断层面高精度形貌学定量研究
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摘要
?地震时大部分形变发生在断层带内的主滑动面上,断层表面形貌是断层活动的产物并随断层滑动距离而演化。断层面形貌已成为研究破裂成核作用及应力的非均匀分布、断层面凸体磨损、断层泥生成、滑润作用、抗剪强度与临界滑动距离的相关内容,因此断层面形貌研究对地震和断层力学具有重要意义。任何一个野外天然断层面露头,它所表现的几何和形貌特征都是内、外营力共同作用的结果,断层面形貌特征不仅仅反映了断层的力学机制和运动特征,还与断层出露后各种侵蚀、风化作用相关。因此断层面形貌学研究对于判断断层活动时间和古地震研究具有重要意义。
本论文以断层面形貌作为研究对象,利用3D激光测量技术和分形方法在野外微观尺度上分析汶川地震地表破裂面、出露基岩断层面形貌风化特征,定量研究断层面形貌与断层运动、破裂方式和风化侵蚀作用的关系。另外,为研究断层崖形态的演化过程,建立一组不同角度人工坡面,通过高精度、长期的观测,力图获取坡面演化过程中各模型参数,最终推导出可应用于断层崖演化的精确数学模型。
1、断层面形貌描述与测量方法
迄今为止,人们对断层面形态进行了大量的研究,总结起来,研究方法大致可分为统计学方法和分形几何方法两大类。统计学参数虽然简单、直观、容易计算,但由于断层面形貌的复杂性和尺度效应,统计学方法的平均化处理的方式很难提供断层面粗糙度形态的全面信息,而这一点又恰恰在断层面力学行为研究中至关重要。分形几何方法提供了一种十分有效的手段,能够获得独立于测量尺度的参数来表征表面形貌的几何性质。随着分形几何方法对断层面形貌特征研究的深入,人们认识到断层面无论是局部还是整体都表现出很好的自相似和自相仿结构。因此,分形几何学中的自相似性和自相仿性两类分形模型,是目前描述断层面形貌特征的较为适用的方法。
计算破裂面形貌分形几何学特征的方法很多,本文选用能谱密度方法和均方值粗糙度方法计算天然断层面形貌分形特征。能谱密度法是基于时间序列分析的数学方法,它是把空域(或时域)信息转换到频率域的强有力工具,更加突出单个频率或波长的信息,可以揭示不同波长成分对表面粗糙度的影响及表征表面形貌各向异性特征。均方值粗糙度法通过在不同取样尺度、不同方向下计算剖面均方值,突出表现形貌的各向异性特征。
这两种方法是基于大量平行的1D剖面线来分析断层面形貌特征的。对于一断层面,在?断层面数字高程模型(DEM)上提取一组特定方向的剖面线,然后平均所有1D剖面线计算结果来描述断层面在这个方向的形貌特征。在0°～180°方向(断层面走向为0°)上重复上述分析过程,这样就可以量化断层面形貌各向异性特征。为了调查分析方法的可靠性和准确性,我们还使用人工合成自相仿表面模拟在野外所观察的天然断层面,分析方法的准确性通过评估应用于生成人工表面的“输入信号”与分析方法计算出的结果之间的差异进行判断,这些研究结果为分析断层面形貌特征提供量化可靠性估计。测试结果显示这两种计算方法对于描述各向同性破裂面是可靠的,对于描述各向异性破裂面时,误差不超过10%。
岩石破裂面形态的测量方法,主要有机械测量法和光学测量方法。本论文是基于高精度测量数据研究断层面形貌,因此选用目前较为先进三维激光测量技术。该技术在精度上完全满足野外微观尺度上数十平方米断层面形貌的测量,相对于传统表面粗糙测量仪器,大大提高了野外工作效率和测量精度,解决了断层面在野外微观尺度上形貌高精度测量问题。应用地面三维激光测量技术采集数据的工作过程大致可以分为计划制定、外业数据采集和内业数据处理三部分。在野外工作展开之前首先制定工作计划,根据测量任务确定测量目标和测量范围;测量过程中,根据测量需要布设测量控制点、确定扫描目标的分辨率;扫描得到的点云数据是一组三维点集,有效数据和无用的噪声混合在一起,在处理生成DEM之前必须经过数据处理,包括数据的滤波、控制点的拟合、空间坐标转换等。
2、汶川地震地表破裂面形貌特征
准确描述破裂面形貌对于我们理解地震断层作用是非常重要的,破裂面的形貌特征包含了许多关于地震和断层机制的有用信息。2008年汶川Ms8.0地震产生了两个新鲜的破裂面,八角庙破裂面和沙坝破裂面,我们使用3D激光扫描仪(Trimble GX)对两个破裂表面进行测量,在野外微观尺度上研究了汶川地震破裂面的形貌特征。
通过能谱密度和均方值粗糙度两个方法分析破裂面形貌,分析结果表明新鲜的破裂面表现为自相仿性,能谱密度和均方值均与剖面长度存在幂律关系,破裂面在垂直滑动方向比平行滑动方向粗糙。在能谱密度与空间频率的对数图中,能谱密度曲线存在明显的拐点,表明单一分形不能准确描述破裂面形貌。该拐点所对应的波长称为“特征坡长”,八角庙破裂面在平行滑动方向上的特征波长为7mm,在垂直方向上特征波长略大一些(区域Ⅰ为10mm,区域Ⅱ为9mm);沙坝破裂面在平行滑动方向上的特征波长为8mm,但垂直方向上特征波长略小(6mm)。在均方值与剖面长度的对数图中,均方值曲线的最小二乘拟合直线的斜率为Hurst指数,该指数依赖于剖面方向与断层面擦痕方向的关系,H指数的最小值和最大值分别与平行擦痕和垂直擦痕方向对应。各破裂面的H指数极坐标图所标识出的断层擦痕方向与在野外破裂面擦痕侧伏角测量结果一致。沙坝破裂面的H指数极坐标图中存在次级H指数极值(对应剖面线方向为85o和160o),这揭示破裂面上存在一组隐匿擦痕。该组隐匿擦痕为汶川地震之前断层活动中形成的,但目前我们获得的该破裂的分型特征还不足以推测上一次断层活动的时间和规模。
另外,以往的研究表明未受错动改造的天然张裂面的H指数等于0.8,天然正断层面在垂直擦痕方向H指数小于0.8。沙坝破裂面虽然在深部逆冲造成西北盘上升,但西北盘近地表在上升的过程中存在向西的旋转,造成在近地表的拉张正断特征,在垂直擦痕方向上H指数小于0.8(0.72±0.029);八角庙破裂面在垂直擦痕方向上H指数为(域Ⅰ,0.84±0.024)和(域Ⅱ,0.83±0.041),均大于0.8,与该破裂面为挤压逆冲性质相关。这个观测结果表明,与前人结论基本一致,垂直擦痕方向的H指数与断层类型相关。
能谱密度曲线斜率(-α)与能谱曲线斜率(H)在理论上存在一个简单的线性关系,然而,我们用上述两种方法得到的结果不能严格满足公式α=1+2×H。通过线性拟合,在全频率域上α和H满足线性关系:α=1.22+1.72×H。这个差异是由于测量信号噪音、破裂面的多分形性和分析方法的差异造成的。
3、基岩断层面形貌风化特征
任何一个野外天然基岩断层面露头,其所表现的几何和形貌特征都是内、外营力共同作用的结果。断层面形貌特征不仅仅反映了断层的力学机制和运动特征,还与断层出露后各种侵蚀、风化作用有关。在许多活动构造区域,基岩断层崖是断层多次活动的长期结果,理论上这些基岩断层面的形貌特征记录了很多关于断层活动的信息,隐含着有价值的“古地震”记录,但很难被识别出来,因此,基岩断层崖不被认为是判断过去地震事件的“灵敏指示器”。实际上,在不同时期地震活动而出露的断层面之间,还是存在表面风化程度和生物(藓类)集群规模的区别,如果能够建立一种断层面的出露时间与风化程度的经验关系,就可以推测出地震发生时代。本文通过对施庄断裂不同出露历史的断层面形貌特征的研究,定量分析了风化作用对断层面形貌的影响。
无论是遭受风化侵蚀的断层面,还是新剥露出的断层面,破裂面的能谱密度和均方值均与取样长度存在幂率关系,断层面形貌表现为自相仿性。各扫描断层面H指数极坐标图极值的分布特征表明,近水平方向擦痕是控制断层面形貌特征的最主要因素。将施庄断层面能谱密度曲线与其他滑动距离不等断层面进行比较,发现施庄断层属于大滑距断层,在近水平方向上滑动距离不小于十米。除了内营力,外营力也是决定断层面形貌特征重要因素。风化作用不但使断层面形貌变得粗糙,而且改变断层面各向异性特征。断层面出露时间越长,断层面形貌的各向同性特征越明显。断层面形貌各向异性减弱和各向同性的增强是由于外营力(水和空气)的风化和侵蚀作用具有的随机性造成的。
