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水系分布方向计算的密集度方法

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A CONCENTRATED DEGREE METHOD FOR CALCULATION OF VALLEY TRENDS

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构造应力场是地球动力学的关键问题,也是地貌学、尤其是构造地貌学的重要问题。应力是张量,它有六个独立的分量。地壳的应力是位置的函数,同时也是时间的函数。由于影响应力场的因素很多,因而要揭示区域应力场的趋势和特征,通常用单个的应力值(如单个的地震断层面解或其他应力测量值)是不完备的,而应采取对众多的观测值加以统计“平均”或其他的“平均”方法。

余庆余, 蒋柱中, 艾南山
. 水系分布方向计算的密集度方法[J]. *地理科学*, 1985
, 5(1)
: 1
-9
.
DOI: 10.13249/j.cnki.sgs.1985.01.1

Stress is physically a tensorial quantity which varies from point to point within the earth. Therefore, the stresses form a field in the earth. The present-day stress field manifests itself in a variety of phenomena, in turn, from a study and interpretation of these phenomena the stress field can be inferred and deduced. Many geomorphic features, such as orientation structure of a river network are first found by Prof. Scheidegger to be due to the action of a tectonic stress field, If the valley are supposed to be Mohr-type fractures, one obtains as predicted stress direction the bisectries of the prefferred valley trends. For calculation of the preferred directions a computational method has been developed by Kohlbeck and Scheidegger. But the program is too large for ordinary computer. The distribution pattern of valley trends is caused by the antagonistic interaction between the endogenetic and exogenetic effects. The exogentic effects give the distribution pattern randomness, meanwhile the endogenetic ones result its non randomness. According to the law of large numbers, the exogenetic effects will offset each other,the distribution will have non-random pattern. Therefore, we can research this pattern without the random statistical method, but with the method of the deterministic mathematics. In this paper we will give a new compStress is physically a tensorial quantity which varies from point to point within the earth. Therefore, the stresses form a field in the earth. The present-day stress field manifests itself in a variety of phenomena, in turn, from a study and interpretation of these phenomena the stress field can be inferred and deduced. Many geomorphic features, such as orientation structure of a river network are first found by Prof. Scheidegger to be due to the action of a tectonic stress field, If the valley are supposed to be Mohr-type fractures, one obtains as predicted stress direction the bisectries of the prefferred valley trends. For calculation of the preferred directions a computational method has been developed by Kohlbeck and Scheidegger. But the program is too large for ordinary computer. The distribution pattern of valley trends is caused by the antagonistic interaction between the endogenetic and exogenetic effects. The exogentic effects give the distribution pattern randomness, meanwhile the endogenetic ones result its non randomness. According to the law of large numbers, the exogenetic effects will offset each other,the distribution will have non-random pattern. Therefore, we can research this pattern without the random statistical method, but with the method of the deterministic mathematics. In this paper we will give a new computational method. Let θ_{i} be the direction of a river section and Li correspounding langth. A concept of concentrated degree is introduced as following: where {λ_{-k},......,λ0,......,λ_{k}} are a group of powers, λ_{i}=λ_{-i}>0, λ_{0} is maximum of {λ_{i}}, and if j>i, then λ_{j}<λ_{i}. Obviously, reflects the concentrated degree of the directions of a river network at θ_{m}. The prefferred directions can be calculated by the following steps:1) compute 2) Suppose Max/n = _{a1}, look for the maximum of , where n varies in (0°, 180°), (α_{1}-45°, α_{1}+45°) 3) Denote A=(α_{1}+α_{2})/2, B=A+90, then compute new concentrated degree . in and 4) Suppose _{β1}=max , then β_{1} is the first preffered direction. Similarly, if _{β2}=max, then β_{2} is the second preffered direction. By computing it is found that the choice of power {λ_{i}} is important. We call η=λ_{0}/λ_{k} by propertion of amplitude. η can be taken near 1 when the variance of data is rather small, on the contrary, it should be taken rather more.
utational method. Let θ_{i} be the direction of a river section and Li correspounding langth. A concept of concentrated degree is introduced as following: where {λ_{-k},......,λ0,......,λ_{k}} are a group of powers, λ_{i}=λ_{-i}>0, λ_{0} is maximum of {λ_{i}}, and if j>i, then λ_{j}<λ_{i}. Obviously, _{m} reflects the concentrated degree of the directions of a river network at θ_{m}. The prefferred directions can be calculated by the following steps:1) compute _{m} 2) Suppose Max/n =_{al}, look for the maximum of , where n varies in (0°, 180°), (α_{1}-45°, α_{1}+45°) 3) Denote A=(α_{1}+α_{2})/2, B=A+90, then compute new concentrated degree _{z}. in and 4) Suppose _{β1}=max , then β_{1} is the first preffered direction. Similarly, if _{β2}=max, then β_{2} is the second preffered direction. By computing it is found that the choice of power {λ_{i}} is important. We call η=λ_{0}/λ_{k} by propertion of amplitude. η can be taken near 1 when the variance of data is rather small, on the contrary, it should be taken rather more.

