Incorporation of incomplete fault-slip data into stress tensor inversion

A fault-slip datum used in the stress tensor inversion techniques is composed of fault orientation, slip orientation and the sense of slip. Sometimes the latter two items are not available. This paper proposes a method to deal with such incomplete fault-slip data. Firstly, the constraints on stress state from full and incomplete data are theoretically specified. The admissible stresses are expressed by the probability distributions in the parameter space. The objective function of inversion is given by superposing the probability distributions for all data including full and incomplete ones. Finally, the peaks of the objective function are detected to enumerate possible solutions. The validity of the present method is tested by simulated data. The incorporation of incomplete data can enhance the detectability of stress states and expands the applicability of stress tensor inversion.     

基于断层滑动数据古应力反演的影响因素及其误差分析

古构造应力场是构造动力学研究中的一个重要内容,且断层滑动数据古应力反演已经成为古构造应力场恢复研究中比较常用的重要方法之一。近年来,断层滑动数据古应力反演方法研究和应用取得了一系列重要进展,但有关反演结果的解释仍存歧义,反演结果的影响因素及其误差范围等并未得到深入研究与定量分析。本文总结指出,影响断层滑动数据古应力反演结果的主要因素包括变形体制、剪切破裂面类型、断层面的形态以及地质体内薄弱面的存在等。在此基础上,分别对新生断层和先存薄弱面滑动数据的古应力反演综合误差进行了定量分析。研究指出,在可以大致厘定变形体制或误差在允许范围内的前提下,将断层滑动数据反演结果解释为应力状态是合理可行的。各种因素导致的反演误差定量分析表明,同一期构造应力场形成的破裂面滑动数据的古应力方位反演误差最大不超过35°。换言之,在没有证据表明存在不同期次的应力作用情况下,主应力方位变化小于35° 的应力状态,可以划归同一期应力场。     

A computerized method to estimate friction coefficient from orientation distribution of meso-scale faults

The friction coefficient controls the brittle strength of the Earth’s crust for deformation recorded by faults. This study proposes a computerized method to determine the friction coefficient of meso-scale faults. The method is based on the analysis of orientation distribution of faults, and the principal stress axes and the stress ratio calculated by a stress tensor inversion technique. The method assumes that faults are activated according to the cohesionless Coulomb’s failure criterion, where the fluctuations of fluid pressure and the magnitude of differential stress are assumed to induce faulting. In this case, the orientation distribution of fault planes is described by a probability density function that is visualized as linear contours on a Mohr diagram. The parametric optimization of the function for an observed fault population yields the friction coefficient. A test using an artificial fault-slip dataset successfully determines the internal friction angle (the arctangent of the friction coefficient) with its confidence interval of several degrees estimated by the bootstrap resampling technique. An application to natural faults cutting a Pleistocene forearc basin fill yields a friction coefficient around 0.7 which is experimentally predicted by the Byerlee’s law.     

Inversion of fault data with low diversity for stress: Principles and applications

Although a minimum of four independent, single-phase fault data are required to solve for a unique reduced stress tensor, we prove in this paper that a smaller number of fault data are sufficient in some instances to solve for part of the reduced stress tensor. One of the principal stress directions is determinable from either two faults with a common null shear direction on the fault planes or three faults with a common intersection in a principal stress plane of the fault planes. This direction is combined with the fault data to determine the possible ranges of other principal stress directions. Determining whether the direction is for the maximum, intermediate or minimum principal stress depends upon constraints provided by slip tendency or more fault data. This approach can also be applied to a set of four or more fault data with low orientation diversity. This new method is finally applied to two different sets of fault data from along the active Chelungpu fault, western Taiwan. The stress orientations determined from the method lie in acceptable ranges for the maximum/minimum principal stresses using other existing and comparable methods, such as the right dihedra/trihedra methods. They differ moderately in the maximum/minimum principal stress directions when compared to the moment tensor method for fault kinematic analysis. The new method has advantages over the right dihedra/trihedra methods in the accuracy of stress estimate and the independence of stress estimate upon the small number of faults that are not parallel to the dominant fault set(s).     