在垂直滑动方向和平行滑动方向的断层面能谱密度图中,可分别用不同变量表示断层面形貌的风化程度。在垂直断层滑动方向,断层面短波长(高频)起伏更易受到侵蚀风化。随着风化程度的加深,垂直滑动方向的能谱曲线偏离天然断裂能谱范围,存在一个简单的规律:断层面出露时间越长,起始偏离能谱范围的波长越长。平行于滑动方向能谱密度曲线上存在一个值得注意的现象,波长在5mm～30mm范围上,平行滑动方向的能谱密度曲线存在一个向上凸起的变化,以至于平行于滑动方向能谱接近垂直滑动方向的能谱。拐点波长与断层面风化程度相关,风化越严重,拐点波长越长。将垂直擦痕方向上的偏离能谱范围的起始波长和平行擦痕方向上的能谱曲线拐点波长之间进行线性分析,分析结果显示两者之间存在很好的线性关系。这说明断层面形貌与风化历史成线性关系,这与其他研究者在不同地区所获得的结论相一致。
通过3D激光扫描仪对断层面进行高精度测量,我们发现断层面上存在明显的椭圆凸起,这些椭圆凸起的长轴平行于近水平擦痕,即平行于断层滑动方向。沿整个施庄断裂出露的断层面上,分布多个椭圆凸起结构,凸起结构表现不完整,多数凸起被斜交的阶步破坏。这些凸起是基岩研磨物质和角砾混杂固结而成的,类似于透镜体并依附于断层面上。这些凸起可以看作是在野外微观尺度上的凹凸体,微观尺度上的凹凸体是影响断层面近场应力分布和滑动分布的重要因素。椭圆形凸起在其他断层面也曾被报道过,表明这些凸起是断层成熟过程中的断层面形貌特征之一。
4、人工坡面形态演化
在松散沉积物中断层崖形态的演化可以被准确的模拟,在加以适当校正的情况下,可以提供一些断层崖演化的高精度数字模型,这些模型是确定断层崖出露年龄的基础。本文通过建立一组不同角度人工坡面研究断层崖演化过程,所修建的不同角度坡面代表了断层崖演化过程中的不同阶段,高角度坡面代表了断层崖演化初期阶段,低角度坡面代表断层崖演化晚期阶段。通过长期的高精度观测,获取坡面演化过程中各模型参数,最终推导出断层崖演化的精确数学模型,为判断断层面(或断层崖)出露时代提供一个实用的手段。
松散堆积组成的断层崖一般经历2个不同的演化过程:早期的不稳定过程和晚期的扩散过程,处于这两个阶段的断层崖分别称为松散限制型断层崖和搬运限制型断层崖,不稳定阶段自由面后退速率C和扩散阶段物质扩散系数K是断层崖反演断层活动时间的重要参数。对于同一坡面,每期测量使用相同的控制点,因此可将各期测量结果转化到相同坐标系统中,通过比较不同期次测量结果,可以获得坡面在不同时期内的坡面的侵蚀情况。目前人工坡面正处于不稳定阶段,自由面后退速率可直接应用于该阶段演化模型的校正。根据一年的测量数据分析,不同角度坡面的后退速率存在差异。30°坡面后退速率为8.19±1.16mm,但由于30°坡面小于休止角,黄土碎屑物很快将自由面覆盖,之后进入扩散演化阶段。大于休止角的坡面中,50°坡面后退速率最大,为7.41±0.84;其次是80°坡面,为6.74±0.26 mm;70°坡面后退速率最小,为5.34±0.15 mm。由于观测随时间较短以及坡面未被厚层松散堆积物覆盖,目前还未能得到精确的坡面扩散方程。
Principal slip surfaces in fault zones accommodate most of the displacement during earthquakes, and the topography of fault surface is the result of faulting and would evolve with slip. Fault surfaces affect all aspects of fault and earthquake mechanics, including rupture nucleation, fault gouge generation, lubrication, the near-fault stress field, resistance to shear, and critical slip distance. So the study of the fault surface has important significance to earthquake and fault mechanics. To any outcrop of a natural fault in the field, its characters of geometry and topography on the surface are the interacting result between the endogenetic force and the exogenic force. The topographic characters of the fault the surface can reflect not only the fault mechanics, motion and fracture mechanisms, but also the relation to the weathering and erosion after it outcropped in the field. So the study on the topography of fault surfaces has important significance to the determine the date of faulting and the research of ancient earthquakes.
This thesis focuses on the topography of fault surfaces, and uses the technique of 3D laser scanning and the fractal method to analyze the topographic characters of the rupture surfaces during the Wenchuan earthquake and the outcrop of natural faults on the field scale. The relationships were quantitatively analyzed among the surface topography , the type of fractures and the weathering and erosion. Moreover, to study the fault-scarp degradation process, a set of artificial fault-scarps with different slope angles were built. Through the high precise observation in a long time, this work attempts to get the model parameters in the evolutionary process, and finally deduce to the accurate mathematical model which can be applied to other fault scarps in the same region.
1. Description and field measuring method for topography of fault surface
