A comparative study on the three calculation methods of grain-size parameters for aeolian sediments

doi:10.7522/j.issn.1000-694X.2020.00028

Journal of Desert Research ›› 2020, Vol. 40 ›› Issue (4): 95-102.DOI: 10.7522/j.issn.1000-694X.2020.00028

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A comparative study on the three calculation methods of grain-size parameters for aeolian sediments

Xixi Ma¹^,²(), Jianhua Xiao¹, Zhengyi Yao¹()

^1.Key Laboratory of Desert and Desertification, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou 730000, China
^2.College of Natural Resources and Environment, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2020-03-02 Revised:2020-03-17 Online:2020-08-20 Published:2020-09-01
Contact: Zhengyi Yao

Abstract

Abstract:

The grain-size characteristics of sediments are the key indicators that reflect the sediment sources and the sedimentary environment. The diversity of granular analysis methods restricts the systematic integration and analysis of multi-source data. Based on three groups of aeolian sediment samples (a total of 222), the grain-size parameters including Average Grain-Size (M_z), Sorting-Coefficient (σ), Skewness (SK), and Kurtosis(K_g) are calculated by Folk-Word Graphical-Method, McManus Moment and Friedman Moment Methods. The results show that the linear correlativity of M_z and σ,respectively obtained by the Graphical-Method and the Moment-Method, is prominent in the three groups of samples，which is not related to the sedimentary environment. SK and K_g obtained by the three calculation methods are basically not correlated and non-interchangeable, which is closely related to the differences of sedimentary environment and the morphology of frequency curve of grain-size. Statistically, the numerical significance of K_g should be contrary to that of σ, i.e. negative correlation. Therefore, the Friedman Moment-Method is more applicable. In the process of granularity analysis, we should fully consider the differences in different calculation methods and establish corresponding qualitative grading standards.

Key words: aeolian sediments, grain-size parameters, moment method, correlativity, sedimentary environment

CLC Number:

P931.3

Xixi Ma, Jianhua Xiao, Zhengyi Yao. A comparative study on the three calculation methods of grain-size parameters for aeolian sediments[J]. Journal of Desert Research, 2020, 40(4): 95-102.

Figures/Tables 6

Table 1 The formulae of grain-size parameters for graphical-method and moment-method

粒度参数	Folk-Word图解法^[10]	McManus矩法^[11]	Friedman矩法^[13]
平均粒径	$M z = Φ 16 + Φ 50 + Φ 84 3$	$M z = ∑ i = 1 n X i f i 100$	$M z = ∑ i = 1 n X i f i 100$
分选系数	$σ = Φ 84 - Φ 16 4 + Φ 95 - Φ 5 6.6$	$σ = ∑ i = 1 n X i - X ˉ 2 ? f i 100$	$σ = ∑ i = 1 n X i - X ˉ 2 ? f i 100$
偏度	$S K = Φ 16 + Φ 84 - 2 Φ 50 2 Φ 84 - Φ 16 + Φ 5 + Φ 95 - 2 Φ 50 2 Φ 95 - Φ 5$	$S K = ∑ i = 1 n X i - X ˉ 3 f i 100 3$	$S K = ∑ i = 1 n X i - X ˉ 3 f i 100 σ 3$
峰度	$K g = Φ 95 - Φ 5 2.44 Φ 75 - Φ 25$	$K g = ∑ i = 1 n X i - X ˉ 4 f i 100 4$	$K g = ∑ i = 1 n X i - X ˉ 4 f i 100 σ 4$

Table 1 The formulae of grain-size parameters for graphical-method and moment-method

