Abstract
Optimization principles play a key role in mathematical sedimentology in at least three ways.
-
(1)
The data-gathering process is optimized so as either to maximize the amount of information to be obtained with limited cost of sampling and measurement or to minimize the cost of obtaining at least a certain known amount of information.
-
(2)
Many commonly used data-analysis models have been formulated using optimization criteria. Examples include: regression by minimizing the sum of squares; principal component analysis by maximizing the amount of variation associated with each successive component axis, subject to constraints; discriminant-function analysis by placing decision surfaces so as to maximize the separation of predefined groups; cluster analysis by maximizing the compactness of groups; and several others.
-
(3)
Simulation modeling may involve optimization. First, principles of least work or similar optimization criteria may provide keys to the mathematical formulation of a model. This follows as a consequence of the optimization inherent in nature. Second, a basic goal in simulation is to adjust the parameters so as to minimize the difference between the model’s output and the real-world response. Furthermore, the process of exploring the sensitivity of a simulation model to systematic changes in parameters is a natural extension of optimization.
An appreciation of basic optimization principles leads to a clearer understanding as to how mathematics can help to solve sedimentological problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Allen, J. R. L., 1970, Physical processes of sedimentation: American Elsevier, New York, 248 p.
Bagnold, R. A., 1956, The flow of cohesionless grains in fluids: Roy Soc. London Phil. Trans., v. 249, ser. A, p. 235–297.
Bonham-Carter, G. F., and Sutherland, A. J., 1968, Mathematical model and FORTRAN IV program for computer simulation of deltaic sedimentation: Kansas Geol. Survey, Computer Contr. 24, 56 p.
Briggs, L. I., and Pollack, H. N., 1967, Digital model of evaporite sedimentation: Science, v. 155, no. 3761, p. 453–456.
Brush, L. M., 1965, Sediment sorting in alluvial channels, in Primary sedimentary structures and their hydrodynamic interpretation: Soc. Econ. Paleon. and Mineral. Sp. Publ., no. 12, p. 25–33.
Cochran, W. G., 1963, Sampling techniques ( 2nd ed. ): John Wiley & Sons, New York, 413 p.
Dacey, M. F., and Krumbein, W. C, 1970, Markovian models in stratigraphic analysis: Jour. Intern. Assoc. Math. Geol., v. 2, no. 2, p. 175–191.
Farmer, D. G., 1971, A computer-simulation model of sedimentation in a salt-wedge estuary: Marine Geology, v. 10, no. 2, p. 133–143.
Gibbs, R. J., Matthews, M. D., and Link, D. A., 1971, The relationship between sphere size and settling velocity: Jour. Sed. Pet., v. 41, no. 1, p. 1–7.
Goldstein, H., 1950, Classical mechanics: Addison-Wesley, Reading, Mass., p. 46–47.
Griffiths, J. C., 1967, Scientific method in analysis of sediments: McGraw-Hill Book Co., New York, 508 p.
Guy, H. P., Simons, D. B., and Richardson, E. V., 1966, Summary of alluvial-channel data from flume experiments, 1956–61: U. S. Geol. Survey Prof. Paper 462–I, 96 p.
Harbaugh, J. W., and Bonham-Carter, G. F., 1970, Computer simulation in geology: John Wiley & Sons, New York, 575 p.
Harbaugh, J. W., 1966, Mathematical simulation of marine sedimentation with IBM 7090/7094 computers: Kansas Geol. Survey, Computer Contr. 1, 52 p.
Harbaugh, J. W., and Merriam, D. F., 1968, Computer applications in stratigraphic analysis: John Wiley & Sons, New York, 282 p.
Kelley, J. C., and McManus, D. A., 1969, Optimizing sediment-sampling plans: Marine Geology, v. 7, no. 5, p. 465–471.
Kelley, J. C., 1971, Multivariate oceanographic sampling: Jour. Intern. Assoc. Math. Geol., v. 3, no. 1, p. 43–50.
King, C. A, M., and McCullagh, M. J., 1971, A simulation model of a complex recurved spit: Jour. Geology, v. 72, no. 1, p. 22–37.
Krumbein, W. C., and Graybill, F. A., 1965, An introduction to statistical models in geology: McGraw-Hill, New York, 475 p.
Langbein, W. B., 1966, River geometry: minimum variance adjustment U. S. Geol. Survey Prof. Paper 500-C, p. C6–C11.
Leopold, L. B., and Langbein, W. B., 1966, River meanders: Scientific American, v. 214, no. 6, p. 60–70.
Lumsden, D. N., 1971, Markov-chain analysis of carbonate rocks: applications, limitations, and implications as exemplified by the Pennsylvanian System in southern Nevada: Geol. Soc. America Bull., v. 82, no. 2, p. 447–462.
McCammon, R. B., 1970, Component estimation under uncertainty, in Geostatistics: Plenum Press, New York, p. 45–61.
Read, W. A., 1969, Analysis and simulation of Namurian sediments in central Scotland using a Markov-process model: Jour. Intern. Math. Geol., v. 1, no. 2, p. 199–219.
Rosen, R. R., 1967, Optimality principles in biology: Butterworths London, 198 p.
Schwarzacher, W., 1969, The use of Markov chains in the study of sedimentary cycles: Jour. Intern. Assoc. Math. Geol., v. 1, no. 1, p. 17–41.
Slaughter, M., and Hamil, M., 1970, Model for deposition of volcanic ash and resulting bentonite: Geol. Soc. Amer. Bull., v. 81, no. 31, p. 961–968.
Vanoni, V. A., Brooks, N. H., and Kennedy, J. F., 1961, Lecture notes on sediment transportation and channel stability: W. M. Keck Lab. for Hydraulics and Water Res., California Inst. Tech., Tech. Rept. KH-R-1.
Wilde, D. J., and Beightler, C. S., 1967, Foundations of optimization: Prentice-Hall, Englewood Cliffs, N. J., 480 p.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1972 Plenum Press, New York
About this chapter
Cite this chapter
Bonham-Carter, G. (1972). Optimization Criteria for Mathematical Models Used in Sedimentology. In: Merriam, D.F. (eds) Mathematical Models of Sedimentary Processes. Computer Applications in the Earth Sciences. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1995-5_1
Download citation
DOI: https://doi.org/10.1007/978-1-4684-1995-5_1
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-1997-9
Online ISBN: 978-1-4684-1995-5
eBook Packages: Springer Book Archive