Abstract
This chapter consists of two main parts, an introduction to adjustment techniques (Sects. 2.1, 2.2) and an overview of geostatistical methods (Sect. 2.3). The contents has many relations to other chapters of the handbook. In particular, the adjustment technology is a foundation of many data capture methods and geostatistical methods are applied in marine GIS and geology. Section 2.1 starts with an introduction to the Gauss–Markov model, discusses error propagation, and explains the role of covariance. The positional accuracy improvement, a key method for the reduction of geometrical errors present in old paper maps, is the main topic of the remainder of Sects. 2.1, 2.2. Many related topics of positional accuracy improvement are addressed such as datum and conformal transformation as well as the consideration of geometric constraints. Section 2.3 starts with an example and then describes the most common methods for processing and analysis of huge amounts of geodata, random fields and variograms. Important terms such as stationarity, intrinsic model, and ergodicity are explained. The chapter concludes with a discourse about kriging (Sect. 2.3.6), which is a common method for the interpolation of geodata in order to estimate the contents of unknown and inaccessible mineral deposits.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsAbbreviations
- 2-D:
-
two-dimensional
- 3-D:
-
three-dimensional
- GIS:
-
Geographic Information System
- GNSS:
-
Global Navigation Satellite System
- PAI:
-
Positional Accuracy Improvement
- SGS:
-
sequential Gaussian simulation
- TIN:
-
Triangulated Irregular Network
- UTM:
-
Universal Transversal Mercator
- dpi:
-
dots per inch
References
E. Mikhail, F. Ackermann: Observations and Least Squares (Univ. Press America, New York 1976)
W. Niemeier: Ausgleichungsrechnung (De Gruyter, Berlin 2002)
Conformal map, http://en.wikipedia.org/wiki/Conformal_map (Wikipedia 2011)
Studentʼs t-test, http://en.wikipedia.org/wiki/T-test (Wikipedia 2011)
http://en.wikipedia.org/wiki/Graph_(mathematics) (Wikipedia 2011)
Event-driven process chain, http://en.wikipedia.org/wiki/Event-driven_process_chain (Wikipedia 2011)
N.A.C. Cressie: Statistics for Spatial Data (Wiley, New York 1991)
G. Matheron: Estimating an Choosing (Springer, Berlin, Heidelberg 1989)
S. Meier, W. Keller: Geostatistik: Einführung in die Theorie der Zufallsprozesse (Akademie, Berlin 1990)
H. Wackernagel: Multivariate geostatistics (Springer, Berlin, Heidelberg 2003)
J. Menz: Geostatistische Vorhersage des Schichtenverlaufes im Gebirge auf der Grundlage von Bohrungen, Stoßbemusterungen und geophysikalischen Messungen, Markscheidewesen 98(2), 70–73 (1991)
A.G. Journel: Nonparametric estimation of spatial distributions, Math. Geol. 15, 445–468 (1991)
D.E. Myers: Pseudo-cross variograms, positive-definitness, and cokriging, Math. Geol. 23, 805–816 (1991)
M. Armstrong, P. Diamond: Testing variograms for positive-definitness, Math. Geol. 16(4), 407–421 (1992)
M. Stone: Cross-validadory choice and assesment of statistical predictions, J. R. Stat. Soc. 36, 111–133 (1974)
S. Geisser: The predictive sample reuse method with apllications, J. Am. Stat. Assoc. 70, 320–328 (1975)
E.H. Isaaks, R.M. Srivastava: An Introduction to Applied Geostatistics (Oxford Univ. Press, New York 1989) p. 561
J. Menz, J. Pilz: Kollokation, Universelles Kriging und Bayesʼscher Zugang, Markscheidewesen 101(2), 62–66 (1994)
P.A. Dowd: A review of recent developments in geostatistics, Comput. Geosci. 17(10), 1481–1500 (1991)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag
About this chapter
Cite this chapter
Gielsdorf, F., Hillmann, T. (2011). Mathematics and Statistics. In: Kresse, W., Danko, D. (eds) Springer Handbook of Geographic Information. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72680-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-540-72680-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72678-4
Online ISBN: 978-3-540-72680-7
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)