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1.
The power-law exponent (n) in the equation: D=cL n , with D = maximum displacement and L = fault length, would be affected by deviations of fault trace length. (1) Assuming n=1, numerical simulations on the effect of sampling and linkage on fault length and length–displacement relationship are done in this paper. The results show that: (a) uniform relative deviations, which means all faults within a dataset have the same relative deviation, do not affect the value of n; (b) deviations of the fault length due to unresolved fault tip decrease the values of n and the deviations of n increase with the increasing length deviations; (c) fault linkage and observed dimensions either increase or decrease the value of n depending on the distribution of deviations within a dataset; (d) mixed deviations of the fault lengths are either negative or positive and cause the values of n to either decrease or increase; (e) a dataset combined from two or more datasets with different values of c and orders of magnitude also cause the values of n to deviate. (2) Data including 19 datasets and spanning more than eight orders of fault length magnitudes (10−2–105 m) collected from the published literature indicate that the values of n range from 0.55 to 1.5, the average value being 1.0813, and the peak value of n d (double regression) is 1.0–1.1. Based on above results from the simulations and published data, we propose that the relationship between the maximum displacement and fault length in a single tectonic environment with uniform mechanical properties is linear, and the value of n deviated from 1 is mainly caused by the sampling and linkage effects.  相似文献   

2.
Grain size and grain shape analysis of fault rocks   总被引：4，自引：0，他引：4  
  相似文献   

3.
Observations of the threshold of movement of loosely packed gravel in a tidal current are described. For gravel with equivalent ‘spherical’ diameters D in the range 0.2 ?D? 5.0cm the critical friction velocity u*c, corresponding to the initiation of sediment transport, is given by u*c=7.0 D0.2. At large values of D within the quoted range, the value u*c is significantly lower than would be obtained by a Shields experiment (u*c∞D0.5). By comparing our values of u*c with those obtained under well-controlled laboratory conditions, the discrepancy with Shields is shown to be due to the open spacing between, and exposure of, individual pebbles on the seabed. By comparing our results with those from upland gravel streams and flume experiments, it is suggested that Shields assumed an excessively large water depth to particle size ratio as a constraint within which the critical sediment entrainment number 0c is valid.  相似文献   

4.
An analysis of the possible relationship between fractal dimensions of the active fault network, spatial distribution of earthquake epicenters, and parameter b in the Gutenberg-Richter law is presented. The quantitative characteristics of self-similarity of the seismic process and the active fault network of seismically active areas of Eurasia are obtained. This self-similarity manifests itself over a range of at least two orders of spatial scales and magnitudes. The obtained estimations of the fractal dimensions of the fault network D f and epicenter field D e are close for all the areas analyzed. It is established that the average value connecting values D and b for all the investigated areas is slightly higher than the theoretical value (2.0) and varies within the range of 1.7–2.4.  相似文献   

5.
断裂长度与最大位移的关系及其影响因素   总被引：1，自引：0，他引：1  
断裂最大位移与断裂迹长遵循幂律关系 :D =cLn,但幂指数n的大小有很大的变化范围。为探索幂指数n的大小和断裂机制 ,从已发表的文献中收集了 18组数据 ,这些数据的断裂长度具有 8个数量级的跨度。经相关分析 ,我们得到n值的大小变化于 0 5 5和 1 6 5之间 ,平均值为 1 0 839。由于走滑断裂的最大长度在其倾向方向 ,不宜与倾滑断裂一起统计 ,我们去掉一组走向滑动断裂的数据 ,幂指数平均值为 1 10 6 6。用双回归方法得到的幂指数峰值 (nd)是 1 0～ 1 1。这些结果表明断裂最大位移与断裂迹长应该是非常接近线性关系。这种线性关系可以用Dugdale模型加以解释。该模型认为弹塑性物质拉张裂缝端点的变形是非弹性变形。模型的适用范围是单一岩性 ,一次构造力作用。我们认为n值的大小之所以有很大的变化范围 ,有可能受到断裂迹线长度偏差的影响 ,造成长度偏差的因素包括 :不同的观察平面 ,断裂端点的分辨率 ,断裂连接作用 ,岩石力学性质变化 ,断裂多期活动等。  相似文献   

