张会平,
郑德文,
李朝鹏,
肖霖,
李又娟
中国地震局地质研究所, 地震动力学国家重点实验室, 北京 100029
基金项目: 国家自然科学基金项目（批准号：41772198）和国家自然科学基金优秀青年项目（批准号：41622204）共同资助
详细信息
作者简介: 王一舟, 男, 28岁, 博士后, 构造地质学专业, E-mail:wangyizhou2017@sina.com
中图分类号: P931.2;P542 收稿日期:2017-09-03
修回日期:2017-11-10
刊出日期:2018-01-30
River longitudinal profiles under transient state and the related tectonic signals
Wang Yizhou,Zhang Huiping,
Zheng Dewen,
Li Chaopeng,
Xiao Lin,
Li Youjuan
State Key Laboratory of Earthquake Dynamics, Institute of Geology, China Earthquake Administration, Beijing 100029
MSC: P931.2;P542
--> Received Date: 03 September 2017
Revised Date: 10 November 2017
Publish Date: 30 January 2018
摘要
摘要:活动造山带的河流水系深受区域构造活动影响，记录了丰富的构造活动信息。水力侵蚀方程将构造抬升、河流侵蚀与地形变化相结合，使得可以从河流高程剖面中恢复区域的隆升历史。传统的研究主要利用稳态方程计算河道陡峭系数来表征区域隆升的空间分布特征。随着数学物理方法和计算机技术的发展，越来越多的****开展了对非稳态方程的研究。这些研究主要包括：1）依据裂点溯源迁移模型，计算裂点迁移速率（包括垂直和水平分量），以此估算流域的地貌响应时间；2）对于满足线性条件（河流侵蚀速率与河道坡度呈线性关系）的流域，求得线性非稳态方程的解析解，以此模拟区域隆升历史；3）对于非线性的情况，一般假设区域隆升速率不随空间变化，计算非线性方程的解析解，并据此判别不同时期的构造活动的信号是否可以被全部保留在河道上，即判断是否存在构造信息丢失。对于隆升速率随时间和空间均存在变化的情况，如何求解这一类方程，是一大难点，也是水力侵蚀模型今后的发展方向。
关键词: 水力侵蚀方程/
非稳态/
裂点/
χ-z plot/
构造活动
Abstract:The landscape evolution of active orogens can be regarded as the coupling between climatic change and tectonic movement. Rivers originating from and flowing through orogens have been affected and reshaped by regional rock uplift and deformation. The related tectonic signals, as a result, can be recorded and stored in stream longitudinal profiles. The stream-power river incision model, combing bedrock uplift, river incision, and topographic evolution, makes it possible to extract the spatial and temporary details of rock uplift.
The well known stream-power river incision model is expressed as a non-linear partial differential equation (PDE), in which the temporal variation of bedrock channel elevation is the competition between rock uplift and channel incision. During the past 40 years, studies had been on its steady-state form. Assuming that the river profile is under a steady state with spatially invariant rock uplift, a power-law scaling between channel slope and drainage area can be derived. Then, a steepness index is yielded to quantify the spatial pattern of rock uplift rates.
However, the landforms in active orogens are usually in a transient state where rock uplift cannot be balanced by river incision. With the development of mathematics and computer science, more and more scholars have been working on the solutions (both analytical and numerical)of the transient PDE. Based on the stream power incision model (allowing both spatially and temporarily variant rock uplift and a non-linear relationship between river incision and channel gradient), the velocity of knickpoint migration was derived. Then, the landscape response time could be calculated by dividing the river length by the horizontal velocity of knickpoint migration. Both knickpoint migration velocity and landscape time vary a lot between linear and non-linear conditions.
For the linear condition, knickpoints migrate upstream in the same horizontal velocity that depends on erodibility and drainage area. The landscape response time shows no relation with rock uplift rate. Thus, the "older" knickpoints cannot be erased by "younger" ones, leaving a full rock uplift history. To model the rock uplift history, the χ-z plot is divided into a series of segments. Each segment can be regarded as a normalized time interval and elevation difference. By dividing the elevation difference by time interval, we can get the transformed rock uplift rate at the specified time.
While for the non-linear condition, the horizontal velocities of knickpoints migrating upstream vary largely. Those "older" knickpoints might be erased by "younger" ones. The landscape response time depends on the rock uplift rates before and after the tectonic event. Therefore, some details of rock uplift will be lost owing to the non-uniform velocities. Assuming spatially invariant rock uplift, the analytical solution to the PDE was derived. For two conditions (n < 1, rock uplift rate increases, or n > 1, rock uplift rate decreases), a full rock uplift history will be stored and a "stretch zone" was present along the χ-z plot. When n > 1, rock uplift rate decreases, or n < 1, rock uplift rate increases, the "slope patch" generated elder will be partly eased, resulting into a "consuming knickpoint". However, spatial information from the non-linear transient equation is still confusing.
Key words:stream-power river incision model/
unsteady state/
knickpoint/
χ-z plot/
tectonics
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