2015, Vol. 58
2. 中国科学院大学, 北京 100049
2. University of Chinese Academy of Sciences, Beijing 100049, China
The tectono-thermal modeling is based on a two-dimensional non-instantaneous extension model using the finite element algorithm in the Lagrangian system. By solving the heat conduction equation, the thermal history and tectonic subsidence history of the basin are modeled simultaneously.
The results are as follows: (1) Initial crustal and lithospheric thicknesses have great influence on tectono-thermal modeling, especially on the tectonic subsidence. (2) Compared to the model considering heat conduction in the asthenosphere only, the heat convection model has slower tectonic subsidence and thermal decay rates, and temperature from lower crust to the bottom of the model is significantly higher. (3) The fixed or moving upper boundary during the modeling affects the calculated heat flow and tectonic subsidence in the thermal subsidence phase, and has remarkable influence on the temperature field. The effect increases with the increasing of the stretching factor. (4) Rift flank uplift of the water loading model would disappear within 200 Ma while the uplift would be stable at a certain value for the sediment loading model.
If the initial crustal and lithospheric thicknesses are uncertain in the modeling, sets of initial thicknesses should be given. The optimum initial crustal and lithospheric thicknesses can be determined when the calculated heat flow, Moho depth and lithospheric thickness fit observed values best. Pure heat conduction and pure heat convection in the asthenosphere are two limiting cases for extension models. In the rheological boundary layer, effects of both heat conduction and convection should be considered. For strong extensional areas, using the fixed upper boundary model would generate large calculation errors, especially in the temperature field. The thermal effect of sediment cannot be ignored when calculating the rift flank uplift.
沉积盆地构造-热演化模拟是盆地模拟的主要内容之一.构造沉降史与热流演化史构成其两大核心研究内容.拉张模型在描述拉张盆地沉降和热流演化方面取得了极大的成功，实现了构造和热的完美结合(何丽娟和汪集暘，2007).
McKenzie(1978)提出了一维瞬时均匀拉张模型.该模型认为，岩石圈的拉张在瞬时完成，由于岩石圈减薄，引起热的软流圈物质被动上涌，导致岩石圈被加热，在Airy均衡作用下形成初始沉降.拉张结束后，岩石圈进入热冷却阶段，地表在初始沉降的基础上继续发生热沉降.该模型是运动学模型的代表模型，能很好地预测盆地主要观测数据，为以后研究拉张盆地构造热演化奠定了基础.考虑到岩石圈拉张不可能瞬时完成，学者们进一步提出有限匀速拉张模型(Jarvis and McKenzie， 1980).何丽娟(1999)提出了匀减速拉张速率模式，更接近实际情况.一些学者在均匀拉张模型的基础上提出了纵向非均匀拉张模型，如双层非均匀拉张模型(Royden and Keen， 1980; Hellinger and Sclater， 1983; Dehler et al., 1997)、 与深度相关的拉张模型(Rowley and Sahagian， 1986; Davis and Kusznir， 2004; Kusznir and Karner， 2007; Rosenbaum et al., 2008).上述拉张模型多假设岩石圈拉张变形为纯剪变形，但实际上变形并非总是对称的.Wernicke(1985)提出了简单剪切拉张模型，但迄今研究者并未观测到切穿整个岩石圈的断裂.为此，学者们用耦合的简单剪切/纯剪切模型来描述不对称拉张的情形，具有一定的实用性(Kusznir and Ziegler， 1992; Clift et al., 2002; Baur et al., 2010; Chen et al., 2013).一些盆地在地质历史时期曾经历过多期拉张，且具有继承性，多期拉张模型由此被提出(Wang et al., 1996; Dehler et al., 1997; He et al., 2002; Lin et al., 2002). White(1994)以及White和Bellingham(2002)提出了利用沉降数据反演岩石圈拉张期间一维和二维应变速率的方法，该方法不需要知道岩石圈拉张持续时间、拉张期次等先验信息，在一些地区得到了较好的应用(Xie et al., 2006; Shillington et al., 2008; Song et al. 2010; Chen，2014).考虑到盆地拉张过程中可能的构造反转，研究者们进一步建立了适用于多期伸展和挤压交替的复杂过程的数值计算模型(Negredo et al., 1999; He and Wang， 2004; 赵长煜等，2010).以上模型均为运动学模型，岩石圈变形通过定义的速度场来实现，它们在预测盆地热流演化方面具有优势，但岩石圈流变性隐含在其均衡补偿模式中，无法反映岩石圈流变性及其变化对盆地构造热演化的影响，在预测盆地几何形态方面存在一定的缺陷(何丽娟，2000).
