Geometry of stress function surfaces for an asymmetric continuum

A two-dimensional stress field of dislocation or fault is geometrically studied for an asymmetric continuum. For geometric surfaces of the stress and couple-stress functions, the mean and Gaussian curvatures are derived. The mean curvature of couple-stress function surface is connected with the asymmetric of stress tensor. Moreover, the Gaussian curvature of stress function surface is characterized by both the stress and couple-stress. On the other hand, the mean curvature of stress function surface is not affected by the asymmetry of stress. Based on these geometric expressions, the Coulomb’s failure criterion and the friction coefficient are expressed by the curvatures of couple-stress function surface. Moreover, geometric structures of stress and couple stress function surfaces are shown for edge and wedge dislocations as faults. The curvatures of these surfaces show that the effect of couple-stress is constrained around the dislocations only.     

基于Monte Carlo方法数值反演区域初始构造应力场——以巴颜喀拉块体为例

构造应力场往往对地震活动性具有控制作用,应力快速集中的地方常常是地震频繁发生的地方.本文以巴颜喀拉块体及其边界断裂带近20年来的7次中强震为例,结合区域历史地震震源信息、地质背景及GPS等观测数据,利用Monte Carlo方法和库仑-摩尔破裂准则为计算依据,反演该块体的震前初始构造应力场.通过将初始应力场反演中不确定部分限定在一个合理的上下限范围内进行独立的重复性随机试验,并运用统计学方法得到了巴颜喀拉块体1997年玛尼M_W7.5地震震前区域初始应力场.计算结果显示：（1）巴颜喀拉块体10 km深度处最大水平主应力方向自西向东呈顺时针旋转趋势,由NS向转变为近EW向,与浅部实测地应力数据、历史地震类型和板块运动方向吻合较好.（2）最大/最小水平主应力和二者差值自西向东均逐渐增加,最大水平主压应力值~400 MPa,最小水平主压应力值~250 MPa.差应力在昆仑山断裂带与阿尔金断裂带交汇处及甘孜—玉树断裂带西段较低（~150 MPa）;在昆仑山断裂带东端和甘孜—玉树断裂带的东南段局部地区较高（~220 MPa）.     

Morphometric analysis and tectonic interpretation of digital terrain data: a case study

Tectonic movement along faults is often re?ected by characteristic geomorphological features such as linear valleys, ridgelines and slope‐breaks, steep slopes of uniform aspect, regional anisotropy and tilt of terrain. Analysis of digital elevation models, by means of numerical geomorphology, provides a means of recognizing fractures and characterizing the tectonics of an area in a quantitative way. The objective of this study is to investigate the use of numerical geomorphometric methods for tectonic geomorphology through a case study. The methodology is based on general geomorphometry. In this study, the basic geometric attributes (elevation, slope, aspect and curvatures) are complemented with the automatic extraction of ridge and valley lines and surface speci?c points. Evans' univariate and bivariate methodology of general geomorphometry is extended with texture (spatial) analysis methods, such as trend, autocorrelation, spectral, and network analysis. Terrain modelling is implemented with the integrated use of: (1) numerical differential geometry; (2) digital drainage network analysis; (3) digital image processing; and (4) statistical and geostatistical analysis. Application of digital drainage network analysis is emphasized. A simple shear model with principal displacement zone with an NE–SW orientation can account for most of the the morphotectonic features found in the basin by geological and digital tectonic geomorphology analyses. Copyright © 2003 John Wiley & Sons, Ltd.     

根据走滑大地震前后应力轴偏转和应力降求取偏应力量值的研究

运用走滑地震造成的地震前后应力方向偏转和地震应力降Δτ推导得到地震震源处偏应力量值τ的解析表达式为τ=［Δτcos2(φ′[KG-*2]P-E)］/sin2(φ′[KG-*2]P-φP)(其中,φ\-P和φ′[KG-*2]P分别为地震前后的统计P轴走向,E为地震断层走向.).当震前P轴与震后P轴与断层走向夹角为45°时,该公式失效.对偏应力值与应力降比值随应力场主压应力轴与断层走向夹角及应力场主压应力轴偏转的变化进行分析表明,相同应力降造成的应力轴偏转越大,地下偏应力越小; 断层走向越接近主压应力轴方向,地震应力降场对偏应力场的贡献越小.将该方法运用于Landers地震震源区,求得了该地震Homestead Valley段的偏应力量值为10MPa.     