[1] Scheidegger,A.E.,Orientationsstruktur der Talanlagen in der Schweiz,Geogr,Helv.(34)9-15,1979.

[2] Scheidegger,A.E.,The principle of antagonism in the Earth’s evolution,Tectophys,(55)T7-T10,1979.

[3] 艾南山、唐少卿,地表形态发育的对抗性原理,兰州大学学报,社会科学版,11卷,2期,122-130,1983.

[4] Gerber,E,K.,Scheidegger,A,E,,Erosional and stress-induced features on steep slopes,Z.Geomorph.Suppl.(18)38-49,1973.

[5] 艾南山,顾恒岳,华北地区水系及新构造应力场分析,重庆交通学院学报,2期,18-27,1982.

[6] Ai Nanshan,Scheidegger,A,E.,Yalley trends in Tibet,Z,Geomorph.,(25)203-212,1981.

[7] Ai Nanshan,Scheidegger,A,E.,The tectonic stress field in North Chiaa.兰州大学学报,自然科学版,18卷4期,157-176,1962.

[8] Scheidegger,A,E.,Principles of Geodynamics,Spting-Vcrlag,1982.

[9] Kohlbeck,F.,Scheidegger,A,E.,On the theory of the evaluation of joint orientation measuremeLts,Rock Mech.,(9)9-25,1977.

[10] 徐叔鹰、李吉均、艾南山,巴基斯坦波特瓦尔高原构造地貌研究,地理科学,2卷 2期,125-134,1982.

[11] 艾南山、伍光和,赵镇,祁连山冷龙岭冰川分布与新构造应力场,兰州大学学报,自然科学版,18卷4期,182-183 1982.

[12] 复旦大学数学系主编,概率论与数理统计,第二版,上海科学技术出版社,1961.

[13] 艾南山、架国昭、Scheidegger,A,E.,东南沿海水系与新构造应力场,地理学报,37卷2期,111-122,1982.

[14] 张志安、吕鸿图、艾南山、马鸿良,洒勒山滑坡的构造应力分析,水土保持通报,3期,67-70,1983.

[2] Scheidegger,A.E.,The principle of antagonism in the Earth’s evolution,Tectophys,(55)T7-T10,1979.

[3] 艾南山、唐少卿,地表形态发育的对抗性原理,兰州大学学报,社会科学版,11卷,2期,122-130,1983.

[4] Gerber,E,K.,Scheidegger,A,E,,Erosional and stress-induced features on steep slopes,Z.Geomorph.Suppl.(18)38-49,1973.

[5] 艾南山,顾恒岳,华北地区水系及新构造应力场分析,重庆交通学院学报,2期,18-27,1982.

[6] Ai Nanshan,Scheidegger,A,E.,Yalley trends in Tibet,Z,Geomorph.,(25)203-212,1981.

[7] Ai Nanshan,Scheidegger,A,E.,The tectonic stress field in North Chiaa.兰州大学学报,自然科学版,18卷4期,157-176,1962.

[8] Scheidegger,A,E.,Principles of Geodynamics,Spting-Vcrlag,1982.

[9] Kohlbeck,F.,Scheidegger,A,E.,On the theory of the evaluation of joint orientation measuremeLts,Rock Mech.,(9)9-25,1977.

[10] 徐叔鹰、李吉均、艾南山,巴基斯坦波特瓦尔高原构造地貌研究,地理科学,2卷 2期,125-134,1982.

[11] 艾南山、伍光和,赵镇,祁连山冷龙岭冰川分布与新构造应力场,兰州大学学报,自然科学版,18卷4期,182-183 1982.

[12] 复旦大学数学系主编,概率论与数理统计,第二版,上海科学技术出版社,1961.

[13] 艾南山、架国昭、Scheidegger,A,E.,东南沿海水系与新构造应力场,地理学报,37卷2期,111-122,1982.

[14] 张志安、吕鸿图、艾南山、马鸿良,洒勒山滑坡的构造应力分析,水土保持通报,3期,67-70,1983.

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