Stress,strain and fault patterns

If faulting is treated as a stress-controlled phenomenon, the generation of a single fault set, or two sets in conjugate arrangement are inevitably predicted implying plane strain. Alternatively, considering faulting as a strain-controlled process, multiple-set patterns can be predicted. The analysis of multiple-set patterns requires identifying the type of fault pattern from four possibilities: Coulomb, isolated, orthorhombic and complex fault patterns.There are techniques that permit a unique solution of strain tensor for Coulomb and orthorhombic fault patterns. For isolated fault patterns, the principal paleostress directions could be used to approximate the principal strain directions. In this case, we need to assume a homogeneous stress field, independence between faults, and parallelism between shear stress and slip vector on the sliding plane.For complex fault patterns, it is not possible to uniquely determine the total strain tensor without knowledge of all the slip planes. Furthermore, inverting fault-slip data to determine the stress tensor is not correct because the assumptions of the inversion methods are not satisfied. Only a rough approximation is possible assuming that strain produced by major faults represents the total strain tensor.     

基于断层擦痕侧伏角公式的构造应力张量反演

利用Aleksandrowski推导的断层擦痕侧伏角公式,提出了一种改进的构造应力张量反演法。根据不同应力比值下构造应力与断层擦痕侧伏角的关系,利用最小二乘法,详细推导了构造应力张量的反演方法,最后利用Matlab软件编制程序实现了该计算过程。在此基础上,现场调查了江西武山铜矿北矿带的断层滑动数据,利用上述改进方法反演了该地区的构造应力张量方向特征。将上述反演结果与由震源机制解获得的最新构造应力场结果进行对比分析,并结合研究区断层的展布特征及所在的地质构造背景,获得了该地区自晚侏罗世以来的构造应力场特征,表明该地区构造应力场具有一定的稳定性。改进后的构造应力张量求解过程及工程应用表明,将Aleksandrowski的图示法和Etchecopar等的反演法结合起来反演构造应力张量,是对已有方法的改进,具有更加简单、实现容易等特点,计算结果比较符合实际。     

The 2002 Molise earthquake sequence: What can we learn about the tectonics of southern Italy?

On October 31, 2002 a M_L = 5.4 earthquake occurred in southern Italy, at the margin between the Apenninic thrust belt (to the west) and the Adriatic plate (to the east). In this area, neither historical event nor seismogenic fault is reported in the literature. In spite of its moderate magnitude, the earthquake caused severe damage in cities close to the epicenter and 27 people, out of a total of 29 casualties, were killed by the collapse of a primary school in S. Giuliano di Puglia. By inverting broadband regional waveforms, we computed moment tensor solutions for 15 events, as small as M_L = 3.5 (M_w = 3.7). The obtained focal mechanisms show pure strike-slip geometry, mainly with focal planes oriented to NS (sinistral) and EW (dextral). In several solutions focal planes are rotated counterclockwise, in particular for later events, occurring west of the mainshock. From the relocated aftershock distribution, we found that the mainshock ruptured along an EW plane, and the fault mechanisms of some aftershocks were not consistent with the mainshock fault plane. The observed stress field, resulting from the stress tensor inversion, shows a maximum principal stress axis with an east–west trend (N83°W), whereas the minimum stress direction is almost N–S. Considering both the aftershock distribution and moment tensor solutions, it appears that several pre-existing faults were activated rather than a single planar fault associated with the mainshock. The finite fault analysis shows a very simple slip distribution with a slow rupture velocity of 1.1 km/s, that could explain the occurrence of a second mainshock about 30 h after. Finally, we attempt to interpret how the Molise sequence is related to the normal faulting system to the west (along the Apennines) and the dextral strike-slip Mattinata fault to the east.     

