Temperature control of continental lithosphere elastic thickness,Te vs Vs

The elastic thickness of the continental lithosphere is closely related to its total strength and therefore to its susceptibility to tectonic deformation and earthquakes. Recently it has been questioned whether the lithosphere thickness and strength are dependent on crustal and upper mantle temperatures and compositions as predicted by laboratory data. We test this dependence regionally by comparison in northwestern North America of the effective elastic thickness Te, from topography–gravity coherence, with upper mantle temperatures mapped by shear wave tomography velocities Vs and other temperature indicators. The Te values are strongly bimodal as found globally, less than 20 km for the hot Cordillera backarc and over 60 km for the cold stable Craton. These Te correspond to low Vs beneath the Cordillera and high Vs beneath the Craton. Model temperature-depth profiles are used to estimate model Te for comparison with those observed. Only limited areas of intermediate thermal regimes, i.e., thermotectonic ages of ~ 300 Ma, have intermediate Te that suggest a weak lower crust over a stronger upper mantle. There are large uncertainties in model Te associated with composition, water content, strain rate, and decoupling stress threshold. However, with reasonable parameters, model yield stress envelopes correspond to observed Te for thermal regimes with 800–900 °C at the Cordillera Moho and 400–500 °C for the Shield, in agreement with temperatures from Vs and other estimators. Our study supports the conclusion that lithosphere elastic thickness and strength are controlled primarily by temperature, and that laboratory-based rheology generally provides a good estimate of the deformation behaviour of the crust and upper mantle on geological time scales.     

海洋岩石圈板块有效弹性厚度研究

本文在前人研究大陆岩石圈板块有效弹性厚度的基础上,建立研究海洋岩石圈板块有效弹性厚度的理论模型,推导出与大陆岩石圈不同的海洋岩石圈板块响应函数 Z(k,Te) 理论计算公式.并分析海洋岩石圈板块响应函数 Z(k,Te) 的特点.文中对实际的海洋测量数据的响应函数 Z(k,Te) 进行计算和分析,估算我国南海南沙海域和南海中央海盆岩石圈板块有效弹性厚度分别约为10 km和6~7 km.     

Effective elastic thickness of island arc lithosphere under Japan

Abstract Using topography and observed gravity anomalies, we have estimated the effective elastic thickness as a measure of strength of Japanese island arc lithosphere. The thickness is found to range from about 3 km to >20 km. The thickness seems to be controlled primarily by the thermal state of the lithosphere. The higher the heat flow, the thinner is the elastic plate. However, several areas show significant deviations. The smaller effective elastic thickness in the northern Ryukyu arc than that inferred from heat flow may be attributed to the stress regime. In Japan, extensional tectonics are going on only in the Ryukyu arc region. Shallow subducting slab under the south-western Japan frontal arc probably increases the effective thickness by several kilometers. The determined effective elastic thickness suggests that when we consider vertical movements in the volcanic arc, we should take account of topographic and subsurface loading over a few hundred kilometers. However, if the dip of the slab is shallow, the flexural responses of the underlying slab, not only that of the island arc lithosphere, should be taken into account for the compensation, as is the case of the south-western Japan frontal arc.     

The elastic thickness of the lithosphere in the Pacific Ocean

In this study, we present determinations of the effective elastic thicknessT_e of the oceanic lithosphere along Pacific chains or archipelagoes.T_e is determined by computing the deflection of a continuous elastic plate under the load of volcanoes, and constrained by geoid heights provided by SEASAT. In the South Central Pacific, estimates of 14 km for the Marquesas and 6 km or less for the Pitcairn-Mururoa-Gloucester chain are in good agreement with a previous work in this region (Cook-Austral and Society chains). Around the Line Islands chain, SEASAT data reveal that the bathymetry is poorly known, preventing fine analysis. Meanwhile,T_e looks globally very low ( 6 km), except for three volcanoes but these results may be unreliable. The Easter chain features lowT_e values ( 6 km), with no noticeable variation along the chain. Higher values are found for a Samoan island, Manuae (24 km), and along the Hawaiian-Emperor seamounts chain (from 32 km at the eastern end of the chain to 21.5 km for the Hawaiian volcanoes, and from 25.5 to 15 km for the Emperor seamounts). The large number ofT_e estimates obtained in this study points out a noticeable difference between North and South Pacific results. Those from the North Pacific agree with the general trend (increase with the square root of age plate at loading time), while those from the South Central Pacific are much lower, according to their plate age. These lowT_e results from the South Pacific are only partly explained by taking account of thermal perturbations using the rejuvenation model. Therefore, these results then point out a regional difference in oceanic lithosphere.     

