zbMATH — the first resource for mathematics

Grain-size control on petrographic composition of sediments: Compositional regression and rounded zeros. (English) Zbl 1178.86025
Summary: It is well-known that sediment composition strongly depends on grain size. A number of studies have tried to quantify this relationship focusing on the sand fraction, but only very limited data exists covering wider grain size ranges. Geologists have a clear conceptual model of the relation between grain size and sediment petrograpic composition, typically displayed in evolution diagrams. We chose a classical model covering grain sizes from fine gravel to clay, and distinguishing five types of grains (rock fragments, poly- and mono crystalline quartz, feldspar and mica/clay). A compositional linear process is fitted here to a digitized version of this model, by (i) applying classical regression to the set of all pairwise log-ratios of the 5-part composition against grain size, and (ii) looking for the compositions that best approximate the set of estimated parameters, one acting as slope and one as intercept. The method is useful even in the presence of several missing values. The linear fit suggests that the relative influence of the processes controlling the relationship between grain size and sediment composition is constant along most of the grain size spectrum.

86A32 Geostatistics
Full Text: DOI
[1] Aitchison J (1986) The statistical analysis of compositional data. Monographs on statistics and applied probability. Chapman & Hall, London. (Reprinted in 2003 with additional material by The Blackburn Press) · Zbl 0688.62004
[2] Aitchison J (1997) The one-hour course in compositional data analysis or compositional data analysis is simple. In: Pawlowsky-Glahn V (ed) Proceedings of IAMG’97–The third annual conference of the International Association for Mathematical Geology, vol 1. International Center for Numerical Methods in Engineering (CIMNE), Barcelona, pp 3–35
[3] Aitchison J (2002) Simplicial inference. In: Viana MAG, Richards DSP (eds) Algebraic methods in statistics and probability. Contemporary mathematics series, vol 287. American Mathematical Society, Providence, pp 1–22
[4] Arribas J, Tortosa A (2003) Detrital modes in sedimenticlastic sands from low-order streams in the Iberian Range, Spain: the potential for sand generation by different sedimentary rocks. Sedimentary Geol 159:275–303 · doi:10.1016/S0037-0738(02)00332-9
[5] Ben-Israel A, Greville TNE (2003) Generalized inverses: theory and applications, 2nd edn. Springer, New York · Zbl 1026.15004
[6] Billheimer D, Guttorp P, Fagan W (2001) Statistical interpretation of species composition. J Am Stat Assoc 96(456):1205–1214 · Zbl 1073.62573 · doi:10.1198/016214501753381850
[7] Blatt H, Middleton GV, Murray RC (1972) Origin of sedimentary rocks. Prentice-Hall, Englewood Cliffs
[8] Buccianti A, Mateu-Figueras G, Pawlowsky-Glahn V (eds) (2006) Compositional data analysis: from theory to practice. Special publication, vol 264. The Geological Society, London · Zbl 1155.86002
[9] Chandrajith R, Dissanayake CB, Tobschall HJ (2001) Application of multi-element relationships in stream sediments to mineral exploration: a case study of Walawe Ganga Basin, Sri Lanka. Appl Geochem 16:339–350 · doi:10.1016/S0883-2927(00)00038-X
[10] Daunis-i-Estadella J, Egozcue JJ, Pawlowsky-Glahn VV (2002) Least squares regression in the simplex. In: Bayer U, Burger H, Skala W (eds) Proceedings of IAMG’02–The eighth annual conference of the International Association for Mathematical Geology. Selbstverlag der Alfred-Wegener-Stiftung, Berlin, pp 411–416
[11] Egozcue JJ, Pawlowsky-Glahn V (2006) Simplicial geometry for compositional data. See Buccianti, Mateu-Figueras, and Glahn (2006), pp 145–160 · Zbl 1156.86307
[12] Grantham JH, Velbel MA (1988) The influence of climate and topography on rock-fragment abundance in modern fluvial sands of the southern Blue Ridge Mountains, North Carolina. J Sedimentary Res 58:219–227
[13] Johnsson M (1993) The system controlling the composition of clastic sediments. Geol Soc Am Spec Paper 284:1–19
[14] Kiminami K, Fujii K (2007) The relationship between major element concentration and grain size within sandstones from four turbidite sequences in Japan. Sedimentary Geol 195:203–215 · doi:10.1016/j.sedgeo.2006.08.002