Many studies have been done to the topography of fault surfaces heretofore, and the research methods can be divided into two categories, the statistical method and fractal geometry method. Statistical parameters can be calculated easily, but they cannot provide complete information which is very important to the study of mechanics of fracture surfaces. Moreover, as a result of the complexity and the scaling of the fault surface, and the traditional statistics cannot completely describe the topography of the fault surface. With the further research, the fault surfaces show the similar structures and the affine structure. The fractal is a mathematics model which is able to express unconventional geometry, and the two fractal concept, self-similar and self-affine, provide useful models which can be compared to natural fault surfaces.
There are many methods to calculate the characteristics of topography, Two methods, power spectral density and Root-mean-square (RMS) roughness, were used to quantitatively describe the topography of natural fault surfaces in this thesis. The power spectral density is a mathematical algorithm which is based on the time series analysis, and it converts the spatial information into frequency information. This method can reveal the influence of composition with different wavelength on the surface roughness. The RMS roughness method can highlight the characteristics of the anisotropic properties on the fault surface.?
For each surface, a set of 1D parallel profiles in a specific direction are extracted, descended and the analyzed. The properties are averaged over all the 1D profiles to characterize 2D surface in the chose direction. To study the azimuthal dependence of the properties of the surface, I have repeated to extract profiles in directions in the range 0°to 180°(the fault strike in0°). The reliability analysis for the methods is made using synthetic self-affine surfaces with a directional morphological anisotropy, and the results showed the methods were accurate to delineate the isotropic surfaces, and the calculation error is less than 10% for anisotropic surfaces.
The study of surface topography was based on the measuring with high accuracy, so the 3D laser scanning technology was used to survey and map the topography of the fault surfaces. According to the purposes of the work and the performances of the 3D scanner, the working-flow was set up, and the precision and reliability were evaluated. The results from the subsequent applications indicate that the accuracy of 3D laser scanning is satisfied for the surface measuring over an area as large as tens of square meters with high accuracy. Compared to the traditional technologies, 3D laser scanning technology greatly improved the field work efficiency and the accuracy of measuring, and solved the problem of measuring accuracy in the scale of field micro-topography for fault surfaces, so it provided a chance to study the topography of fault surfaces on this scale. The work of applying 3D laser scanner to collect data consists of making plane, field measuring and indoor data processing.
2. Topographic characteristics of rupture surface associated with the Wenchuan earthquake
It is very important to describe accurately the topography of rupture surfaces for understanding of seismic faulting, because the topographic characteristics of the rupture contain much information about the earthquake and fault mechanics. Two fresh rupture surfaces of the Mw7.9 Wenchuan earthquake in 2008, referred to as the Bajiaomiao surface and the Shaba surface, have been measured by scanning with a 3D portable laser scanner.