The existence of a thin low-viscosity layer beneath the lithosphere

The horizontal temperature gradient at the base of the lithosphere at an oceanic fracture zone, where plate of different ages is juxtaposed, is expected to drive a local circulation, the characteristics of which can be constrained by the amplitude, wavelength and age-dependence of the geoid. Two-dimensional numerical models of convection in a fluid layer overlain by a solid conducting lid have been used to generate theoretical geoid profiles at right angles to the fracture zone. Only a thin, low-viscosity layer provides a reasonable fit to the data. The best model so far obtained has a fluid layer 150 km thick with viscosity 1.5 × 10¹⁹ Pa s under a 75 km lid. Such a layer, which is incapable of transmitting strong horizontal shear stresses, could provide the decoupling mechanism between plate and deep mantle flow required to balance the forces on the plates.     

利用Moho地形导纳法(MDDF)反演中国大陆岩石圈有效弹性厚度

本文用数值实验方法验证了,在Moho地形导纳法(MDDF)中使用先由重力数据反演的Moho面相对起伏数据,能较传统的重力地形导纳法获得更高的反演精度.之后作者应用Moho地形导纳法(MDDF)反演获得了精度较高的中国大陆区域岩石圈有效弹性厚度.结果显示:(1)中国地区岩石圈有效弹性厚度Te从东向西大体上呈阶梯状上升;(2)Te与岩石圈地震-热厚度、地表热流、上地幔顶部的地震波速度等数据密切相关;(3)在中国中东部, Te较低的区域以及Te的高低值转换带对应较强的地震活动性.但在西部,Te与地震活动性的相关性并不明显.     

A comparison of the estimated effective elastic thickness of the lithosphere using terrestrial and satellite-derived data in Iran

The effective elastic thickness of the lithosphere has an important role in constraining compositional structure, geothermal gradient and tectonic forces within the lithosphere and the thickness of this layer can be used to evaluate the earthquakes’ focal depth. Hence, assessment of the elastic thickness of the lithosphere by gravitational admittance method in Iran is the main objective of this paper. Although the global geopotential models estimated from the satellite missions and surface data can portray the Earth’s gravity field in high precision and resolution, there are some debates about using them for lithosphere investigations. We used both the terrestrial data which have been provided by NCC (National Cartographic Center of Iran) and BGI (Bureau Gravimetrique International), and the satellite-derived gravity and topography which are generated by EIGEN-GL04C and ETOPO5, respectively. Finally, it is concluded that signal content of the satellite-derived data is as rich as the terrestrial one and it can be used for the determination of the lithosphere bending.     

The role of elastic stored energy in controlling the long term rheological behaviour of the lithosphere

The traditional definition of lithospheric strength is derived from the differential stresses required to form brittle and ductile structures at a constant strain rate. This definition is based on dissipative brittle and ductile deformation and does not take into account the ability of the lithosphere to store elastic strain. Here we show the important role of elasticity in controlling the long-term behaviour of the lithosphere. This is particularly evident when describing deformation in a thermodynamic framework, which differentiates between stored (Helmholtz free energy) and dissipative (entropy) energy potentials. In our model calculations we stretch a continental lithosphere with a wide range of crustal thickness (30–60 km) and heat flow (50–80 mW/m²) at a constant velocity. We show that the Helmholtz free energy, which in our simple calculation describes the energy stored elastically, converges for all models within a 25% range, while the dissipated energy varies over an order of magnitude. This variation stems from complex patterns in the local strain distributions of the different models, which together operate to minimize the Helmholtz free energy. This energy minimization is a fundamental material behaviour of the lithosphere, which in our simple case is defined by its elastic properties. We conclude from this result that elasticity (more generally Helmholtz free energy) is an important regulator of the long-term geological strength of the lithosphere.     

利用Moho面起伏及地表地形数据反演岩石圈有效弹性厚度的莫霍地形导纳法(MDDF)

区域岩石圈有效弹性厚度Te的确定对认识其力学性质及演化等动力学问题具有重要意义.长期以来,大陆地区有效弹性厚度的确定一直存在着争议.尽管Pérez-Gussinyé等2004年的研究消除了不同方法(自由空气导纳法和布格相关法)之间的分歧,但其确定有效弹性厚度的误差仍然非常大.本文提出了利用Moho面起伏及地表地形反演岩石圈有效弹性厚度的Moho地形导纳法(MDDF),并利用合成的地表地形和Moho面起伏模型验证了该方法的可行性.结果表明,与传统的重力地形导纳法相比,使用Moho地形导纳法(MDDF)反演岩石圈有效弹性厚度,能较好地提高反演精度.     