[15] Lim DI, Jung HS, Choi JY, Yang S, Ahn KS (2006) Geochemical compositions of river and shelf sediments in the Yellow Sea: grain-size normalization and sediment provenance. Cont Shelf Res 26:15–24 · doi:10.1016/j.csr.2005.10.001
[16] Martín-Fernández JA (2001) Medidas de diferencia y clasificación no paramétrica de datos composicionales (Measures of difference and non-parametric classification of compositional data). PhD thesis, Universitat Politècnica de Catalunya, Barcelona
[17] Martín-Fernández JA, Barceló-Vidal C, Pawlowsky-Glahn V (2000) Zero replacement in compositional data sets. In: Kiers H, Rasson J, Groenen P, Shader M (eds) Studies in classification, data analysis, and knowledge organization (Proceedings of the 7th conference of the International Federation of Classification Societies (IFCS’2000), University of Namur, Namur, 11–14 July, Springer, Berlin, pp 155–160
[18] Murray GD (1979) The estimation of multivariate normal density functions using incomplete data. Biometrika 66:375–380 · Zbl 0406.62032 · doi:10.1093/biomet/66.2.375
[19] Nesbitt H, Markovics G (1997) Weathering of granodioritic crust, long-term storage of elements in weathering profiles and petrogenesis of siliciclastic sediments. Geochim Cosmochim Acta 61:1653–1670 · doi:10.1016/S0016-7037(97)00031-8
[20] Nesbitt H, Young G (1984) Prediction of some weathering trends of plutonic and volcanic rocks based on thermodynamic and kinetic considerations. Geochim Cosmochim Acta 41:1523–1534 · doi:10.1016/0016-7037(84)90408-3
[21] Nesbitt H, Young G (1996) Petrogenesis of sediments in the absence of chemical weathering: Effects of abrasion and sorting on bulk composition and mineralogy. Sedimentology 43:341–358 · doi:10.1046/j.1365-3091.1996.d01-12.x
[22] Noda A (2005) Texture and petrology of modern river, beach and shelf sands in a volcanic back-arc setting, northeastern Japan. Isl Arc 14:687–707 · doi:10.1111/j.1440-1738.2005.00477.x
[23] Palarea-Albaladejo J, Martín-Fernández JA, Gómez-García J (2007) A parametric approach for dealing with compositional rounded zeros. Math Geol 359(7):625–645 · Zbl 1130.86001 · doi:10.1007/s11004-007-9100-1
[24] Palomares M, Arribas J (1993) Modern stream sands from compound crystalline sources: Composition and sand generation index. Geol Soc Am Spec Paper 284:313–322
[25] Pawlowsky-Glahn V, Egozcue JJ (2001) Geometric approach to statistical analysis on the simplex. Stoch Environ Res Risk Assess 15(5):384–398 · Zbl 0987.62001 · doi:10.1007/s004770100077
[26] Pettijohn F (1957) Sedimentary rocks. Harper, New York
[27] Pettijohn F, Potter P, Siever R (1987) Sand and sandstone, 2nd edn. Springer, New York
[28] Potter P (1994) Modern sands of South America: composition, provenance and global significance. Int J Earth Sci 83(1):212–232
[29] Rubin DB (1976) Inference and missing data. Biometrika 63:592–581 · Zbl 0344.62034 · doi:10.1093/biomet/63.3.581
[30] Solano-Acosta W, Dutta PK (2005) Unexpected trend in the compositional maturity of second-cycle sand. Sedimentary Geol 178:275–283 · doi:10.1016/j.sedgeo.2005.05.008
[31] van den Boogaart KG, Tolosana-Delgado R, Bren M (2006) Concepts for handling zeroes and missing values in compositional data. In: Pirard E, Dassargues A, Havenith HB (eds) Proceedings of IAMG’06–The XI annual conference of the International Association for Mathematical Geology. University of Liège, Belgium, CD-ROM
[32] von Eynatten H (2004) Statistical modelling of compositional trends in sediments. Sedimentary Geol 171:79–89 · doi:10.1016/j.sedgeo.2004.05.011
[33] von Eynatten H, Barceló-Vidal C, Pawlowsky-Glahn V (2003) Modelling compositional change: the example of chemical weathering of granitoid rocks. Math Geol 35(3):231–251 · doi:10.1023/A:1023835513705
[34] Wentworth C (1922) A scale of grade and class terms for clastic sediments. J Geol 30:377–392 · doi:10.1086/622910
[35] Whitmore GP, Crook KAW, Johnson DP (2004) Grain size control of mineralogy and geochemistry in modem river sediment, New Guinea Collision, Papua New Guinea. Sedimentary Geol 171:129–157 · doi:10.1016/j.sedgeo.2004.03.011
[36] Zhang C, Wang L, Li G, Dong S, Yang J, Wang X (2002) Grain size effect on multi-element concentrations in sediments from the intertidal flats of Bohai Bay, China. Appl Geochem 17:59–68 · doi:10.1016/S0883-2927(01)00079-8
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.