The acquired sets of DEM data are analyzed using power spectral and root-mean-square (RMS) roughness. The fresh rupture surfaces exhibit self-affine behavior, and the power spectral density and RMS roughness both have a power law relationship with the length of profiles. The roughness of the surface parallel to the slip direction is generally less than the roughness perpendicular to the slip direction. In log-log plot of power spectral density versus spatial frequency, there is an obvious inflexion which divides the spatial frequency into a lower frequency domain and higher frequency domain. The wavelength corresponding to the inflexion is called "characteristic wavelength" or "characteristic scale". It is 7 mm in the direction parallel to slip for the Bajiaomiao surface (both in PatchⅠandⅡ), smaller than that in the direction perpendicular to slip (10 mm in PatchⅠand 9 mm in PatchⅡ), and 8 mm in the direction parallel to slip, but larger than that in the direction perpendicular to slip(6 mm). The slope of the least squares fitting line to the RMS roughness curve in log-log plot is the H exponent, which depends on the direction of the profile and describe the morphological anisotropy of the fault surface . The slip directions indicated by the minimum H values, 85o and 75o on the Bajiaomiao surface, and 45o on the Shaba surface, are equal to the slip directions measured in the field. A secondary set of H-value peaks (85o and 160o) in Shaba rupture surfaces reveals a set of concealed striations produced by an earthquake prior to the Wenchuan event. But it is not sufficient to determine the time and magnitude of this inferred faulting event.
? Moreover, H value(PatchⅠ: H=0.84±0.024, PatchⅡ: H=0.83±0.041) of the topographic profile perpendicular to slip on the Bajiaomiao surface occurred on the reverse fault is larger than 0.8, and H value(H=0.72±0.029) of the profile perpendicular to slip on the Shaba surface occured on the normal fault is smaller than 0.8. Whether H value is larger than 0.8 probably relates to the type of the fault.
The H value of the topographic profile perpendicular to slip on the Bajiaomiao surface occurred on reverse fault is larger than 0.8, and that of the profile perpendicular to slip on the Shaba surface occurred on normal fault is smaller than 0.8. Whether the H value is larger than 0.8 is probably related with the type of the fault. By linear fitting between the slopes of power spectral density(-α) and the slope of RMS roughness (H) on whole length of profile, a relationship is constructed,α=1.22+1.72×H , it do not obey to theory relationship strictly,α=1+2×H. This variance probably is caused by the multi-fractal of the rupture surface and the statistic error.
3. characteristics of weathering topographic on bedrock fault surface
To any outcrop of a natural bedrock fault in the field, the geometry and morphological features are the interacting result between internal forcing and external forcing. The topographic characters of fault surface can reflect not only the fault mechanics, motion and fracture mechanism, but also relate to the weathering and erosion after being outcropped in field. Bedrock fault scarps potentially preserve valuable 'palacoscismic' records, interpreting this is difficult, and as a result , bed rock scarps are not considered to be sensitive indicators of the timing and magnitude of past faulting events. In fact, the weathering morphology of bedrock surfaces had recorded the information about faulting. In this work accurate measuring and analysis were done at five sites with different outcropped history on the Shizhuang fault, and influence of weathering erosion on the fault surfaces were quantitatively analyzed.
Regardless of the fault surfaces with weathering or the fault surface without weathering, the power spectrum density and root-mean-square(RMS)roughness have power law relationships to the length of profiles, and the topography of fault surfaces show the self-affine. Compared to other fault surfaces in terms of profile and power density, the Shizhuang fault is a large-slip fault, and the slip displacement is no less than 10 meters in nearly horizontal direction. The weathering not only made the fault surface rougher, but also changed the anisotropic characteristics of the surfaces. With the increase of the outcropping time, the isotropy characteristics of the topography of surface became more obvious, which is caused by the stochastic character of the external forcing.
In the power density plot of fault surfaces in directions of perpendicular to slip and parallel to slip, different variables can be used to quantify the weathering level of fault surfaces. The power density curve of profile perpendicular to slip gradually deviated from the range of power spectrum of natural fracture with the increasing of weathering degree, and it obeys a simple rule that the longer of weathering time , the wavelength deviated from the power spectrum range is longer. The power density curve of profile parallel to slip has a upward inflection point, and the wavelengths corresponded to inflection points related to the weathering level of the fault surface. The more serious the weathering , and longer the wavelengths correspond to inflection points. There is a linear relationship between these two kinds of wavelengths.
This work found many obvious elliptic bumps on fault surfaces by accurate measurements using 3D laser scanner, with the long axis parallel to the horizontal striations. These elliptic bumps, consists of the wear production of bedrock and the gravels, are similar to the lens and attach to the fault surface. These bumps can be regarded as "asperities" on a field scale, and the asperity is an important factor influencing near field of the stress distribution and slip. The elliptic asperity has been reported in others faults, which show that the elliptic asperities are one of topographic characteristics in the maturing process of the fault.
4. Degradation of artificial fault scarp
The degradation of fault scarps in unconsolidated deposits can be accurately simulated, and under the appropriate correction, the morphology of fault scarps provides a method to estimate the age of faulting . This work constructed a group of artificial fault scarps with different slope angle, and managed to get parameters of degradation model, and finally deduce the accuracy mathematic model of degradation in this region.
The degradation process of fault scarp has two stages, the unstable stage in the early period and the diffusion stage in the later period. At present, the artificial fault scarps are in an unstable stage, and the retreating rate of free face can be used directly to calibrate the model of this stage. According to the measuring data in one year, the backward rate of free face is not equal for different slope. The retreating rate of 30°slope is 8.19±1.16mm, and The loess detrital covered the free face soon and the degradation process entered the diffusion stage from the unstable stage. For the slopes with angle larger than the reposed angle, the retreating rate of a 50°slope is as high as 7.41±0.84mm; the backward rate of 70°slope is the lowest as 5.34±0.15mm. Owing to the limit of observation time and the slopes non-covered by unconsolidated deposits, the accurate diffusion equation has not been established yet.