而在拉张模型的另一类模型，动力学模型中，岩石圈流变性则是通过本构方程明确体现，能够实现热学与流变学的耦合，深入理解盆地动力学的基本过程(Fernàndez and Ranalli， 1997).根据其本构方程，动力学模型可分为平面应变模型(Braun and Beaumont， 1989; Bassi，1991; Chéry et al., 1992; Huismans and Beaumont， 2008; Van Avendonk et al., 2009; Huismans and Beaumont， 2011)和平面应力模型(Sonder and Engl and ，1989; Bassi and Sabadini， 1994; Polyansky，2002).由于目前对盆地成因的动力学根本机制还不甚了解，以及模型初始扰动的给定、岩石圈流变学参数的不确定性等都在一定程度上阻碍了动力学模型的发展.
现有的拉张模型多采用固定的初始岩石圈、地壳厚度，软流圈多被赋予和岩石圈地幔相同的热参数，模型上边界的给定存在争议，且模型中较少地考虑沉积盖层的热效应.本文拟重点探讨拉张模型中初始地壳、岩石圈厚度、软流圈对流、模型上边界对构造热演化的影响，以及沉积盖层存在的情况下拉张盆地侧翼抬升的演化.文中的模拟均使用运动学模型，假定岩石圈为纯剪变形，利用有限元方法，在拉格朗日坐标系下，通过求解二维瞬态热传导方程来模拟盆地构造位移发生变化的同时，温度场和热流在时间、空间上的演化历史.
2 初始岩石圈、地壳厚度对构造热演化的影响多数拉张模型都假定拉张开始前模型的初始岩石圈厚度为125 km(McKenzie，1978; Jarvis and McKenzie， 1980; He et al., 2002; Lin et al., 2002; He and Wang， 2004; 陈林等，2008; Song et al., 2010; Chen，2014)，这也是大洋岩石圈厚度的渐进值(Parsons and Sclater， 1977)，该值在拉张开始前岩石圈未经历拉张或破坏的情况下往往是适用的.然而，在一些地区拉张开始前岩石圈厚度已经发生了较大的变化，比如中生代的华北克拉通.这时，需要根据实际需要选取合适的初始岩石圈厚度.
对于初始地壳厚度的选取，往往依赖于现今的Moho面深度.Dehler等(1997)在计算加拿大西缘夏洛特皇后盆地的构造热演化时使用的初始地壳厚度为34 km，He和Wang(2004)在模拟济阳坳陷 的热史时给定的初始地壳厚度是36km，Chen(2014)模拟南海白云凹陷时采用的初始地壳厚度为30 km，这些模型预测的剖面现今Moho面深度都和实际观测值接近.
为了了解初始地壳、岩石圈厚度对构造热演化的影响，本文建立了两组模型(图 1).图 1a和b固定初始地壳厚度为35 km，模型拉张10 Ma，拉张系数为1.5，热沉降20 Ma，计算不同初始岩石圈厚度下的构造沉降史及热流演化史.图 1c和d是固定初始岩石圈厚度为110 km，改变初始地壳厚度，计算构造沉降量及热流值.模拟中使用的参数见表 1.结 果显示，当初始地壳厚度恒定，初始岩石圈厚度从70 km增加到120 km时，计算得到的构造沉降量会随之减小，最大差异达660 m以上；热流也随着初 始岩石圈厚度的增加而降低，最大差异近25 mW·m-2. 当初始岩石圈厚度恒定，初始地壳厚度从31 km增加到41 km时，构造沉降量随之增大，最大差异超过900 m；热流也与初始地壳厚度成正比，但最大差异不到6 mW·m-2.由此看出，初始岩石圈、地壳厚度的选择，对构造热演化的影响非常大，尤其是对构造沉降量的影响尤为显著.
 | 图 1 初始地壳、岩石圈厚度对构造-热演化的影响Fig. 1 Effects of initial crustal and lithospheric thicknesses on tectono-thermal modeling |
 | 表 1 模型中使用的参数Table 1 Parameters and values used in modeling |
实际计算中，当拉张开始前的初始地壳、岩石圈厚度未知时，可给出多组初始厚度值.每给出一组初始地壳、岩石圈厚度值，通过模拟就可以计算得到一组现今热流、Moho面深度及热岩石圈厚度值，将计算值与观测值相对比，通过不断调整初始地壳、岩石圈厚度值，即可反推得到模拟剖面的最佳初始地壳、岩石圈厚度值.
