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。

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, λ₀ 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°), (α₁-45°, α₁+45°) 3) Denote A=(α₁+α₂)/2, B=A+90, then compute new concentrated degree . in and 4) Suppose _β1=max , then β₁ is the first preffered direction. Similarly, if _β2=max, then β₂ is the second preffered direction. By computing it is found that the choice of power {λ_i} is important. We call η=λ₀/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, λ₀ 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°), (α₁-45°, α₁+45°) 3) Denote A=(α₁+α₂)/2, B=A+90, then compute new concentrated degree _z. in and 4) Suppose _β1=max , then β₁ is the first preffered direction. Similarly, if _β2=max, then β₂ is the second preffered direction. By computing it is found that the choice of power {λ_i} is important. We call η=λ₀/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.