本论文以断层面形貌作为研究对象,利用3D激光测量技术和分形方法在野外微观尺度上分析汶川地震地表破裂面、出露基岩断层面形貌风化特征,定量研究断层面形貌与断层运动、破裂方式和风化侵蚀作用的关系。另外,为研究断层崖形态的演化过程,建立一组不同角度人工坡面,通过高精度、长期的观测,力图获取坡面演化过程中各模型参数,最终推导出可应用于断层崖演化的精确数学模型。
1、断层面形貌描述与测量方法
迄今为止,人们对断层面形态进行了大量的研究,总结起来,研究方法大致可分为统计学方法和分形几何方法两大类。统计学参数虽然简单、直观、容易计算,但由于断层面形貌的复杂性和尺度效应,统计学方法的平均化处理的方式很难提供断层面粗糙度形态的全面信息,而这一点又恰恰在断层面力学行为研究中至关重要。分形几何方法提供了一种十分有效的手段,能够获得独立于测量尺度的参数来表征表面形貌的几何性质。随着分形几何方法对断层面形貌特征研究的深入,人们认识到断层面无论是局部还是整体都表现出很好的自相似和自相仿结构。因此,分形几何学中的自相似性和自相仿性两类分形模型,是目前描述断层面形貌特征的较为适用的方法。
计算破裂面形貌分形几何学特征的方法很多,本文选用能谱密度方法和均方值粗糙度方法计算天然断层面形貌分形特征。能谱密度法是基于时间序列分析的数学方法,它是把空域(或时域)信息转换到频率域的强有力工具,更加突出单个频率或波长的信息,可以揭示不同波长成分对表面粗糙度的影响及表征表面形貌各向异性特征。均方值粗糙度法通过在不同取样尺度、不同方向下计算剖面均方值,突出表现形貌的各向异性特征。
这两种方法是基于大量平行的1D剖面线来分析断层面形貌特征的。对于一断层面,在?断层面数字高程模型(DEM)上提取一组特定方向的剖面线,然后平均所有1D剖面线计算结果来描述断层面在这个方向的形貌特征。在0°～180°方向(断层面走向为0°)上重复上述分析过程,这样就可以量化断层面形貌各向异性特征。为了调查分析方法的可靠性和准确性,我们还使用人工合成自相仿表面模拟在野外所观察的天然断层面,分析方法的准确性通过评估应用于生成人工表面的“输入信号”与分析方法计算出的结果之间的差异进行判断,这些研究结果为分析断层面形貌特征提供量化可靠性估计。测试结果显示这两种计算方法对于描述各向同性破裂面是可靠的,对于描述各向异性破裂面时,误差不超过10%。
岩石破裂面形态的测量方法,主要有机械测量法和光学测量方法。本论文是基于高精度测量数据研究断层面形貌,因此选用目前较为先进三维激光测量技术。该技术在精度上完全满足野外微观尺度上数十平方米断层面形貌的测量,相对于传统表面粗糙测量仪器,大大提高了野外工作效率和测量精度,解决了断层面在野外微观尺度上形貌高精度测量问题。应用地面三维激光测量技术采集数据的工作过程大致可以分为计划制定、外业数据采集和内业数据处理三部分。在野外工作展开之前首先制定工作计划,根据测量任务确定测量目标和测量范围;测量过程中,根据测量需要布设测量控制点、确定扫描目标的分辨率;扫描得到的点云数据是一组三维点集,有效数据和无用的噪声混合在一起,在处理生成DEM之前必须经过数据处理,包括数据的滤波、控制点的拟合、空间坐标转换等。
2、汶川地震地表破裂面形貌特征
准确描述破裂面形貌对于我们理解地震断层作用是非常重要的,破裂面的形貌特征包含了许多关于地震和断层机制的有用信息。2008年汶川Ms8.0地震产生了两个新鲜的破裂面,八角庙破裂面和沙坝破裂面,我们使用3D激光扫描仪(Trimble GX)对两个破裂表面进行测量,在野外微观尺度上研究了汶川地震破裂面的形貌特征。
通过能谱密度和均方值粗糙度两个方法分析破裂面形貌,分析结果表明新鲜的破裂面表现为自相仿性,能谱密度和均方值均与剖面长度存在幂律关系,破裂面在垂直滑动方向比平行滑动方向粗糙。在能谱密度与空间频率的对数图中,能谱密度曲线存在明显的拐点,表明单一分形不能准确描述破裂面形貌。该拐点所对应的波长称为“特征坡长”,八角庙破裂面在平行滑动方向上的特征波长为7mm,在垂直方向上特征波长略大一些(区域Ⅰ为10mm,区域Ⅱ为9mm);沙坝破裂面在平行滑动方向上的特征波长为8mm,但垂直方向上特征波长略小(6mm)。在均方值与剖面长度的对数图中,均方值曲线的最小二乘拟合直线的斜率为Hurst指数,该指数依赖于剖面方向与断层面擦痕方向的关系,H指数的最小值和最大值分别与平行擦痕和垂直擦痕方向对应。各破裂面的H指数极坐标图所标识出的断层擦痕方向与在野外破裂面擦痕侧伏角测量结果一致。沙坝破裂面的H指数极坐标图中存在次级H指数极值(对应剖面线方向为85o和160o),这揭示破裂面上存在一组隐匿擦痕。该组隐匿擦痕为汶川地震之前断层活动中形成的,但目前我们获得的该破裂的分型特征还不足以推测上一次断层活动的时间和规模。
另外,以往的研究表明未受错动改造的天然张裂面的H指数等于0.8,天然正断层面在垂直擦痕方向H指数小于0.8。沙坝破裂面虽然在深部逆冲造成西北盘上升,但西北盘近地表在上升的过程中存在向西的旋转,造成在近地表的拉张正断特征,在垂直擦痕方向上H指数小于0.8(0.72±0.029);八角庙破裂面在垂直擦痕方向上H指数为(域Ⅰ,0.84±0.024)和(域Ⅱ,0.83±0.041),均大于0.8,与该破裂面为挤压逆冲性质相关。这个观测结果表明,与前人结论基本一致,垂直擦痕方向的H指数与断层类型相关。
能谱密度曲线斜率(-α)与能谱曲线斜率(H)在理论上存在一个简单的线性关系,然而,我们用上述两种方法得到的结果不能严格满足公式α=1+2×H。通过线性拟合,在全频率域上α和H满足线性关系:α=1.22+1.72×H。这个差异是由于测量信号噪音、破裂面的多分形性和分析方法的差异造成的。
3、基岩断层面形貌风化特征
任何一个野外天然基岩断层面露头,其所表现的几何和形貌特征都是内、外营力共同作用的结果。断层面形貌特征不仅仅反映了断层的力学机制和运动特征,还与断层出露后各种侵蚀、风化作用有关。在许多活动构造区域,基岩断层崖是断层多次活动的长期结果,理论上这些基岩断层面的形貌特征记录了很多关于断层活动的信息,隐含着有价值的“古地震”记录,但很难被识别出来,因此,基岩断层崖不被认为是判断过去地震事件的“灵敏指示器”。实际上,在不同时期地震活动而出露的断层面之间,还是存在表面风化程度和生物(藓类)集群规模的区别,如果能够建立一种断层面的出露时间与风化程度的经验关系,就可以推测出地震发生时代。本文通过对施庄断裂不同出露历史的断层面形貌特征的研究,定量分析了风化作用对断层面形貌的影响。
无论是遭受风化侵蚀的断层面,还是新剥露出的断层面,破裂面的能谱密度和均方值均与取样长度存在幂率关系,断层面形貌表现为自相仿性。各扫描断层面H指数极坐标图极值的分布特征表明,近水平方向擦痕是控制断层面形貌特征的最主要因素。将施庄断层面能谱密度曲线与其他滑动距离不等断层面进行比较,发现施庄断层属于大滑距断层,在近水平方向上滑动距离不小于十米。除了内营力,外营力也是决定断层面形貌特征重要因素。风化作用不但使断层面形貌变得粗糙,而且改变断层面各向异性特征。断层面出露时间越长,断层面形貌的各向同性特征越明显。断层面形貌各向异性减弱和各向同性的增强是由于外营力(水和空气)的风化和侵蚀作用具有的随机性造成的。
在垂直滑动方向和平行滑动方向的断层面能谱密度图中,可分别用不同变量表示断层面形貌的风化程度。在垂直断层滑动方向,断层面短波长(高频)起伏更易受到侵蚀风化。随着风化程度的加深,垂直滑动方向的能谱曲线偏离天然断裂能谱范围,存在一个简单的规律:断层面出露时间越长,起始偏离能谱范围的波长越长。平行于滑动方向能谱密度曲线上存在一个值得注意的现象,波长在5mm～30mm范围上,平行滑动方向的能谱密度曲线存在一个向上凸起的变化,以至于平行于滑动方向能谱接近垂直滑动方向的能谱。拐点波长与断层面风化程度相关,风化越严重,拐点波长越长。将垂直擦痕方向上的偏离能谱范围的起始波长和平行擦痕方向上的能谱曲线拐点波长之间进行线性分析,分析结果显示两者之间存在很好的线性关系。这说明断层面形貌与风化历史成线性关系,这与其他研究者在不同地区所获得的结论相一致。