3 软流圈对流对构造热演化的影响大部分拉张模型是将软流圈和岩石圈地幔赋予 相同的热导率，在计算中仅考虑热传导作用(McKenzie，1978; Keen and Dehler， 1993; He et al., 2002; Lin et al., 2009; Chen，2014).而Lachenbruch(1978)首次指出了拉张背景下对流在热传递中的重要性.Steckler(1985)、Buck(1986)、van Wijk等(2008)都进一步指出被动裂谷作用会引起软流圈的小范围对流，其作为额外的热源会对沉降、抬升史及温度场产生重要影响.
为了讨论软流圈对流对构造热演化的影响，本文采用等效热传导率综合考虑软流圈热传导和热对流因素(范桃园和安美建，2009).事实上，通过在热传导方程中提高热导率以等效模拟对流的热效应的 方法已广泛被学者们采用(Morgan and Chen， 1993; Chen，2001; Spinelli and Harris， 2011; 杨少华和石耀霖，2013; Schmeling and Marquart， 2014).在纯对流的情况下，相对于正常的热导率，提高的倍数往往为表征对流传热效率与单纯的热传导效率之比的努塞尔特数，Nu(Morgan and Chen， 1993; Chen，2001; Cochran and Buck， 2001; 杨少华和石耀霖，2013).在研究Nu随系统总体热状态变化特征中，实验和数值模拟都给出如下规律(Schubert et al., 2001; Turcotte and Schubert， 2002)：
 | 图 2 软流圈等效热导率对构造热演化的影响(拉张期为10 Ma，拉张系数为1.5，热沉降期为20 Ma) (a)构造沉降史；(b)热流随时间的变化；(c)温度-深度曲线.Fig. 2 Effects of asthenosphere equivalent thermal conductivity on tectono-thermal modeling (The extension lasts 10 Ma with a stretching factor of 1.5， and then enters thermal subsidence until 30 Ma)(a)Tectonic subsidence history；(b)Heat flow history；(c)Temperature-depth curve. |
软流圈纯传导模型的热流随时间的降低速度要比实际情况快得多，而软流圈纯对流模型计算的沉降量要比实际小得多，二者都与实际偏差较大.事实 上，纯传导的固体岩石圈与纯对流的流体软流圈之 间存在一过渡层，即流变边界层(Sleep，2006; Artemieva，2011; 图 3)，其间传导与对流共同作用来传递热量.在拉张模型中，同时考虑软流圈的热传导与对流更 接近真实的情况，纯传导与纯对流应作为其下限与上限.在模拟中，得知地幔对流的努塞尔特数Nu或瑞利数Ra时，可相应的判断软流圈等效热导率的上限.流变边界层的厚度对岩石圈本身的结构特征并不敏感，而主要受软流圈黏性系数η控制，其厚度与lg(η)成正比(He，2014).考虑到软流圈对流的瑞利数Ra与黏性系数η成反比，而由式(1)可知努塞尔特数Nu正比于Raβ，由此可推断地幔对流的努塞尔特数Nu越大，则流变边界层的厚度越小.这也意味着在拉张模型中，流变边界层厚度小的地方，流变边界层中等效热传导率的上限变大，而其下纯对流软流圈的等效热导率为Nu倍的正常地幔热导率，也相应大于流变边界层厚的地方的软流圈等效热导率.其对构造热演化的影响由上述模拟结果可以得知，流变边界层厚度小的地方，构造沉降量速率变慢，总构造沉降量变小，而热沉降过程中热衰减变缓，热流降低的总幅度变小.