6.
CodaQ (Q c) estimates for the Kumaun Himalaya region have been obtained in high frequency range. Local earthquakes, recorded by a digital seismic network in the region, which fall in the epicentral distances range of 10 to 80 km and with a local magnitude range of 1.4 to 2.8, have been used. The coda waves of 30 sec window length, filtered at seven frequency bands centered at 1.5, 3, 6, 9, 12, 18 and 24Hz, have been analysed using the single backscattering model. The values ofQ c estimates vary from 65 to 283 at 1.5 Hz to 2119 to 3279 at 24.0 Hz which showed thatQ c is frequency dependent and its value increases as frequency increases. A frequency-dependentQ c relationship,Q c = (92 ± 4.73)f(1.07±.023), is obtained for the region representing the average attenuation characteristics of seismic waves for Kumaun Himalaya region.  相似文献   

7.
Displacement–length data from dilatant fractures (joints, veins, igneous dikes) and several varieties of deformation bands were analyzed statistically to investigate the applicability of mechanical models proposed for their formation. All 17 datasets are generally consistent with equilibrium or long-term power-law slopes on the displacement–length diagram of either 1.0 or 0.5. Similar to many faults, disaggregation deformation bands are consistent with a power-law scaling relation having a slope of approximately c = 1, implying a linear dependence of maximum displacement and discontinuity length (Dmax = γL). In contrast, dilatant fractures, cataclastic deformation bands, and shear-enhanced compaction bands are consistent with a power-law scaling relation with a slope of approximately c = 0.5, implying a dependence of maximum displacement on the square root of length (Dmax = αL1/2). The scaling relations represent an average, or long-term equilibrium outcome of deformation for conditions such as length-scale, time-scale, temperature, chemistry, and an effectively homogeneous far-field stress field, allowing for variations such as rapid and/or localized behaviors. The displacement–length scaling of these geologic structures follows systematic relationships that provide information on host-rock properties and the physics of fracture and deformation-band propagation.  相似文献   

8.
Pumping tests in discontinuous media are commonly interpreted using radial/non-radial flow analytical models, which do not account for a large range of multistage real signatures that combine both flow types. The term radial is employed in Barker??s sense, referring to the cross-flow area growth with a flow dimension (n) equal to 2, while multistage refers to a flow response of several time periods with successive n values. Synthetic domains are used to numerically investigate the flow behaviour of faulted media, specifically the effect of fault inclination on multistage signatures. Simulations are performed using single faults surrounded by a permeable matrix to characterize drawdown series and to identify hydrodynamic scenarios associated with some diagnostic multistage n sequences. The n sequence 2 ?C <?2 ?C 2 results from interactions between the matrix and a horizontal to weakly inclined fault, while 2 ?C 1.5 ?C 2 corresponds to a higher fault inclination and is a combination of the generalized horizontally and vertically faulted models. These results improve the interpretation of ambiguous drawdown series from long-term pumping tests. This provides a better hydraulic characterization of faulted environments, allowing assessment of fault and matrix properties such as fault inclination. The approach is successfully tested on real datasets.  相似文献   

9.
Fault-creep events measured on the San Andreas and related faults near Hollister, California, can be described by a rheological model consisting of a spring, power-law dashpotand sliding block connected in series. An empirical creep-event law, derived from many creep-event records analyzed within the constraints of the model, provides a remarkably simple and accurate representation of creep-event behavior. The empirical creep law is expressed by the equation: D(t)= Df [1?1/{ct(n?1)Dfn?1+1}/(n?1)] where D is the value of displacement at time t following the onset of an event, Df is the final equilibrium value of the event displacementand C is a proportionality constant. This discovery should help determine whether the time—displacement character of creep events is controlled by the material properties of fault gouge, or by other parameters.  相似文献   

