A Quantitative Study Of The Topography Of Fault Surfaces With High Accuracy

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 surfaceMany 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 earthquakeIt 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 surfaceTo 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 scarpThe 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.