Stress field analysis at the El Teniente Mine: evidence for N–S compression in the modern Andes

There is a large database of triaxial stress measurements at the El Teniente Mine, Central Chile, but the complex geology, severe topography, and proximity of all measurements to extensive mining excavations made interpretation of the stress field difficult. The measurements were analyzed using three-dimensional numerical stress analysis and decomposition of the stress field into gravitational and tectonic components. By removing gravitational stresses plus local effects from the tectonic component of the stress field a calculation of the far-field tectonic stress tensor is made. It is shown that variations in the tectonic component of stress are related to shear zones cutting through the mine. The far-field major principal component of the tectonic stress field was found to be oriented approximately N–S. This is consistent with the most recent direction of local shortening based on kinematic analysis of faults, but is perpendicular to the direction of regional crustal shortening. There appears to be a limiting envelope to the magnitude of the stress field implying that the shear zones are in a state of limiting equilibrium with regional tectonic driving forces.     

Active faults of the northern Tien Shan: tectonophysical zoning of seismic risk

This study continues the work by Mikhail Gzovsky on geological (tectonophysical) criteria for seismic risk. It is suggested to perform seismic-risk zoning according to parameters of normal and shear stresses on fault planes converted from results of tectonophysical stress reconstructions. The approach requires the knowledge of both dip and strike of the respective fault segments. Slip geometry is estimated from stress tensor, assuming that it is directed along shear stress. The suggested approach is applied to faults in the northern Tien Shan, and the current stress parameters are reconstructed using source mechanisms of catalogued earthquakes recorded by the KNET seismological network of the RAS Science Station in Bishkek. Stress modeling is performed by the method of cataclastic analysis providing constraints on stress ellipsoids, as well as on relations between the spherical and deviatoric components of the stress tensor. Plotted on the Mohr diagram, the fault stress points allow estimating whether the respective fault segments are close to the critical state (brittle failure). The suggested seismic-risk zoning of faults in the northern Tien Shan reveals up to 25 km long hazardous fault segments.     

Effect of block rotation on the pitch of slickenlines

Rotation of faults or pre-existing weakness planes produce two effects on the slickenlines of fault planes. First, the rotation leads to changes in the pitch of slickenlines. As a result, the aspect of the pre-existing fault may change. For example, after rotation, a normal fault may show features of an oblique fault, a strike-slip fault, or a thrust fault. Second, due to rotation, stress states on the fault planes are different from those before the rotation. As a consequence some previous planes may be reactivated. For an isolated plane, the reactivation due to rotation can produce new sets of slickenlines. With block rotation, superimposed slickenlines can be generated in the same tectonic phase. Thus, it is not appropriate to use fault-slip data from slickenlines to analyze the stress tensor in a region where there is evidence of block rotation. As an example, we present the data of slickenlines from core samples in the Tunich area of the Gulf of Mexico. The results wrongly indicate that the calculated stress tensor deviates from the far-field stress tensor.     

Evolution of paleostress fields and brittle deformation of the Tornquist Zone in Scania (Sweden) during Permo-Mesozoic and Cenozoic times

The NW-SE oriented Sorgenfrei–Tornquist Zone (STZ) has been thoroughly studied during the last 25 years, especially by means of well data and seismic profiles. We present the results of a first brittle tectonic analysis based on about 850 dykes, veins and minor fault-slip data measured in the field in Scania, including paleostress reconstruction. We discuss the relationships between normal and strike-slip faulting in Scania since the Permian extension to the Late Cretaceous–Tertiary structural inversions. Our paleostress determinations reveal six successive or coeval main stress states in the evolution of Scania since the Permian. Two stress states correspond to normal faulting with NE-SW and NW-SE extensions, one stress state is mainly of reverse type with NE-SW compression, and three stress states are strike-slip in type with NNW-SSE, WNW-ESE and NNE-SSW directions of compression.The NE-SW extension partly corresponds to the Late Carboniferous–Permian important extensional period, dated by dykes and fault mineralisations. However extension existed along a similar direction during the Mesozoic. It has been locally observed until within the Danian. A perpendicular NW-SE extension reveals the occurrence of stress permutations. The NNW-SSE strike-slip episode is also expected to belong to the Late Carboniferous–Permian episode and is interpreted in terms of right-lateral wrench faulting along STZ-oriented faults. The inversion process has been characterised by reverse and strike-slip faulting related to the NE-SW compressional stress state.This study highlights the importance of extensional tectonics in northwest Europe since the end of the Palaeozoic until the end of the Cretaceous. The importance and role of wrench faulting in the tectonic evolution of the Sorgenfrei–Tornquist Zone are discussed.     