10.
断层附近地应力扰动带宽度及其影响因素   总被引：3，自引：3，他引：0  
在建立正断层模型的基础上,利用三维有限元数值模拟方法研究了断层附近地层中的地应力变化规律。其结果表明,由于断层活动,在断层附近普遍发育应力扰动带;在应力扰动带范围内,地应力方向和大小发生明显的变化,断层中部附近应力值普遍较低,而断层端部的应力值通常异常增大。应力扰动带的分布范围主要受断层规模的控制,与断裂带的岩石力学性质、断层走向、断层面形态和边界应力条件等因素也密切相关。随断层长度和断距逐步增大,应力扰动带的宽度相应增加。断裂带的岩石越破碎,其岩石弹性模量越低,断层对地应力的影响宽度越大。断层走向与区域最大水平主应力方向越接近垂直、断距与断层长度的比值越大,区域内的差应力越大,则扰动带宽度与断层规模的比值也越大。选择渤海湾盆地BZ-X油田进行验证,在建立油田实际三维地质模型基础上,根据边界应力条件,利用三维有限元方法对沙河街组二段的地应力分布进行了数值模拟计算。根据断层周围的地应力变化,确定了应力扰动带的分布范围,断层附近应力扰动带宽度的分布规律与正断层模型分析结果相一致。   相似文献   

11.
A new earthquake catalogue for central, northern and northwestern Europe with unified Mw magnitudes, in part derived from chi-square maximum likelihood regressions, forms the basis for seismic hazard calculations for the Lower Rhine Embayment. Uncertainties in the various input parameters are introduced, a detailed seismic zonation is performed and a recently developed technique for maximum expected magnitude estimation is adopted and quantified. Applying the logic tree algorithm, resulting hazard values with error estimates are obtained as fractile curves (median, 16% and 84% fractiles and mean) plotted for pga (peak ground acceleration; median values for Cologne 0.7 and 1.2 m/s2 for probabilities of exceedence of 10% and 2%, respectively, in 50 years), 0.4 s (0.8 and 1.5 m/s2) and 1.0 s (0.3 and 0.5 m/s2) pseudoacclerations, and intensity (I0 = 6.5 and 7.2). For the ground motion parameters, rock foundation is assumed. For the area near Cologne and Aachen, maps show the median and 84% fractile hazard for 2% probability of exceedence in 50 years based on pga (maximum median value about 1.5 m/s2), and 0.4 s (>2 m/s2) and 1.0 s (about 0.8 m/s2) pseudoaccelerations, all for rock. The pga 84% fractile map also has a maximum value above 2 m/s2 and shows similarities with the median map for 0.4 s. In all maps, the maximum values fall within the area 6.2–6.3° E and 50.8–50.9° N, i.e., east of Aachen.  相似文献   

12.
A fault scaling law suggests that, over eight orders of magnitude, fault length L is linearly related to maximum displacement D. Individual faults may therefore retain a constant ratio of D/L as they grow. If erosion is minor compared with tectonic uplift, the length and along‐strike relief of young mountain ranges should thus reflect fault growth. Topographic profiles along the crests of mountain ranges in the actively deforming foreland of north‐east Tibet exhibit a characteristic shape with maximum height near their centre and decreasing elevation toward the tips. We interpret the along‐strike relief of these ranges to reflect the slip distribution on high‐angle reverse faults. A geometric model illustrates that the lateral propagation rate of such mountain ranges may be deciphered if their length‐to‐height ratio has remained constant. As an application of the model, we reconstruct the growth of the Heli Shan using a long‐term uplift rate of ～1.3 mm yr?1 derived from 21Ne and 10Be exposure dating.  相似文献   

13.
The progressive bond breakage of artificially cemented sands induced by shear straining was investigated through conventional isotropically consolidated drained triaxial compression tests. Sand specimens were prepared with a low degree of cementation by adopting a chemical grout. Test results were interpreted in terms of two stress–dilatancy theories for cohesive-frictional materials proposed in literature. The influence of debonding on the stress–dilatancy behaviour of cemented sands was analysed with particular emphasis on the ‘delayed dilatancy’ phenomenon. A bonding degradation curve was determined for each test relating the interparticle cohesion (c) to the magnitude of the total plastic strain vector (εd) and a bond degradation rate factor (Dc) was assessed from each curve. The maximum value of interparticle cohesion (c0) before the onset of bond degradation under shearing was found to correspond with a sharp decrease in the soil stiffness of the specimens. The influence of the effective confining stress (p′c) on both c0 and Dc parameters gathered from each test was also ascertained.  相似文献   

