always attempting to identify new ways to address it. Geostatistical methods are important additions to the geoscientist's and engineer's toolbox to quantitatively address the uncertainty associated with spatial data at varying scales. While a geostatistical approach alone may not be the only tool, it is certainly a valuable complement to other tools. As noted by Dr. Carle, "It merges the quantitative with the subjective, providing bridges between numerical models and geologic interpretation."

The course accomplished a great deal in two days, condensing material usually occupying a semester long graduate course. As the subject of geostatistics involves material from linear algebra, probability theory, and other branches of mathematics, the material can be overwhelming for some. Nevertheless, the concepts are inherently simple, and the computer codes for geostatistical analysis are freely available, averting the need for users to be expert mathematicians. On a difficulty skill, one participant views the underlying mathematics as simpler than the mathematics behind groundwater flow modeling.

Watch GRA's web site for more information on geostatistical methods. Since geostatistical methods are gaining recognition in the context of environmental and hydrogeological applications, GRA plans to post related information to its web site. We are going to initiate the web site addition by posting references contained in the course notes. Other information will follow. If you have any additional references (software, books, articles, applications, etc.) that you would like to share, please e-mail admin@grac.org.

The next offering of "Geostatistics for Hydrogeological and Environmental Applications" is anticipated for early 2002, and may include an evening session to allow presentations of GRA-member applications of geostatistical methods, discussion, software demonstrations, and a social hour. Participants in the August 2001 course would be invited to attend the evening session, which may double as a special GRA branch meeting.