廊固凹陷沙四晚期构造应力场模拟及低级序断层预测

在了解区域构造背景、分析断层活动特征及构造演化特征的基础上,对廊固凹陷沙四晚期构造应力场进行数值模拟,并对低级序断层发育进行预测。研究结果表明,研究区在沙四晚期活动的主要断层包括大兴断层、半截河断层等6条,牛北斜坡构造带与河西务构造带在该时期隆起明显,综合分析可知该时期最小主应力方向为SE144°—NW324°;低级序断层发育受最小主应力、剪应力等的影响,最小主应力和最大主应力与最小主应力的差值控制断层的优势发育区,平面剪应力控制断层走向,该区主要发育北北东—北东走向的断层;剖面剪应力在大部分区域为左旋,表明断层视倾向以北西向为主。     

汊涧斜坡带阜宁期应力场数值模拟及低级序断层发育规律预测

汊涧斜坡带位于金湖凹陷西斜坡南部,第三系沉积期间主要经历了吴堡和三垛运动,形成了复杂的断裂体系,属复杂断块油藏,区内低级序断层较为发育。根据断层平面展布确定阜宁期最小主应力方向为北北西350°,采用有限元法建立地质模型并进行构造应力场数值模拟,计算得出各应力分布,并据此对低级序断层发育规律进行预测。研究表明,汊涧斜坡带阜宁期最大、最小主应力均为水平方向,形成的低级序断层具有张扭性特征;低级序断层的发育主要受最大与最小主应力差值及剪应力控制,主应力差值控制断层优势发育地区,平面剪应力控制断层走向,剖面剪应力控制断层倾向。     

Present-day stress tensors along the southern Caribbean plate boundary zone from inversion of focal mechanism solutions: A successful trial

This paper presents a compilation of 16 present-day stress tensors along the southern Caribbean plate boundary zone (PBZ), and particularly in western and along northern Venezuela. As a trial, these new stress tensors along PBZ have been calculated from inversion of 125 focal mechanism solutions (FMS) by applying the Angelier & Mechler's dihedral method, which were originally gathered by the first author and published in 2005. These new tensors are compared to those 59 tensors inverted from fault-slip data measured only in Plio-Quaternary sedimentary rocks, compiled in Audemard et al. (2005), which were originally calculated by several researchers through the inversion methods developed by Angelier and Mechler or Etchecopar et al.The two sets of stress tensors, one derived from geological data and the other one from seismological data, compare very well throughout the PBZ in terms of both stress orientation and shape of the stress tensor. This region is characterized by a compressive strike-slip (transpressional senso lato), occasionally compressional, regime from the southern Mérida Andes on the southwest to the gulf of Paria in the east. Significant changes in direction of the maximum horizontal stress (σ_H = σ₁) can be established along it though. The σ₁ direction varies progressively from nearly east-west in the southern Andes (SW Venezuela) to between NW-SE and NNW-SSE in northwestern Venezuela; this direction remaining constant across northern Venezuela, from Colombia to Trinidad. In addition, the σ_V defined by inversion of focal mechanisms or by the shape of the stress ellipsoid derived from the Etchecopar et al.'s method better characterize whether the stress regime is transpressional or compressional, or even very rarely trantensional at local scale.The orientation and space variation of this regional stress field in western Venezuela results from the addition of the two major neighbouring interplate maximum horizontal stress orientations (σ_H): roughly east-west trending stress across the Nazca-South America type-B subduction along the pacific coast of Colombia and NNW-SSE oriented one across the southern Caribbean PBZ. Meanwhile, northern Venezuela, although dextral strike-slip (SS) is the dominant process, NW-SE to NNW-SSE compression is also taking place, which are both also supported by recent GPS results.     