Syntheses of the regional stress fields of the Japanese islands

The principal stresses in northern Honshu and in central-southwest Japan are synthesized on the basis of the ridge push, slab pull and across-arc variation of differential forces due to crust/plate structural variation. Assuming a more compressive north–south horizontal stress in central Japan-northern Honshu than that of southwest Japan, the calculated principal stress profiles explain the observed stress fields in these areas: namely, a strike–slip fault type for southwest-central Japan and a reverse fault type for northern Honshu, both having east–west σ_Hmax. Kyushu is characterized by the gradient of horizontal stresses both in the east–west and north–south directions, which cannot be explained by simple plate interactions or by crust/plate structural variation. Combined with other lines of evidence for existence of mantle upwelling in the East China Sea west of Kyushu, it is proposed that the stress gradient is produced by the viscous drag exerted by the flow spread laterally from the upwelling plume. The eastward movement of Kyushu and southwest Japan relative to Eurasia revealed by the recent Global Positioning System measurements conducted by the Geographical Survey Institute of Japan would be partly explained by this basal drag.     

应用震源机制方法研究鹤岗煤田开采区的构造应力环境

求解鹤岗强矿震震源机制解结果,表现出走滑伴随逆断层和正断层活动、非双力偶型的多样性。两组节面优势分布方向和节面的倾角优势分布不显著,两者分布无明显规律,反映出矿井下破裂面比较复杂。矿震震源主压应力释放优势方向北西310°左右,优势倾角为25°～60°;主张应力轴走向NE,主张应力场优势方向为北东60°左右,仰角在30～70°之间;中等应力轴(N)近于垂直,优势倾角为70～90°。矿震震源机制解显示的矿区最大主应力方向与区域构造应力场的最大主应力方向近似正交,矿震震源机制主应力轴优势倾角远大于区域构造地震,反映的是矿区采煤生产的次生构造应力环境重力应力场的贡献明显。     

雁列断层应力场影响因素数值模拟分析

利用有限元法,建立具有黏弹性力学参数的断层接触对,采用对比分析的方法,通过改变雁列断层的几何间距和黏滞系数,分析影响雁列断层构造应力场的因素和分布状态,模拟出雁列断层在失稳过程中,地震所产生的应力降和应力应变等以及第一、第二、第三主应力与断层之间的角度关系等。     

汶川MS8.0级地震断层滑动机制研究

汶川M_S8.0级地震的发震构造为龙门山断裂带,地震地表破裂主要分布在其中的北川－映秀断裂和江油－灌县断裂上,尤其是沿前者发育了长达240 km左右的地表破裂带.通过对龙门山断裂带震后断层擦痕的测量,得到311条断层擦痕数据,利用由断层滑动资料反演构造应力张量的计算方法,得到研究区8个测点的构造应力张量数据,并获得了研究区构造应力场特征：区域现代构造应力场以近水平挤压为主,最大主应力方向（σ1）为76°～121°,平均倾角9°,应力结构以逆断型为主.受构造应力场及断层几何特征的影响,地表破裂呈现出分段性：映秀—北川段主要以NW盘逆冲为主,垂直位移明显;北川以北段为逆冲兼走滑,水平位移量与垂直位移量基本相当,或水平位移略大.     

Numerical Simulation of Displacement and Stress Fields Associated with the 1993 Kushiro-oki, Japan, Earthquake

—We constructed a three-dimensional finite element model to simulate coseismic and postseismic displacement and stress fields associated with the 1993 Kushiro-oki earthquake, which was a very large intermediate-depth earthquake that occurred within the subducted Pacific plate at a depth of 107 km beneath the southeastern part of Hokkaido, Japan. Taking the configuration of the subducted Pacific plate into account, we constructed a realistic model with lateral heterogeneity of viscoelastic structure. We assigned a variable slip distribution to the fault plane, which was obtained from inversion analysis of near-field seismic waveforms. The result shows that elastic deformation associated with the faulting reflects the assigned inhomogeneous slip distribution on the fault plane near the fault region, while it does not reflect the distribution on the free surface of the model. The calculated postseismic deformation does not reflect the slip distribution, but shows symmetric spatial patterns concerning the dipping direction of the fault both near the fault region and on the model surface. For the next 20 years following the earthquake, the amount of the calculated deformation is a fraction of the coseismic deformation. The calculated coeseismic deformation is large just above and below the fault plane, reaching 1 m, while the postseismic deformation is dominant near the upper and lower material boundaries between the subducted plate and the surrounding asthenosphere. The spatial distribution of maximum shear stress near the fault plane corresponds to the assigned slip distribution, amounting to 32 MPa. The directions of principal stress-change axes represent reverse fault type in the SSE region of the fault, whereas normal fault type is dominant in the NNW region with the exception of some asymmetrical spatial patterns of the principal stress-change axes on the fault due to the inhomogeneous slip distribution. Time variations both in the amount and the directions of stresses are minor, suggesting that the coseismic state of the stress would remain unchanged for two decades after the event.     