 | 图 3 温度(T)、地温梯度(G)随深度的变化(纯传导的 岩石圈与纯对流的软流圈之间为流变边界层RBL，改自He，2014)Fig. 3 Variations in temperature(T) and temperature gradient(G)with depth(The transition layer between the conductive lithosphere and the convective asthenosphere is the rheological boundary layer RBL，modified from He，2014). |
现有的拉张模型对其上边界采用两种处理方法.一种是整个过程一直固定上边界，其并不随计算 出的沉降量而作调整(McKenzie，1978; Rowley and Sahagian， 1986; Keen and Dehler， 1993)，是对模型的一种简化；另一种则是根据均衡补偿得到的构造沉降量对模型上边界在垂向上不断进行调整，更真实的还原盆地的演化过程(Wang et al., 1996; He and Wang， 2004; Wangen et al., 2008).为了探讨固定与移动边界对构造热演化的影响，我们建立了以下两组模型.一组模型的拉张时间为10 Ma，之后裂后热松弛持续100 Ma(图 4a和b).另一组模型的拉张时间为40 Ma，裂后热沉降时间同为100 Ma(图 4c和d).两组模型都在拉张系数分别为2、4和6时，对比固定与移动上边界模型的计算结果.结果显示，当拉张时间为10 Ma时，固定与移动上边界对拉张期的热流及沉降量影响甚微；但当拉张时间增加为40 Ma时，模型上边界的处理方式对拉张期的热流及初始沉降产生了明显的影响，尤其是在拉张系数较大的情况下，但这种影响小于热沉降期两种模型的构造-热演化差异.当拉张系数为6时，拉张结束时两种模型的热流差异为0.3 mW·m-2，初始沉降量差异为30 m(图 4c和d).在热沉降阶段，无论拉张时间的长短，固定与移动上边界模型的热流及构造沉降的差异随热沉降的持续均逐渐变大，移动边界模型的热流大于固定边界的，而构造沉降量小于固定边界模型求得的值.但上述两组拉张时间不同、热沉降时间相同的模型在热沉降结束时，由于上边界处理方式不同造成的热流、总沉降量及温度场的差异相差并不大，以下结果以拉张时间为40 Ma的一组模拟为例.拉张系数为2时，固定与移动上边界模型的热流及构造沉降的最大差值分别为0.7 mW·m-2及85 m；当拉张系数为4时，二者的热流及构造沉降最大差异增大为1.7 mW·m-2和162 m；当拉张系数进一步增大到6时，两种模型的热流最大差异变为2.4 mW·m-2，构造沉降量的最大差异为198 m(图 4c和d).在温度场方面，从图 4e—g可以看出，固定与移动上边界模型的温度结构有着明显的差别，尤其是在岩石圈部分，相同深度上，固定边界模型的温度比移动边界模型的温度高几十到上百摄氏度.当拉张系数分别为2、4和6时，两种模型在同一深度上温度的最大差异分别为95、161及185 ℃.
 | 图 4 固定与移动上边界模型的构造热演化结果对比 图a和b是拉张时间为10 Ma、热沉降时间为100 Ma时的计算结果，图c—g是拉张时间为40 Ma、热沉降时间为100 Ma的结果，图a和c为两种模型计算的热流差值的绝对值随时间的变化，图b和d为构造沉降量差值的绝对值，图e—g为不同拉张系数下热沉降结束时的温度-深度曲线.Fig. 4 Comparison of tectono-thermal evolution between fixed and moving upper boundary models (a) and (b)The extension lasts 10 Ma.(c)—(g)The stretching period is 40 Ma. In all figures，the thermal subsidence period lasts 100 Ma.(a) and (c)are absolute values of differences of the calculated heat flow between the two models.(b) and (d)are absolute values of differences of the calculated tectonic subsidence.(e)，(f) and (g)are temperature-depth curves at the end of post-rift thermal subsidence stage with different stretching factors. |
总体上看，模型上边界对构造热演化的影响随着拉张系数的增大而增强.相比于模型上边界的给定对热流及构造沉降量的影响，其对模型温度场有着更为显著的影响.从上述讨论也可以看到，当计算主要针对热流及构造沉降量时，在拉张系数小于2或是拉张时间小于10 Ma且只关注于拉张期的热流及构造沉降变化时，两种模型的计算结果差异并不大，使用固定上边界模型的计算结果也是可接受的.但在拉张强度较大的地区，如中国南海的莺歌海盆地等(拉张系数大于4，He et al., 2002)，使用简化的固定上边界模型将对计算带来较大的误差.
5 拉张盆地的侧翼隆起裂谷的侧翼隆起常作为拉张盆地及张裂大陆边缘的边界，其是拉张盆地模拟的重要组成.学者们提出了多种机制来解释拉张盆地的侧翼隆起：(1)由拉张岩石圈向未拉张区域的侧向热传导(Alvarez et al., 1984; Buck et al., 1988; Leroy et al., 2008)；(2)由拉张引起的小规模地幔对流造成的裂谷之下向侧翼的热传递(Keen，1985; Buck，1986)；(3)裂谷侧翼之下相比于地壳减薄更强的岩石圈地幔减薄(Hellinger and Sclater， 1983; White and McKenzie， 1988; Dehler et al., 1997)；(4)拉张过程中通过向上挠曲对裂谷侧翼的力学支持(Braun and Beaumont， 1989; Weissel and Karner， 1989; Chéry et al., 1992; Kooi et al., 1992; van der Beek et al., 1994). 一般认为裂谷的侧翼隆起会在拉张结束后的几百万年内随着热衰减而消失(Weissel and Karner， 1989; ten Brink and Stern， 1992).而另有观测数据显示一些裂谷侧翼的隆升可以长期维持，如非洲南部的大陡崖，有学者用具较大强度的岩石圈的挠曲均衡回弹来解释这一现象(Weissel and Karner， 1989; ten Brink and Stern， 1992).但这些模型是在空盆载水的前提下讨论的，忽略了沉积物的热效应.本文重点讨论在载水及载沉积物两种情况下由侧向热传导造成的盆地边缘抬升的差异.