Structural and stress analysis based on fault-slip data in the Amman area, Jordan

This study presents a structural analysis based on hundreds of striated small faults (fault-slip data) in the Amman area east of the Dead Sea Transform System. Stress inversion of the fault-slip data was performed using an improved Right-Dihedral method, followed by rotational optimization (TENSOR Program, Delvaux, 1993). Fault-slip data (totaling 212) include fault planes, striations and sense of movements, are obtained from the Turonian Wadi As Sir Formation, distributed mainly along the southern side of the Amman – Hallabat structure in Jordan the study area. Results show that σ1 (SHmax) and σ3 (SHmin) are generally sub-horizontal and σ2 is sub-vertical in 8 of 11 paleostress tensors, which are belonging to a major strike-slip system with σ1 swinging around N to NW direction. The other three stress tensors show σ2 (SHmax), σ1 vertical and σ3 is NE oriented. This situation explained as permutation of stress axes σ1 and σ2 that occur during tectonic events and partitioned strike slip deformation. NW compressional stresses affected the area and produced the major Amman – Hallabat strike-slip fault and its related structures, e.g., NW trending normal faults and NE trending folds in the study area.The new paleostress results related with the active major stress field of the region the Dead Sea Stress Field (DSS) during the Miocene to Recent.     

Modeling of source parameters of the 15 December 2015 Deogarh earthquake of M<Subscript>w</Subscript> 4.0

We herein present source parameters and focal mechanism of a rare cratonic upper crustal earthquake of M_w4.0, which occurred at 8 km depth (centroid depth) below a region near Deogarh, Jharkhand. For our study, we used broadband waveform data from a seismic network of 15 three-component seismographs in the eastern Indian craton. The average seismic moment, moment magnitude and source radius are estimated to be 1.1 × 10¹⁵ N-m, 4.0 and 180.6 m, respectively. The high average stress drop of 14.27 MPa could be attributed to its lower-crustal origin. The mean corner frequency is calculated to be 4.1 Hz. To study the source mechanism, we perform a deviatoric constrained full waveform moment tensor inversion of multiple point sources on the band-passed (0.06 – 0.14 Hz) broadband displacement data of the Deogarh event, using ISOLA software. The best fit is obtained for the source at 8 km centroid depth, with a moment magnitude 3.7, and a right-lateral strike-slip mechanism with strike 162°, dip 72° and rake 169°. The P-axis orients N24°E, which is parallel to the direction of the absolute plate motion direction of Indian plate, while T-axis orients E-W, which is parallel to the strike of the pre-existing Damodar Graben (DG) of Gondwana age. The occurrence of this earthquake is attributed to the neotectonic reactivation of a fault associated with the E-W trending DG shear zone.     

Structural analysis of faults related to a heterogeneous stress history: reconstruction of a dismembered gold deposit,Stawell, western Lachlan Fold Belt,Australia

In the internationally significant Victorian goldfields a complex system of faults dismembers the 5 million ounce Magdala gold deposit. These faults represent a combination of neoformed faults and inherited faults that reflect deformation associated with stress tensors of variable orientation and stress shape ratio (φ). The fault geometry is strongly controlled by the pre-existing rheology. Faults have propagated around the flanks of an antiformal basalt dome, along earlier ductile cleavages and the margins of porphyry dykes. Many of the faults do not have Andersonian geometries and there is no correlation between the orientation of the faults and the palaeostress directions. Much of the faulting is associated with the emplacement of porphyry dykes, additional gold mineralisation related to plutonism and late-stage deformation post-dating the intrusion of the Stawell pluton. Systematic mapping of extension veins associated with faults, striations and conjugate joint sets allowed the construction of a revised and more robust history of brittle deformation. This successfully predicted the offset direction of the currently mined Magdala ore body beneath the studied system of faults. The use of extension veins was a critical aspect of the analysis. If striations on the fault surfaces had solely been used, the offset direction of the new Golden Gift orebody would not have been correctly ascertained. The palaeostress history was delineated via use of compression and tension dihedra, stress inversion of slip data and calculation of theoretical resolved shear stress for faults with orientations similar to those mapped. The calculation of theoretical resolved shear stress directions highlights the importance that the intermediate stress has on the slip direction for faults whose pole does not lie in the plane containing σ₁ and σ₃.     

