A complex variable technique for the stress field around an elliptic underground inhomogeneity

Summary The techniques of complex variables are used to obtain the solution for the two dimensional elastostatic problem of an elliptic inclusion, subject to an uniform stress field at infinity. It is required that the displacements are continuous and the stresses balance each other across the interface between the inclusion and the surrounding medium. The solution is general in that it can be used for any required shape of the ellipse representing the inclusion and for any arbitrary choice of the elastic parameters of the inclusion and the medium.     

地球物理学及地球动力学研究与计算数学

地球物理学是20世纪,特别是在其中叶以后迅速发展起来的一门边缘科学.它以物理学、数学和信息科学为依托,并与地质学、地球化学密切结合;以研究和探索地球内部介质的属性、结构变异和深部物质与能量的交换、深层过程和动力学响应.这在促进社会与经济的发展和科学与技术的进步中占有重要地位,因为大量资源的需求和自然灾害的防范在人类生活和生存空间以及可持续发展中乃核心所在.在研究和探索这一系列的地球科学问题的进程中,首先必须通过地表进行高精度的地球物理探测、观测和高分辨率的数据采集,进而利用不同的数学方法反演计算地球内部介质的精细结构和其物理—力学过程与动力学响应.基于此,本文主要讨论了：1）地球物理学和地球动力学的发展趋势及特点;2）地球物理学的发展对计算数学的需求;3）地球动力学和数值模拟与计算地球物理学.最后对这些问题和基本导向进行了讨论.     

Introduction to geodynamics for high- and ultrahigh-pressure metamorphism

Since the first workshop on ultrahigh-pressure (UHP) metamorphism at Stanford in 1994 and the special issue of The Island Arc `Ultrahigh-Pressure Metamorphism and Tectonics' published in December 1995, many symposia and special sessions specifically with regard to the UHP metamorphic terrane have been held. While we are still wondering how exhumation of UHP rocks from mantle depths to the surface takes place, the finding of possible records from the mantle transition zone at 300–400 km depths is astonishing. The study of the UHP regime has expanded to include input from mineral physics, experimental geochemistry and kinetics in addition to the petrochemical and tectonic study of a variety of HP–UHP rocks. It was with this theme that the second workshop for the task group III-6 `Ultrahigh-Pressure Metamorphism and Geodynamics in Collision-type Orogenic Belts' of the International Lithosphere Program was held during the International Geological Congress in Beijing, 1996. The Symposium 8–9 `Dynamic Metamorphic Rocks and High- and Ultrahigh-Pressure Metamorphism' (Cong Bolin & J. G. Liou conveners) had more than 25 presentations in two oral sessions and 70 papers in one poster session. This second special issue of The Island Arc includes nine papers from this symposium and a few related contributions to the geodynamics of HP–UHP metamorphism and tectonics. It is our hope that The Island Arc will continue to publish a special issue on this increasingly recognized subject that is essential to our understanding of continental collision, mantle dynamics and geochemical + fluid cycles.     

A new probabilistic technique to build an age model for complex stratigraphic sequences

The age models of fluvio-lacustrine sedimentary sequences are often subject of discussions in paleoclimate research. The techniques employed to build an age model are very diverse, ranging from visual or intuitive estimation of the age-depth relationship over linear or spline interpolations between age control points to sophisticated Bayesian techniques also taking into account the most likely deposition times of the type of sediment within the sequence. All these methods, however, fail in detecting abrupt variations in sedimentation rates, including the possibility of episodes of no deposition (hiatus), which is the strength of the method presented in this work. The new technique simply compares the deposition time of equally thick sediment slices from the differences of subsequent radiometric age dates and the unit deposition times of the various sediment types. The percentage overlap of the distributions of these two sources of information, together with the evidence from the sedimentary record, helps to build an age model of complex sequences including abrupt variations in the rate of deposition including one or many hiatuses.     

Some applications of elastic notch theory to problems of geodynamics

Summary This paper is concerned with the behavior of surface features of the earth which are, or have been, acted on by a stress field. The theory used in this paper is that of classical elasticity. Mathematical models are made which represent perfectly elastic two-dimensional regions which have a notch (or protrusion as a reversed notch can be considered to be). The regions are assumed to be semi-infinite and the notch on the free surface. The loads, or boundary conditions, are then prescribed. The problem of determining the distribution of stress is then considered. Solutions to this problem are presented for the cases of a circular notch, a generalized circular notch and a type of notch whose mathematical representation is given parametrically. Using these solutions and applying a criterion for failure, it is possible to predict what the general trend of the faulting should be in an actual body which the model may represent. Possible applications to geological structures are indicated.     

数值模拟在地球动力学中的研究进展

本文主要针对有限单元法,对近10几年来数值模拟在地球动力学中的应用和发展作了回顾,分为构造应力场模拟;地幔热对流模拟;板块碰撞模拟;岩石圈流变学模拟;以及地震机制与预测模拟等部分.简单阐述了当前地球动力学数值模拟的发展趋势并论述了其面临的主要问题.     