粒度参数	Folk-Word图解法^[10]	McManus矩法^[11]	Friedman矩法^[13]
平均粒径	$M z = Φ 16 + Φ 50 + Φ 84 3$	$M z = ∑ i = 1 n X i f i 100$	$M z = ∑ i = 1 n X i f i 100$
分选系数	$σ = Φ 84 - Φ 16 4 + Φ 95 - Φ 5 6.6$	$σ = ∑ i = 1 n X i - X ˉ 2 ? f i 100$	$σ = ∑ i = 1 n X i - X ˉ 2 ? f i 100$
偏度	$S K = Φ 16 + Φ 84 - 2 Φ 50 2 Φ 84 - Φ 16 + Φ 5 + Φ 95 - 2 Φ 50 2 Φ 95 - Φ 5$	$S K = ∑ i = 1 n X i - X ˉ 3 f i 100 3$	$S K = ∑ i = 1 n X i - X ˉ 3 f i 100 σ 3$
峰度	$K g = Φ 95 - Φ 5 2.44 Φ 75 - Φ 25$	$K g = ∑ i = 1 n X i - X ˉ 4 f i 100 4$	$K g = ∑ i = 1 n X i - X ˉ 4 f i 100 σ 4$

Table 2 The statistical values of granular parameters for three groups of sediments

粒度参数	E55样品组				M98样品组				R69样品组
粒度参数	最小值	最大值	平均值	标准差	最小值	最大值	平均值	标准差	最小值	最大值	平均值	标准差
M_z1957	1.95	3.41	2.71	0.38	2.10	5.10	3.07	0.57	1.38	3.76	2.77	0.45
M_z1982(M_z1988)	2.07	3.66	2.91	0.43	2.11	4.95	3.22	0.53	0.62	3.82	3.02	0.40
σ₁₉₅₇	0.70	2.06	1.22	0.26	0.52	2.30	1.20	0.35	0.49	2.28	1.28	0.31
σ₁₉₈₂(σ₁₉₈₈)	1.18	1.98	1.46	0.18	0.99	2.12	1.37	0.21	0.98	2.11	0.52	0.21
SK₁₉₅₇	-0.47	0.16	-0.19	0.17	-0.50	0.10	-0.29	0.12	-0.66	-0.06	-0.41	0.10
SK₁₉₈₂	0.73	2.74	1.89	0.48	0.52	3.66	1.89	0.58	0.98	3.71	2.16	0.53
SK₁₉₈₈	1.42	2.17	1.78	0.14	0.92	2.19	1.65	0.16	1.51	2.29	1.93	0.16
K_g1957	0.92	2.87	1.89	0.65	1.00	2.66	1.65	0.35	1.02	3.28	2.29	0.51
K_g1982	3.65	12.01	7.62	1.99	2.02	18.65	7.57	3.08	2.60	19.18	7.55	3.00
K_g1988	2.20	2.78	2.39	0.13	1.73	2.80	2.21	0.16	2.05	2.81	2.45	0.18

Fig.1 The regression models of Mz and σ for Graphical-Method(abscissa) and Moment-Method(ordinate)

Table 3 The statistical values of Mz and σ for typical samples

样品组	编号	M_z1957	M_z1988	σ₁₉₅₇	σ₁₉₈₈	M_z1988- M_z1957	σ₁₉₈₈- σ₁₉₅₇
E55	26	3.41	3.37	2.06	1.96	-0.05	-0.10
M98	MS1-8	4.40	4.37	1.80	1.64	-0.03	-0.16
	MS1-11	4.79	4.74	1.82	1.60	-0.05	-0.22
	MS1-12	5.00	4.89	1.95	1.66	-0.11	-0.29
	MS1-13	5.10	4.95	2.14	1.78	-0.16	-0.35
	MS87	4.20	4.16	2.05	1.85	-0.03	-0.20
	MS1-1	4.07	4.18	1.60	1.57	-0.04	-0.09
	MS1-3	4.08	4.12	1.76	1.67	0.11	-0.03
	MS1-7	3.97	4.08	1.64	1.61	0.10	-0.02
	MS1-10	3.97	4.09	1.68	1.63	0.12	-0.04
R69	R3-2	3.69	3.60	2.28	2.11	-0.09	-0.17
	R16-3	3.38	3.37	1.83	1.83	-0.01	-0.004
	R3-3	3.13	3.15	1.94	1.93	0.02	-0.01
	R45-2	3.32	3.37	2.02	1.98	0.05	-0.04

Fig.2 The frequency curves of grain-size for typical samples

Fig.3 The scatter diagram of σ and Kg

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A comparative study on the three calculation methods of grain-size parameters for aeolian sediments

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