Coseismic stress parameter of three California Earthquakes derived from the stochastic finite fault technique

Stochastic finite fault modeling is used to derive the coseismic stress parameter distribution on the fault surface of three well-recorded California earthquakes: M7.0, 1989, Loma Prieta; M7.3, 1992, Landers; and M6.7, 1994, Northridge. Classical waveform inversion techniques are inherently more powerful than stochastic modeling as a means of deriving detailed source parameters. However, the application of stochastic methods to the source modeling problem is useful to: (1) explore and calibrate the limitations and boundaries of stochastic modeling, (2) understand its relationship to more deterministically based techniques, and (3) provide a view of the source radiation not available from deterministic modeling. The stress parameter distribution for the M7.0 1989 Loma Prieta earthquake fault shows a concentration of stress in the lower part of the northwest side of the fault and another concentration in the upper southeast side of the fault, with an average stress parameter of 80 bars over the fault surface. The stress parameter distribution for the M7.3 1992 Landers earthquake fault shows a gradual increase of stress starting from the southeast side of the fault, close to the hypocenter, towards the center. The maximum stress occurs in the lower central part of the modeled fault surface. The average stress parameter is 70 bars for the Landers earthquake. The stress parameter distribution of the M6.7 1994 Northridge earthquake shows a concentration at the lower southeast end of the fault surface, extending toward the center of the fault surface and stretching to the northwest end. The average stress parameter is 80 bars for Northridge earthquake. The stress parameter distributions derived in this study by stochastic finite-fault modeling of high-frequency motions show considerable similarity to many of the slip distributions provided by different research groups for the same earthquakes, suggesting that the derivation of stress parameter distribution on a fault surface by the method applied in this study is reliable and closely tied to slip on the fault.     

Implications of stress-drop models of earthquakes for the inversion of stress drop from seismic observations

We discuss the inversion of stress drops from seismic observations on the basis of crack or stress-drop models of earthquake mechanism. Since a formal inverse problem cannot be posed at present we discuss implications of solutions to direct problems. We first discuss the static approximations used to obtain stress drop from seismic moment and source dimensions. We show that the geometrical effects are quite significant if only one source dimension has been retrieved from seismic observations. The effect of variable stress drop is discussed and we show that the inverted stress drop is not a simple average of the actual stress drops on the fault. We discuss the energy release during faulting and show that the apparent stress has a complicated relation to the stress drop on the fault. We also show that the static stress drops obtained by seismologists are a lower bound to the actual dynamic stress drops on the fault. This may in part explain disagreements with laboratory results. Finally, we discuss the inversion of source dimensions from the far-field radiation. We analyse two extreme, simple dynamical source models, a circular fault and a rectangular fault and show that geometry has a much more pronounced effect on radiation than is usually acknowledged.     

首都圈地区震源机制解及现今构造应力场时空变化特征研究

基于2009年1月至2017年11月首都圈地区发生的8 061个地震事件的23 293条P波初动极性数据,采用改进的格点尝试法计算了首都圈地区单次地震的震源机制解和小震综合断层面解。在初步分析这些数据的基础上,利用计算得到的单次地震的震源机制解和搜集到的已有历史地震的震源机制解数据,运用线性反演法对首都圈地区构造应力场的时空变化特征进行了研究。结果显示:① 研究区的地震震源机制解类型以走滑型为主,正断型次之,这些地震震源机制解的P轴方位大都为ENE向和近EW向,与该地区的构造应力场方向基本一致,仅有个别地震的P轴方位为NNW向;② 首都圈地区的构造应力场具有较好的一致性和连续性,最大主应力轴方位由西部的ENE向至东部的近EW向呈现顺时针旋转的趋势,应力类型整体上为走滑型,这与以往的研究结果相一致;③ 通过与已有研究结果相比较认为:京西北地区现今构造应力场是相对稳定的,最大主应力轴未呈明显改变;唐山地区和北京地区的构造应力场（最大主应力轴）在1976年唐山地震前后可能发生了变化,唐山地震后一年至今（1977—2017年）是否发生变化,依据现有的计算结果尚不得而知,需要更多的研究来进一步验证.      