通过3D激光扫描仪对断层面进行高精度测量,我们发现断层面上存在明显的椭圆凸起,这些椭圆凸起的长轴平行于近水平擦痕,即平行于断层滑动方向。沿整个施庄断裂出露的断层面上,分布多个椭圆凸起结构,凸起结构表现不完整,多数凸起被斜交的阶步破坏。这些凸起是基岩研磨物质和角砾混杂固结而成的,类似于透镜体并依附于断层面上。这些凸起可以看作是在野外微观尺度上的凹凸体,微观尺度上的凹凸体是影响断层面近场应力分布和滑动分布的重要因素。椭圆形凸起在其他断层面也曾被报道过,表明这些凸起是断层成熟过程中的断层面形貌特征之一。
4、人工坡面形态演化
在松散沉积物中断层崖形态的演化可以被准确的模拟,在加以适当校正的情况下,可以提供一些断层崖演化的高精度数字模型,这些模型是确定断层崖出露年龄的基础。本文通过建立一组不同角度人工坡面研究断层崖演化过程,所修建的不同角度坡面代表了断层崖演化过程中的不同阶段,高角度坡面代表了断层崖演化初期阶段,低角度坡面代表断层崖演化晚期阶段。通过长期的高精度观测,获取坡面演化过程中各模型参数,最终推导出断层崖演化的精确数学模型,为判断断层面(或断层崖)出露时代提供一个实用的手段。
松散堆积组成的断层崖一般经历2个不同的演化过程:早期的不稳定过程和晚期的扩散过程,处于这两个阶段的断层崖分别称为松散限制型断层崖和搬运限制型断层崖,不稳定阶段自由面后退速率C和扩散阶段物质扩散系数K是断层崖反演断层活动时间的重要参数。对于同一坡面,每期测量使用相同的控制点,因此可将各期测量结果转化到相同坐标系统中,通过比较不同期次测量结果,可以获得坡面在不同时期内的坡面的侵蚀情况。目前人工坡面正处于不稳定阶段,自由面后退速率可直接应用于该阶段演化模型的校正。根据一年的测量数据分析,不同角度坡面的后退速率存在差异。30°坡面后退速率为8.19±1.16mm,但由于30°坡面小于休止角,黄土碎屑物很快将自由面覆盖,之后进入扩散演化阶段。大于休止角的坡面中,50°坡面后退速率最大,为7.41±0.84;其次是80°坡面,为6.74±0.26 mm;70°坡面后退速率最小,为5.34±0.15 mm。由于观测随时间较短以及坡面未被厚层松散堆积物覆盖,目前还未能得到精确的坡面扩散方程。
Principal slip surfaces in fault zones accommodate most of the displacement during earthquakes, and the topography of fault surface is the result of faulting and would evolve with slip. Fault surfaces affect all aspects of fault and earthquake mechanics, including rupture nucleation, fault gouge generation, lubrication, the near-fault stress field, resistance to shear, and critical slip distance. So the study of the fault surface has important significance to earthquake and fault mechanics. To any outcrop of a natural fault in the field, its characters of geometry and topography on the surface are the interacting result between the endogenetic force and the exogenic force. The topographic characters of the fault the surface can reflect not only the fault mechanics, motion and fracture mechanisms, but also the relation to the weathering and erosion after it outcropped in the field. So the study on the topography of fault surfaces has important significance to the determine the date of faulting and the research of ancient earthquakes.
This thesis focuses on the topography of fault surfaces, and uses the technique of 3D laser scanning and the fractal method to analyze the topographic characters of the rupture surfaces during the Wenchuan earthquake and the outcrop of natural faults on the field scale. The relationships were quantitatively analyzed among the surface topography , the type of fractures and the weathering and erosion. Moreover, to study the fault-scarp degradation process, a set of artificial fault-scarps with different slope angles were built. Through the high precise observation in a long time, this work attempts to get the model parameters in the evolutionary process, and finally deduce to the accurate mathematical model which can be applied to other fault scarps in the same region.
1. Description and field measuring method for topography of fault surface