14.
The attenuation properties have been estimated in the Nubra-Siachen region situated in the highly mountainous region of Himalayan belt. Coda wave quality factor (Qc) has been determined for this virgin region by using the single backscattering method. A total of thirty earthquakes recorded in this region, which fall in the epicentral distance range of 3 to 115km have been used for the present work. A 30 sec window length of coda waves at different central frequencies 1.5, 3.0, 6.0, 9.0, 12.0, 18.0 and 24.0 Hz have been studied to determine Qc at different recording stations. The frequency dependent coda wave quality factor relationships of the form Qc(f) = Qofn, have been computed at each recording stations separately: BASE: Qc(f) = (137 ± 4.2) f(0.99 ± 0.12), CHALUNKA: Qc(f) = (116±3.8)f(1.0±0.05), PARTA: Qc(f) = (122±3.0)f(1.0±0.02), and SASOMA: Qc(f) = (111±4.1)f(1.0±0.03). A regional Qc relation has been developed for the Nubra-Siachen region by using the average value of Qc at different frequencies obtained at each recording station of the form Qc(f) = (121±7.2)f(1.0±0.04). The average Qc values vary from 183 at 1.5 Hz to 3684 at 24 Hz central frequencies. The present regional relation developed for Nubra-Siachen region indicates heterogeneous and tectonically active region.  相似文献   

15.
Detailed b lattice parameter and illite crystallinity (IC) studies of K-white micas in slates from the Stawell and Ballarat-Bendigo Zones (SZ, BBZ) in the western Lachlan Fold Belt of Victoria, Australia, reveal a metamorphic pattern characterized by regional metamorphism associated with crustal thickening and younger contact metamorphism accompanied by deformation. The IC data indicate that rocks regionally metamorphosed prior to the intrusion of the Early and Late Devonian granitoids, vary in grade from epizonal (greenschist facies) to diagenetic (zeolite facies) and that most are of epizonal to anchizonal (prehnite–pumpellyite facies) grade. In the BBZ, a decrease in grade from west to east occurs. Across fault zones, IC values show little change, indicating that limited vertical displacement has occurred. This is in accord with the thin skinned deformation model proposed for the western Lachlan Fold Belt. The b lattice parameters (x=9.022 Å; n=137; σn=0.009) indicate baric conditions intermediate between those of New Hampshire (P=Al2SiO5 triple point) and Otago (intermediate P ). Thus, a moderately low geothermal gradient existed 450–430 Ma ago, when these rocks were deformed. KD Fe/Mg (actinolite)/Fe/Mg (chlorite) values (0.52–0.70) obtained from coexisting actinolite and chlorite in metabasites from fault zones support the moderately high-P (c. 4 kbar) metamorphism suggested by the b cell parameter values. The metamorphic conditions indicated by these data are contrary to the low-P/high-T conditions proposed by previous authors, who inferred an intimate association between deformation, granitoid intrusion and gold mineralization. The b lattice parameter of white micas in slates adjacent to Early Devonian (c. 400 Ma) granitoids with schist bearing aureoles in the north-eastern part of the BBZ (x=9.002 Å; n=27; σn=0.007), indicate pressures in the order of c. 2.5 kbar which are in accord with those obtained from andalusite–cordierite and zoisite–garnet bearing assemblages observed in the higher grade metapelitic and calcareous rocks. This contrasts with the higher pressure (c. 4 kbar) existing during regional metamorphism and implies that c. 6.5–8 km of metasedimentary rocks in the BBZ were removed before the emplacement of the Early Devonian granitoids. Metamorphic assemblages in hornfelses associated with Late Devonian granitoids indicate a further 5–6 km of metasediment were removed in the next 40 Ma prior to their emplacement. This study shows the value of white mica studies in elucidating the tectonothermal history of a low-grade metamorphic terrane dominated by metapelitic rocks.  相似文献   

16.
Displacement, length and linkage of deformation bands have been studied in Jurassic sandstones in southeastern Utah. Isolated deformation bands with lengths (L) that span more than three orders of magnitude show similar displacement (D) profiles with more or less centrally located maxima and gently increasing gradient toward the tips. Soft- and hard-linked examples exhibit steeper displacement gradients near overlap zones and immature hard links, similar to previously described fault populations. The deformation band population shows power-law length and displacement distributions, but with lower exponents than commonly observed for populations of larger faults or small faults with distinct slip surfaces. Similarly, the Dmax-L relationship of the deformation bands shows a well-defined exponent of ca 0.5, whereas the general disagreement for other fault populations is whether the exponent is 1 or 1.5. We suggest that this important difference in scaling law between deformation bands and other faults has to do with the lack of well-developed slip surfaces in deformation bands. During growth, deformation bands link to form zones of densely spaced bands, and a slip surface is eventually formed (when 100 m < L < 1 km). The growth and scaling relationship for the resulting populations of faults (slip surfaces) is expected to be similar to ‘ordinary’ fault populations. A change in the Dmax-L scaling relationship at the point when zones of deformation bands develop slip surfaces is expected to be a general feature in porous sandstones where faults with slip surfaces develop from deformation bands. Down-scaling of ordinary fault populations into the size domain of deformation bands in porous sandstones is therefore potentially dangerous.  相似文献   