郯庐断裂带肥东桃源韧性剪切带构造分析及时限探究

郯庐断裂带在肥东桃源地区为一混合杂岩带,温压数据显示区域内变形变质环境为中下地壳构造环境。本文对剪切带的应变大小、应变速率、涡度以及应力场等构造特征进行分析测量,结果显示该剪切带所受应力方向为170°左右,夹角为40°～50°,并以简单剪切为主,其变形矿物被拉长。此外,带内发育的长英质糜棱岩流体以及伟晶岩流体均发生同构造变形,本文结合前期年代学研究结果,整合出了3种不同流体之间的关系,并有效限定出带内韧性剪切活动发生在140～124 Ma之间。同时,通过对郯庐断裂带中南段年代学数据统计,发现郯庐断裂带肥东段主要记录了早白垩世的剪切活动,而大别造山带东缘、苏鲁西缘分别记录了同造山年代学数据,断裂带中南段在年代学分布上呈现出明显的空间差异性,反映出郯庐断裂带递进变形的特征。     

跨活动断裂隧洞工程赋存区域地应力场分布特征研究

初始地应力的方向、量值和分布形式是影响岩石地下工程围岩应力、变形和破坏模式的重要因素,在工程区域难以开展大量实测工作,且实测结果具有相当的离散性,引入数值分析方法和数学理论对地应力场综合分析是有效的解决手段之一。结合滇中引水香炉山隧洞穿越龙蟠－乔后断裂段（楚波–白汉场断裂南段）工程,针对实测结果中方向结果离散性较大的问题,基于中国现代构造地应力场特征,对丽江地区复合断裂对区域地应力场影响的理论分析与数值模拟,获取了地应力场方向的定性认识。基于钻孔测试成果,通过基于多元线性回归的三维地应力场反演获取了地应力场方向与量值的定量认识。获得的初步结果表明,龙蟠–乔后断裂F10运动形式以正断错动为主;左旋走滑为辅的滑动,受其影响隧洞工程在穿越F10断裂部位的主应力发生偏转,偏转后最大主应力方向近似平行或小夹角相交于F10断裂走向;反演获得的香炉山隧洞趋近F10-1、F10-2段最大主应力量值范围为13～19 MPa,中间主应力为11～16 MPa,最小主应力为9～13 MPa,应力量值较高,并呈现 > > （ 、 分别为最大、最小水平主应力）的特征;F10断裂F10-1、F10-2主断带成为地应力场的控制性边界,其间应力量值明显小于上下两盘岩体,F10-1、F10-2主断带间岩体最大主应力量值范围在9～10 MPa,最小主应力量值范围在7～10 MPa,地应力最大主应力方向与隧洞纵轴线以约60°夹角相交,相交角度较大,对隧洞稳定性影响较大。     

Kinematics of Late Pliocene-Quaternary Normal Faulting in the Southeastern End of the Gediz Graben,Western Anatolia,Turkey

The kinematic analysis of fault-slip data obtained from lower Pliocene and Pleistocene deposits indicates two successive extensional events in the southeastern end of the Gediz graben. The late Pliocene N-S extensional phase was followed by a NNE-SSW extension in the Pleistocene. This change in extension direction from N-S to NNE-SSW is indicated by slip vectors on active fault planes and historic fault offsets. This younger extensional event is still active, as suggested by recent seismic activity and focal mechanisms of earthquakes in the region. The slip regime has important implications for the Neogene tectonic evolution of western Anatolia.