Many studies have been done to the topography of fault surfaces heretofore, and the research methods can be divided into two categories, the statistical method and fractal geometry method. Statistical parameters can be calculated easily, but they cannot provide complete information which is very important to the study of mechanics of fracture surfaces. Moreover, as a result of the complexity and the scaling of the fault surface, and the traditional statistics cannot completely describe the topography of the fault surface. With the further research, the fault surfaces show the similar structures and the affine structure. The fractal is a mathematics model which is able to express unconventional geometry, and the two fractal concept, self-similar and self-affine, provide useful models which can be compared to natural fault surfaces.
There are many methods to calculate the characteristics of topography, Two methods, power spectral density and Root-mean-square (RMS) roughness, were used to quantitatively describe the topography of natural fault surfaces in this thesis. The power spectral density is a mathematical algorithm which is based on the time series analysis, and it converts the spatial information into frequency information. This method can reveal the influence of composition with different wavelength on the surface roughness. The RMS roughness method can highlight the characteristics of the anisotropic properties on the fault surface.?
For each surface, a set of 1D parallel profiles in a specific direction are extracted, descended and the analyzed. The properties are averaged over all the 1D profiles to characterize 2D surface in the chose direction. To study the azimuthal dependence of the properties of the surface, I have repeated to extract profiles in directions in the range 0°to 180°(the fault strike in0°). The reliability analysis for the methods is made using synthetic self-affine surfaces with a directional morphological anisotropy, and the results showed the methods were accurate to delineate the isotropic surfaces, and the calculation error is less than 10% for anisotropic surfaces.
The study of surface topography was based on the measuring with high accuracy, so the 3D laser scanning technology was used to survey and map the topography of the fault surfaces. According to the purposes of the work and the performances of the 3D scanner, the working-flow was set up, and the precision and reliability were evaluated. The results from the subsequent applications indicate that the accuracy of 3D laser scanning is satisfied for the surface measuring over an area as large as tens of square meters with high accuracy. Compared to the traditional technologies, 3D laser scanning technology greatly improved the field work efficiency and the accuracy of measuring, and solved the problem of measuring accuracy in the scale of field micro-topography for fault surfaces, so it provided a chance to study the topography of fault surfaces on this scale. The work of applying 3D laser scanner to collect data consists of making plane, field measuring and indoor data processing.
2. Topographic characteristics of rupture surface associated with the Wenchuan earthquake
It is very important to describe accurately the topography of rupture surfaces for understanding of seismic faulting, because the topographic characteristics of the rupture contain much information about the earthquake and fault mechanics. Two fresh rupture surfaces of the Mw7.9 Wenchuan earthquake in 2008, referred to as the Bajiaomiao surface and the Shaba surface, have been measured by scanning with a 3D portable laser scanner.