17.
We have experimentally determined the tracer diffusion coefficients (D*) of 44Ca and 26Mg in a natural diopside (~Di96) as function of crystallographic direction and temperature in the range of 950–1,150 °C at 1 bar and f(O2) corresponding to those of the WI buffer. The experimental data parallel to the a*, b, and c crystallographic directions show significant diffusion anisotropy in the a–c and b–c planes, with the fastest diffusion being parallel to the c axis. With the exception of logD*(26Mg) parallel to the a* axis, the experimental data conform to the empirical diffusion “compensation relation”, converging to logD ~ −19.3 m2/s and T ~ 1,155 °C. Our data do not show any change of diffusion mechanism within the temperature range of the experiments. Assuming that D* varies roughly linearly as a function of angle with respect to the c axis in the a–c plane, at least within a limited domain of ~20° from the c-axis, our data do not suggest any significant difference between D*(//c) and D*(⊥(001)), the latter being the diffusion data required to model compositional zoning in the (001) augite exsolution lamellae in natural clinopyroxenes. Since the thermodynamic mixing property of Ca and Mg is highly nonideal, calculation of chemical diffusion coefficient of Ca and Mg must take into account the effect of thermodynamic factor (TF) on diffusion coefficient. We calculate the dependence of the TF and the chemical interdiffusion coefficient, D(Ca–Mg), on composition in the diopside–clinoenstatite mixture, using the available data on mixing property in this binary system. Our D*(Ca) values parallel to the c axis are about 1–1.5 log units larger than those Dimanov et al. (1996). Incorporating the effect of TF, the D(Ca–Mg) values calculated from our data at 1,100–1,200 °C is ~0.6–0.7 log unit greater than the experimental quasibinary D((Ca–Mg + Fe)) data of Fujino et al. (1990) at 1 bar, and ~0.6 log unit smaller than that of Brady and McCallister (1983) at 25 kb, 1,150 °C, if our data are normalized to 25 kb using activation volume (~4 and ~6 cm3/mol for Mg and Ca diffusion, respectively) calculated from theoretical considerations.  相似文献   

18.
Displacement gradients on single fault surfaces are a function of the maximum displacement on a fault and the dimensions of the fault surface. Data on the maximum lateral dimensions (widths) and maximum displacements on normal faults and thrusts, with maximum displacements from 4 mm to 40 km, are used to derive an expression relating width, displacement and material properties. The basis of this expression is a fault growth model in which width is proportional to the square root of displacement. Width/displacement ratios vary systematically with the size of a fault from values of ca 30,000, which are characteristic of a single slip event, to about 10 in the case of thrusts with displacements of 40 km. Rocks from which the fault data are derived have a likely range of shear moduli from ca 0.1 to ca 30 GPa, which is sufficient to account for the range of data.Data on widths and maximum displacements of 308 fault traces recorded on British coalmine plans are shown to be consistent with variation of shear modulus of about half an order of magnitude. Data on 58 further fault traces are shown to be consistent with the fault growth model. Synsedimentary faults may have growth curves characteristically different from those of other faults.It is suggested that the increase in dimensions of a fault is a postseismic process of subcritical crack propagation for which the significant material property is fracture toughness.  相似文献   