Plate kinematics and geodynamics in the Central Mediterranean

We argue that seismotectonic activity in the Central Mediterranean area and the Aegean–Balkan zone is driven by the NNE-ward motion of Africa and westward motion of Anatolia with respect to Eurasia. These boundary conditions can plausibly and coherently account for E–W shortening and roughly S–N extension in the Aegean domain, thrusting and uplift at the boundary between the Aegean–Balkan system and the Adriatic/Ionian domain (Hellenic trench, Cephalonia fault, Epirus, Albanides and Southern Dinarides), the kinematics of the Adria plate (a large block encompassing the Adriatic continental domain, the northern Ionian zone and Hyblean-Adventure block) and consequently, the complex pattern of deformation recognized at its boundaries. Furthermore, the fact that in our scheme Adria moves almost in connection with Africa is consistent with the lack of an active decoupling zone between Adria and Africa, an evidence that can hardly be reconciled with the kinematics so far proposed for these two plates. The reasons why we adopt an Africa–Eurasia relative motion different from that implied by the popular NUVEL-1 global solution are discussed in detail. Finally, we make some considerations about the possible implications of the presently available geodetic data on the long-term plate kinematics.     

Mechanical problems in geodynamics and work done in China

The subject of geodynamics concerns the dynamics of the global motion of the earth, of the motion in the earth's interior and its interaction with surface features, together with mechanical processes in the deformation and rupture of geological structures. A brief historical review is given from Sir I. Newton, Maclauwin, Jacobi, Poincaré, Poisson, Lamé, Darwin, Rayleigh, and Love, who dealt with the homogeneous sphere, to Leibenson, Takeuchi, and Meinesz, concentrating on layered spheres, and after the advent of plate tectonics, on the use of numerical simulation, to the analyses of tectonic features, earthquake mechanism, the application of nonlinear dynamics. By discussing the forward and inverse mechanical problems, and the questions facing the inverse problems of searching for the structural parameters, driving forces, etc. are raised in more detail. Thereafter, some works accomplished in China on the global and regional stress fields analyses; tectonic features' analyses, mantle flow studies; experimental studies of rocks and their constitutive relations are presented. Finally, the interdisciplinary nature of the subject is emphasized, and the main mechanical problems that need special attention are then proposed.     

Predicting phosphorus dynamics in complex terrains using a variable source area hydrology model

Phosphorus (P) loss from agricultural watersheds has long been a critical water quality problem, the control of which has been the focus of considerable research and investment. Preventing P loss depends on accurately representing the hydrological and chemical processes governing P mobilization and transport. The Soil and Water Assessment Tool (SWAT) is a watershed model commonly used to predict run‐off and non‐point source pollution transport. SWAT simulates run‐off employing either the curve number (CN) or the Green and Ampt methods, both assume infiltration‐excess run‐off, although shallow soils underlain by a restricting layer commonly generate saturation‐excess run‐off from variable source areas (VSA). In this study, we compared traditional SWAT with a re‐conceptualized version, SWAT‐VSA, that represents VSA hydrology, in a complex agricultural watershed in east central Pennsylvania. The objectives of this research were to provide further evidence of SWAT‐VSA's integrated and distributed predictive capabilities against measured surface run‐off and stream P loads and to highlight the model's ability to drive sub‐field management of P. Thus, we relied on a detailed field management database to parameterize the models. SWAT and SWAT‐VSA predicted discharge similarly well (daily Nash–Sutcliffe efficiencies of 0.61 and 0.66, respectively), but SWAT‐VSA outperformed SWAT in predicting P export from the watershed. SWAT estimated lower P loss (0.0–0.25 kg ha^?1) from agricultural fields than SWAT‐VSA (0.0–1.0+ kg ha^?1), which also identified critical source areas – those areas generating large run‐off and P losses at the sub‐field level. These results support the use of SWAT‐VSA in predicting watershed‐scale P losses and identifying critical source areas of P loss in landscapes with VSA hydrology. Copyright © 2014 John Wiley & Sons, Ltd.     

Transient creep of the lithosphere and its role in geodynamics

Laboratory experiments with samples of rocks show that at small strains there is transient creep, at which the strain grows with time, and the strain rate decreases. Plate tectonics allows only small strains in the lithospheric plates, so that the lithosphere creep is transient. In geodynamics, the lithosphere is regarded as a cold boundary layer formed by mantle convection. If we assume that the lithosphere has a steady-state creep, which is described by power-law non-Newtonian rheological model, the low effective viscosity of the lower layers of the lithosphere, obtained by data on small-scale postglacial flows, is possible only at high strain rates in these layers. However, the high strain rates in the lithosphere induce large strains that contradict plate tectonics. Transient creep of the lithosphere leads to its mobility at small strains, removing the discrepancy between thermal convection in the mantle and plate tectonics, which holds in the case of power-law rheological model of the lithosphere.     