联合采用定性和定量断层资料的应力张量反演方法及在乌鲁木齐地区的应用

地壳应力场是地球动力学研究和地震孕育环境研究的重要基础资料.求解应力场的一种重要方法是根据断层擦痕资料反演,然而擦痕往往难以观测,但断层滑动性质也与应力场有紧密的关系,这部分资料十分丰富.本研究按照应力张量在断层面上的剪应力方向与擦痕滑动方向及断层滑动性质一致为准则提出了联合采用擦痕数据和定性断层滑动数据求解应力场的网格搜索法,并给出了反演参数的一定置信度下的置信区间.采用假定的走滑型、挤压型和拉张型应力张量产生由7个擦痕数据和80个定性断层滑动数据组成的三组数据集.采用这些人工合成数据求解应力张量的实验结果表明,该方法可以更为准确地反演应力张量参数,定性断层滑动资料的参与使得应力张量的主应力方向更加接近假定的主应力方向,并且,应力张量参数的不确定性大大减小.将该方法应用于乌鲁木齐附近的定量擦痕和定性断层滑动性质数据,得到该地区较为精确的应力张量.结果表明,乌鲁木齐主压应力方向为近南北向、主张应力方向近垂直向,应力形因子为0.03.该地区占主导地位的近东西向的逆冲断层是近南北向挤压和近垂直向拉张形成的.较低的应力形因子表明乌鲁木齐地区在南北向挤压并辅以博罗科努山和博格达山的东、西向挤压的应力状态下处于隆升状态.     

龙门山断裂带形成过程及其地应力状态模拟

以龙门山附近区域运动特征以及深部岩体力学特性为基本条件,采用FLAC模拟软件计算模拟分析了龙门山断裂形成过程和塑性区分布的几何特征.研究结果认为：汶川—茂县断裂F1、映秀—北川断裂F2和灌县—安县断裂F3是从中部开始发育,塑性区上侧逐渐发展至地表;F1断层首先出现,以后才依次形成F2和F3断层.这些塑性区的发育方向与水平面的夹角大致呈40°左右,并出现了各自的共轭断层,与实际的龙门山断裂大致吻合,说明区域构造运动是龙门山断层产生的主因.论文还揭示了区域构造运动过程中区块内主应力的变化规律,主要分为2个阶段,一是在区块挤压初期,主应力随着区块位移量的增大而增大;二是主应力相对稳定阶段,区块岩体内的主应力保持相对稳定的状态,达到临界破坏岩体的最大最小主应力比值一般介于3.31~4.39.     

Co-seismic Coulomb stress changes on the northern Tanlu fault zone caused by the Tohoku-Oki MW9.0 earthquake*

Based on the spherical earth dislocation theory and a fault slip model of the Tohoku-Oki M_W9.0 earthquake, the co-seismic Coulomb failure stress changes (ΔCFS) on the northern Tanlu fault zone at depths of 0–40 km are calculated. By comparing two sets of results from the spherical earth dislocation theory and the semi-infinite space one, the effect of earth curvature on the calculation results is analyzed quantitatively. First, we systematically summarize previous researches related to the northern Tanlu fault zone, divide the fault zone as detailed as possible, give the geometric parameters of each segment, and establish a segmented structural model of the northern Tanlu fault zone. Second, we calculate the Coulomb stress changes on the northern Tanlu fault zone by using the spherical earth dislocation theory. The result shows the Coulomb stress changes are no more than 0.003 MPa, which proves the great earthquake did not significantly change the stress state of the fault zone. Finally, we quantitatively analyze the disparities between the results of semi-infinite space dislocation theory and the spherical earth one. The average disparity between them is about 7.7% on the northern Tanlu fault zone and is 16.8% on the Fangzheng graben, the maximum disparity on this graben reaches up to 25.5%. It indicates that the effect of earth curvature can not be ignored. So it’s necessary to use the spherical earth dislocation theory instead of the semi-infinite space one to study the Coulomb stress change in the far field.     

赣北地区构造应力场分析

采用双差定位方法对赣北地区2008年1月—2019年7月545个地震进行重新定位,重定位地震在九江、宜春和新余等地区分布更为集中.结合地震精定位结果,利用格点尝试法分区计算赣北地区小震综合断层面解.结果表明,九江及周边地区最大主应力轴为近东西向,最小主应力轴为近南北向,这与其他学者的研究结果基本一致,认为该地区构造应力...     