The acquired sets of DEM data are analyzed using power spectral and root-mean-square (RMS) roughness. The fresh rupture surfaces exhibit self-affine behavior, and the power spectral density and RMS roughness both have a power law relationship with the length of profiles. The roughness of the surface parallel to the slip direction is generally less than the roughness perpendicular to the slip direction. In log-log plot of power spectral density versus spatial frequency, there is an obvious inflexion which divides the spatial frequency into a lower frequency domain and higher frequency domain. The wavelength corresponding to the inflexion is called "characteristic wavelength" or "characteristic scale". It is 7 mm in the direction parallel to slip for the Bajiaomiao surface (both in PatchⅠandⅡ), smaller than that in the direction perpendicular to slip (10 mm in PatchⅠand 9 mm in PatchⅡ), and 8 mm in the direction parallel to slip, but larger than that in the direction perpendicular to slip(6 mm). The slope of the least squares fitting line to the RMS roughness curve in log-log plot is the H exponent, which depends on the direction of the profile and describe the morphological anisotropy of the fault surface . The slip directions indicated by the minimum H values, 85o and 75o on the Bajiaomiao surface, and 45o on the Shaba surface, are equal to the slip directions measured in the field. A secondary set of H-value peaks (85o and 160o) in Shaba rupture surfaces reveals a set of concealed striations produced by an earthquake prior to the Wenchuan event. But it is not sufficient to determine the time and magnitude of this inferred faulting event.
? Moreover, H value(PatchⅠ: H=0.84±0.024, PatchⅡ: H=0.83±0.041) of the topographic profile perpendicular to slip on the Bajiaomiao surface occurred on the reverse fault is larger than 0.8, and H value(H=0.72±0.029) of the profile perpendicular to slip on the Shaba surface occured on the normal fault is smaller than 0.8. Whether H value is larger than 0.8 probably relates to the type of the fault.
The H value of the topographic profile perpendicular to slip on the Bajiaomiao surface occurred on reverse fault is larger than 0.8, and that of the profile perpendicular to slip on the Shaba surface occurred on normal fault is smaller than 0.8. Whether the H value is larger than 0.8 is probably related with the type of the fault. By linear fitting between the slopes of power spectral density(-α) and the slope of RMS roughness (H) on whole length of profile, a relationship is constructed,α=1.22+1.72×H , it do not obey to theory relationship strictly,α=1+2×H. This variance probably is caused by the multi-fractal of the rupture surface and the statistic error.
3. characteristics of weathering topographic on bedrock fault surface
To any outcrop of a natural bedrock fault in the field, the geometry and morphological features are the interacting result between internal forcing and external forcing. The topographic characters of fault surface can reflect not only the fault mechanics, motion and fracture mechanism, but also relate to the weathering and erosion after being outcropped in field. Bedrock fault scarps potentially preserve valuable 'palacoscismic' records, interpreting this is difficult, and as a result , bed rock scarps are not considered to be sensitive indicators of the timing and magnitude of past faulting events. In fact, the weathering morphology of bedrock surfaces had recorded the information about faulting. In this work accurate measuring and analysis were done at five sites with different outcropped history on the Shizhuang fault, and influence of weathering erosion on the fault surfaces were quantitatively analyzed.
Regardless of the fault surfaces with weathering or the fault surface without weathering, the power spectrum density and root-mean-square(RMS)roughness have power law relationships to the length of profiles, and the topography of fault surfaces show the self-affine. Compared to other fault surfaces in terms of profile and power density, the Shizhuang fault is a large-slip fault, and the slip displacement is no less than 10 meters in nearly horizontal direction. The weathering not only made the fault surface rougher, but also changed the anisotropic characteristics of the surfaces. With the increase of the outcropping time, the isotropy characteristics of the topography of surface became more obvious, which is caused by the stochastic character of the external forcing.
In the power density plot of fault surfaces in directions of perpendicular to slip and parallel to slip, different variables can be used to quantify the weathering level of fault surfaces. The power density curve of profile perpendicular to slip gradually deviated from the range of power spectrum of natural fracture with the increasing of weathering degree, and it obeys a simple rule that the longer of weathering time , the wavelength deviated from the power spectrum range is longer. The power density curve of profile parallel to slip has a upward inflection point, and the wavelengths corresponded to inflection points related to the weathering level of the fault surface. The more serious the weathering , and longer the wavelengths correspond to inflection points. There is a linear relationship between these two kinds of wavelengths.
This work found many obvious elliptic bumps on fault surfaces by accurate measurements using 3D laser scanner, with the long axis parallel to the horizontal striations. These elliptic bumps, consists of the wear production of bedrock and the gravels, are similar to the lens and attach to the fault surface. These bumps can be regarded as "asperities" on a field scale, and the asperity is an important factor influencing near field of the stress distribution and slip. The elliptic asperity has been reported in others faults, which show that the elliptic asperities are one of topographic characteristics in the maturing process of the fault.
4. Degradation of artificial fault scarp
The degradation of fault scarps in unconsolidated deposits can be accurately simulated, and under the appropriate correction, the morphology of fault scarps provides a method to estimate the age of faulting . This work constructed a group of artificial fault scarps with different slope angle, and managed to get parameters of degradation model, and finally deduce the accuracy mathematic model of degradation in this region.
The degradation process of fault scarp has two stages, the unstable stage in the early period and the diffusion stage in the later period. At present, the artificial fault scarps are in an unstable stage, and the retreating rate of free face can be used directly to calibrate the model of this stage. According to the measuring data in one year, the backward rate of free face is not equal for different slope. The retreating rate of 30°slope is 8.19±1.16mm, and The loess detrital covered the free face soon and the degradation process entered the diffusion stage from the unstable stage. For the slopes with angle larger than the reposed angle, the retreating rate of a 50°slope is as high as 7.41±0.84mm; the backward rate of 70°slope is the lowest as 5.34±0.15mm. Owing to the limit of observation time and the slopes non-covered by unconsolidated deposits, the accurate diffusion equation has not been established yet.
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