变刚度隔震保护装置试验研究

通过在距离隔震层一定位移处设置由弹簧和与其串联的限位挡板组成的变刚度保护装置作为第二道防线,成功地进行了五层框架的变刚度隔震保护模拟地震振动台试验。理论分析和试验结果表明,变刚度隔震保护装置能有效改变结构动力特性,减小隔震层的变形,使之限制在允许的范围内。     

天山造山带深部探测及地球动力学研究进展

为了研究天山造山带的地球动力学,自1970年代以来,国内外在天山造山带开展了大量的深部探测工作,并取得了丰富的成果,本文对这些工作和成果进行了梳理和综述.已有研究结果表明:天山造山带的地壳厚度较大,但并无明显山根;地壳结构具有垂向分层和横向分块特征;壳幔界面不清晰,莫霍面在盆山接合部下方发生错断;壳内普遍发育低速异常体,地壳泊松比较高,暗示了地壳力学上的弱化作用;上地幔也存在波速异常体,低速异常可能与地幔热物质上涌有关,高速体可能是古老板块的岩石圈拆离碎片;莫霍面错断、Q值结构和波速异常特征可以用天山南北侧稳定地质块体往天山造山带之下俯冲来解释,这也得到高分辨率层析成像结果的支持;剪切波分裂结果暗示有相当厚的上地幔卷入了造山过程.上述资料表明天山造山带的变形和隆升是其南北侧稳定地质块体的构造挤压与壳—幔复杂耦合作用的共同结果.     

On the product of legender functions as encountered in geodynamics

Résumé On rencontre souvent des produits de fonctions de Legendre en géodésie mathématique, en mécanique céleste et quantique, et en géophysique. Nous donnons les expressions générales des coefficients de la décomposition d'un produit quelconque sur la base des fonctions de Legendre ellesmêmes. Quelques applications immédiates sont envisagées.     

IDOAS: A new monitoring technique to study the 2D distribution of volcanic gas emissions

Imaging Differential Optical Absorption Spectroscopy (IDOAS) is an optical remote-sensing method using scattered sunlight as light source. It combines a “pushbroom” imaging spectrometer with the DOAS technique and thus allows imaging two-dimensional trace gas distributions, e.g., in volcanic plumes. The highly sensitive and specific detection of many trace gases simultaneously (specific molecules, not just elements, e.g. SO₂, BrO, NO₂, O₃, HCHO, etc.) is possible, and the temporal and spatial variation of these gases can be measured. The IDOAS system presented here enables the taking of two-dimensional images of trace gas distributions in a volcanic plume with a spatial resolution of 100 pixels horizontally × 64 pixels vertically, each with a field of view of 0.087° in horizontal and 0.208° in vertical directions. Therefore, IDOAS provides useful information about the chemical composition and chemical variability in a volcanic plume and allows studying plume dispersal and chemical transformations. The technique was applied to map the SO₂ distribution in the plume of Mt. Etna volcano for the first time in October 2003.     

Preface to the special issue on the crustal and upper mantle structure and geodynamics in Chinese mainland

Over the past decade, one important development was the rapid and significant improvement of instruments and observation techniques, such as the broad- band seismometers and the seismic-array observations, which permit to widespread collect seismic wave and then clearly demonstrate the crustal and upper mantle structure.     

基于小基线DInSAR技术监测太原市2003～2009年地表形变场

基于高相干点目标反演缓慢地表形变已成为当前DInSAR技术的研究热点.本文通过融合PS方法和相干目标法优点,采用小基线DInSAR技术提取城市地表形变场,并重点分析了地表线性形变的反演.在此基础上,以太原市为研究区,利用23景ENVISAT ASAR影像,提取了该市2003～2009年的地表形变场.研究结果表明:(1)...     

Miocene to Quaternary deformation in NE Slovenia: complex paleomagnetic and structural study

Combined paleomagnetic and structural research was carried out in the Mura-Zala Basin including the western and southern surrounding hills in northeastern Slovenia. The Mura-Zala Basin was formed due to ENE–WSW trending crustal extension in the late Early Miocene (18.3–16.5 Ma). First, marine sedimentation took place in several more or less confined depressions, then in a unified basin. During thermal subsidence in the late Miocene deltaic to fluvial sediments were deposited. After sedimentation, the southernmost, deepest depression was inverted. Map-scale folds, reverse and strike-slip faults were originated by NNW–SSE compression. This deformation occurred in the latest Miocene–Pliocene and is reflected also in the magnetic fabric (low field susceptibility anisotropy). After this folding, the Karpatian sediments of the Haloze acquired magnetization, then suffered 30° counterclockwise rotation relative to the present north (40° counterclockwise with respect to stable Europe). This Pliocene (Quaternary?) rotation affected a wide area around the Mura-Zala Basin. The latest Miocene to Quaternary folding and subsequent rotation may be connected to the counterclockwise rotation of the Adriatic microplate.     

大数据时代的地球动力学数值计算方法回顾与展望

随着大数据时代的到来,计算地球动力学数值计算方法体系更加完善.本文系统地回顾了传统数值模拟方法在计算地球动力学领域的应用进展,包括:有限差分法、有限单元法、谱方法和谱元法;并对近年来一些新发展的算法和应用前景进行了综述,如:不连续Galerkin法、小波方法和格子玻尔兹曼方法等.本综述有助于读者以整体视角了解地球动力学数值计算方法的发展脉络,并对大数据时代下研究适应日益丰富的数据和新算法提供有益参考.