于田2008年和2014年两次MS7.3地震孕育的应力环境

2008年3月21日新疆于田发生M_S7.3级地震,2014年2月12日于田再次发生M_S7.3级地震,两次地震相距约110 km.但是,前者震源机制为正断层,后者震源机制为左旋走滑断层.为进一步探讨这两次地震的孕育应力环境、发震机制及其动力学成因,本文进行三维有限元数值试验分析,计算了该区域在GPS约束条件下的速度场、应力和应变场变化,并与实际观测资料进行对比.数值计算得到的区域内几条主要大的走滑断层错动性质,与实际地质观察到的断层左旋或右旋性质吻合,验证了计算结果的可靠性.结果表明于田及其临近区域整体上处于北东-南西向挤压和北西-南东向拉张状态.在GPS速度约束条件下,2008年于田地震震中区域最大主张应变率大于最大主压应变率,处于以拉张为主的应力状态,NE走向断层受到北东-南西方向的拉应力作用,从而形成正断层;2014年于田地震处于拉张应变率与压应变率几乎一致的区域,NEE走向断层在NE-SW主压应力和NW-SE主张应力作用下发生左旋走滑.     

滇西北地区现今构造应力状态及其与地震的关系

基于搜集到的2000—2018年滇西北地区MS≥3.0地震的震源机制解,运用线性叠加反演法进行应力场反演,分析了滇西北地区现今的构造应力状态,进一步探讨了应力张量方差的时空分布与地震活动的关系。结果显示：(1)滇西北地区地震的震源机制解类型复杂,主要以走滑型（46%）为主,正断型（27%）次之;(2)研究区的构造应力场具有整体的一致性和局部的非均匀性,呈现为NNW向挤压和ENE向拉张的走滑型应力结构,说明研究区受到来自NNW向的水平挤压作用,对该地区上地壳运动和断裂活动起主导作用;(3)滇西北地区的应力张量方差大都小于0.2,除北部一些地区外,应力场基本处于均匀状态。根据应力张量方差随时间的变化和后续地震可知,中强地震大都发生在应力张量方差值低于0.2的情形,且主要发生在应力张量方差减小即震源机制解趋于一致的过程中。空间上这些地震基本都发生在应力张量方差的低值分布区及其边缘,这一结果有助于判定发震地点和了解区域应力集中增强过程。     

Evolution characteristics of Quaternary tectonic stress field in the north and east margin of Qinghai-Xizang plateau

By inversion of fault slip data for Quaternary tectonic stress field and the analysis of crustal deformation after late Teriary, we explained the evolution of crustal dynamic about the north and east margin of Qinghai-Xizang (Tibet) plateau since Miocene. From middle or late Miocene to early Pleistocene, the tectonic stress field was featured by a maximum principal compression which was coming from the collision of India Plate perpendicular to the boundary of the plateau, and was basically of reverse faulting type. Since the late period of early Pleistocene, India Plate continued to push northward and the compressional deformation of the plateau interior increased continuously, meanwhile, NW-SE extension appeared on the east side of the plateau. This formed a favorable condition for the interior block of the plateau to slide towards east and southeast, causing the faults surrounding the plateau to change from thrust to strike-slip. The contemporary tectonic stress field was formed from the late period of early Pleistocene and continued to present. The direction of maximum principal compressional stress rotated clockwise with respect to the previous tectonic stress field, the stress field was mainly of strike-slip type.     

SEISMOTECTONICS OF THE 8 AUGUST 2017 JIUZHAIGOU EARTHQUAKE AND THE THREE-DIMENSIONAL FAULT MODELS IN THE SEISMIC REGION

On 8 August 8 2017, an M_S7.0 earthquake occurred in Jiuzhaigou County, Sichuan Province. Field geological investigations did not find any co-seismic surface rupture in the epicenter area, implying that the seismogenic structure is likely a hidden active fault. Based on the results of the relocated aftershocks, the seismogenic fault was simulated and characterized using the SKUA-GOCAD software. The three-dimensional model of the seismogenic fault was preliminarily constructed, which shows that the main shock of the Jiuzhaigou M_S7.0 earthquake occurred at the sharp bending area of the fault surface, similar to the geometry of the active fault that generated several major earthquakes in the Songpan area during 1973-1976. Our study suggests that high seismicity of this area may be closely related to the inhomogeneous geometry of the fault surface. In this work, we collected the historical earthquakes of M ≥ 6.5, and analyzed the geometric and kinematic features of the active faults in the study area. A three-dimensional fault model for the 10 main active faults was constructed, and its limitation in fault modeling was discussed. It could provide evidence for analyzing the seismotectonics of historical earthquakes, exploring the relationships between earthquakes and active faults, and predicting major earthquakes in the future.