模拟采用二维非均匀拉张模型，拉张系数分布 如图 5a所示，拉张10 Ma，之后为热沉降期.本文计算了载水、载热导率分别为2.2 W·m-1K-1及1.6 W·m-1K-1 的沉积物三组模型的构造沉降/抬升史.结果显示，三组模型的盆地侧翼随着拉张逐渐抬升，但最大抬升量都并非出现在拉张刚结束时，而是在拉张结束后的6—10 Ma内侧翼抬升到最高，之后慢慢消减(图 5b—f).上述计算中，载水模型的盆地侧翼最大抬升量为273 m，小于载沉积物模型的侧翼最大抬升量；而热导率为1.6 W·m-1K-1的沉积物模型比热导率为2.2 W·m-1K-1的沉积物模型的侧翼最大抬升量略大，二者分别为497 m及489 m(图 5e).模拟结果同时显示，离拉张区域越远，盆地侧翼的抬升量越小(图 5e和f).值得注意的是，载水模型的盆地侧翼隆升会在200 Ma左右消 失，而考虑了沉积物的模型其侧翼隆升则会在200 Ma 左右稳定于某个数值，也就是说侧翼隆升并没有随时间消失.沉积物 热导率为2.2 W·m-1K-1的模型的盆地侧翼隆升最终维持在180 m左右，而沉积物热导率为1.6 W·m-1K-1 的模型的侧翼隆升量则会稳定于约245 m(图 5e).这可能是由于沉积物与盆地基底热导率差异产生的热折射效应造成的.由于沉积物的热导率较小，盆地基底的热导率大于沉积盖层的，隆起处的温度低于凹陷区的温度，凹陷处的热会向相邻隆起处转移，使得盆地凹陷处的热流降低，而隆起处的热流增加(熊亮萍和高维安，1982; 熊亮萍和张菊明，1984; Wang et al., 1985). 在沉积盖层与基底的交界处，具有最大的水平热流值.经过长时间的热松弛后，温度场达到稳定.载水模型的温度场可以在一定时间的热冷却后恢复到初始值.而由于沉积层的热效应，载沉积物的模型盆地边缘的温度明显比载水模型的温度高，在不考虑剥蚀的情况下，前者的盆地侧翼抬升能维持在某一水平.沉积盖层与基底热导率差异越大，这种效应越明显，也因此产生更大的盆地侧翼抬升.
 | 图 5 载水和载沉积物模型的盆地侧翼隆起效应 拉张时间为10 Ma，拉张系数为a图所示，图b—d为不同模型的构造沉降演化图，图e和f分别为拉张前x=-40 km及x=-30 km处两点的抬升量随时间的变化.Fig. 5 Rift flank uplift of water and sediment loading models The extension lasts 10 Ma.(a)Distribution of stretching factor.(b)，(c) and (d)Graphs of tectonic subsidence history for different models.(e) and (f)Variations of uplift with time at two points x=-40 km and x=-30 km，respectively. |
(1)拉张模型中改变初始地壳、岩石圈厚度会对计算的构造沉降量及热流值产生很大影响.模拟中可根据需要选取多组初始地壳、岩石圈厚度值，将模拟结果与观测值进行对比以确定最佳初始值.
(2)软流圈对流对构造热演化的影响很大.软流圈纯对流及纯传导模型是拉张模型的两种极限，在流变边界层中应同时考虑热传导与对流.得知地幔对流的努塞尔特数Nu时，可相应的判断软流圈等效热导率的上限.
(3)模型上边界对构造热演化的影响随着拉张系数的增大而增强，固定与移动上边界对热沉降期的热流及构造沉降量的影响比拉张期的大.两种模型得到的温度场有着较为明显的差别.
(4)沉积盖层的热效应对裂谷盆地侧翼隆起影响显著.载沉积物模型的盆地边缘抬升可以长时间维持，而载水模型的侧翼抬升则会在拉张结束后逐渐消失.
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