19.
A single crystal of natrolite, Na2Al2Si3O10·2H2O, was studied by X-ray diffraction methods at room temperature. The intensities were measured with MoKα radiation (λ = 0.7107 Å) in a complete sphere of reflection up to sin θ/λ = 0.903 Å?1. The structure was refined in the orthorhombic space group Fdd2 with a = 18.2929 (7) Å, b = 18.6407(9) Å, c = 6.5871(6) Å, V = 2246 Å3, Z = 8. A refinement of high-order diffraction data yielded reliability factors of R(F) = 0.9%, R w(F) = 0.8%, GoF = 1.40 for 1856 high-angle reflections (0.7 ?in θ/λ <0.903 Å?1) and R(F) = 1.0%, R W(F) = 1.2%, GoF = 3.07 for all 3471 independent reflections in the complete sphere of reflection. The T-O distances as well as the T-O-T angles were found to be strongly influenced by the different bond strengths received by the individual oxygen atoms. The T O distances calculated using Baur's extended valence rule agree on average within 0.003 Å with the observed values. An analysis of the mean square displacement amplitudes allowed a separation of the external and internal vibrational amplitudes along the T-O bonds as well as along the Na O and H2O-O bond directions and the calculation of force constants. The internal vibrational amplitudes (ΔU) of the T-O vibrations are in the range of 5 to 11 × 10-4 Å2, that is about one order of magnitude smaller than the mean square displacement amplitudes of the external vibrations. The corresponding force constants are F = 354 to 824 Nm?1. The values of the force constants of the motion of the Na-ion and the water molecule against the framework oxygen atoms lie in the range between F = 57 and 293 Nm?1. This is the first instance where displacement amplitudes from a zeolite structure refinement could be apportioned between contributions from internal and external vibrations for individual bonds.  相似文献   

20.
Abstract Three reactions are calibrated as geothermobarometers for garnet–orthopyroxene–plagioclase–quartz assemblages, namely: 1/2 ferrosilite + 1/3 pyrope ± 1/2 enstatite + 1/3 almandine (A): ferrosilite + anorthite ± 2/3 almandine + 1/3 grossularite + quartz (B); and enstatite + anorthite ± 2/3 pyrope + 1/3 grossularite + quartz (C). The internally consistent geothermobarometers based on reactions (A), (B) and (C) are calibrated from experimental data only. The thermodynamic parameters of reaction (A) are derived from published experimental data in the FMAS system (n= 104) in the range 700–1400°C and 5–50 kbar, while those for reaction (B) are derived by summation of the existing reversed experimental data of the mineral equilibria: ferrosilite ± fayalite + quartz (D) and anorthite + fayalite ± 2/3 almandine + 1/3 grossularite (E). The retrieved thermodynamic parameters for reactions (A), (B) and (C) are, respectively: (ΔH0, cal) -3367 ± 209, -2749 ± 350 and +3985 ± 545; (ΔS0, cal K?1) -1.634 ± 0.163, -8.644 ± 0.298 and -5.376 ± 0.391; and (ΔV01,298, cal bar?1) -0.024, -0.60946 and -0.5614. On a one-cation basis, the derived Margules parameters of the ternary Ca–Fe–Mg in garnet are: WFe–Mg= -1256 + 1.0 (～0.23) T(K), WMg–Fe= 2880 -1.7 (～0.13) T(K), WCa–Mg= 4047 (～77) -1.5 T(K), WMg–Ca= 1000 (～77) -1.5 T(K), WCa–Fe= -723 + 0.332 (～0.02) T(K), WFe–Ca= 1090, (cal) and the ternary constant C123= -4498 + 1.516 (～0.265) T(K) cal (subregular solution model of non-ideal mixing); and Fe–Mg–Al in orthopyroxene: WFe–Mg= 948 (～200) -0.34 (～0.10) T(K), WFe–Al= -1950 (～500) and WMg–Al= 0 (cal) (regular solution model of non-ideal mixing). The anorthite activity in plagioclase is calculated by the ‘Al-avoidance’model of subregular Ca–Na mixing commonly used for geobarometry based on reactions (B) and (C). When the geothermobarometers are applied to garnet–orthopyroxene–plagioclase–quartz assemblages (n= 45) of wide compositional range from the Precambrian South Indian granulites, temperature ranges of 690–860°C (X= 760 ± 45°C) and pressure ranges of 5–10 kbar were obtained. The P–T values were estimated simultaneously and there is no difference in the pressure calculated from PMg (reaction C) and PFe (reaction B). In the existing calibrations this difference is 1 kbar or more. Furthermore, there is no compositional dependence of the ln K of the experimental data in the FMAS (n= 104) and the CFMAS (n= 78) systems at different temperatures and the estimated temperatures of the South Indian granulites.  相似文献   

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