Effective elastic thickness of the lithosphere from joint inversion in western China and its implications*

The western China lies in the convergence zone between Eurasian and Indian plates. It is an ideal place to study the lithosphere dynamics and tectonic evolutions on the continental Earth. The lithospheric strength is a key factor in controlling the lithosphere dynamics and deformations. The effective elastic thickness (T_e) of the lithosphere can be used to address the lithospheric strength. Previous researchers only used one of the admittance or coherence methods to investigate the T_e in the western China. Moreover, most of them ignored the internal loads of the lithosphere during the T_e calculation, which can produce large biases in the T_e estimations. To provide more reliable T_e estimations, we used a new joint inversion method that integrated both admittance and coherence techniques to compute the T_e in this study, with the WGM2012 gravity data, the ETOPO1 topographic data, and the Moho depths from the CRUST1.0 model. The internal loads are considered and investigated using the load ratio (F). Our results show that the joint inversion method can yield reliable T_e and F values. Based on the analysis of T_e and F distributions, we suggest (1) the northern Tibetan Plateau could be the front edge of the plate collision of Eurasian and Indian plates; (2) the southern and part of central Tibetan Plateau have a strong lithospheric mantle related to the rigid underthrusting Indian plate; (3) the southeastern Tibetan Plateau may be experiencing the delamination of lithosphere and upwelling of asthenosphere.     

The effective elastic thickness of the lithosphere in the collision zone between Arabia and Eurasia in Iran

The effective elastic thickness, T_e, has been calculated in the collision zone between Arabia and Eurasia in Iran from the wavelet coherence. The wavelet coherence is calculated from Bouguer anomalies and topography data using the isotropic fan wavelet method, and gives T_e values between 14.2 and 62.2 km. The lower value is found in the Central Iranian Blocks and the East Iranian Belt which are bounded by several large strike-slip faults with lithospheric origin. The higher value occurs in the east of the South Caspian Sea Basin. The resulting T_e map shows positive and negative correlation with shear wave velocity and surface heat flow, respectively. A comparison between the seismogenic thickness (T_s) and T_e in Iran suggests that T_e > T_s. Results of the load ratio in Iran indicate that in most of the study area surface loads are much more prevalent than subsurface loads, except in the Central Iranian Blocks and NW of Iran. Intermediate to low T_e values in Iran were inherited from multiple rifting and orogenic activities from Late Precambrian (∼650 Ma) to present day which are not only reflected in thin and warm lithosphere but also an increasing seismicity rate.     

大型模拟地震振动台的特殊控制

阐述了多度大型地震模拟振动台由于试件重心高,偏心以及几何等原因在一个轴线方向上振动量,造成对其他轴线方向运动的干扰,同时介绍了克服这些干扰的控制原理。     

青藏高原东北缘岩石圈有效弹性厚度与地震分布关系

岩石圈有效弹性厚度（T_e）表征岩石圈综合力学强度,对理解区域深部构造孕震环境具有重要意义.青藏高原东北缘地质构造复杂,强烈地震活动频发.为进一步了解该区域深部岩石圈力学性质特征及其与地震活动的关系,本文利用基于Fan小波的谱方法,使用WGM2012重力异常数据、ETOPO1地形数据和CRUST1.0模型,通过导纳和相关联合反演计算了青藏高原东北缘的岩石圈有效弹性厚度（T_e）与荷载比（F）.结果显示研究区T_e整体呈明显的东高西低分布,青藏块体T_e变化剧烈,西部高值（>40 km）和东部低值（< 20 km）共存;鄂尔多斯地块T_e较高（>30 km）,变化相对平缓;荷载比F存在局部西南高,巴颜喀拉和羌塘地块荷载比F较高（>0.5）,说明以地下荷载为主,其他地块荷载比F较低（< 0.2）,以地表荷载为主.鄂尔多斯地块结构稳定,岩石圈强度较大,T_e值较高;内部构造活动性微弱,深部物质密度横向变化较小,岩石圈所受荷载以地表为主,荷载比F较低.柴达木地块东部与巴颜喀拉地块东部可能发生有下地壳流,岩石圈较为软弱,T_e值较低;巴颜喀拉地块内部与鲜水河断裂的荷载比F较高,岩石圈所受荷载以地下为主,可能是地壳物质向东流动导致岩石圈深部物质密度横向变化较大引起的.通过对比分析研究区T_e和T_e梯度、F和F梯度与地震之间的对应关系,发现地震一般发生在区域相对低T_e值、T_e梯度值和荷载比F梯度值较大的区域,震级较小的地震多发生在荷载比F较小的地区,6级以上强震则较多发生在荷载比F约为0.1和0.8的区域.因此,岩石圈有效弹性厚度T_e值较低、T_e梯度和荷载比F梯度较大的地区,更易出现地震.

     

Open-loop vibration control of elastic structural elements

This paper discusses a general technique for vibration control of simple, continuous mechanical systems. The discussion involves giving the expressions for the response of an illustrative element (fixed-free bars) to a sinusoidal disturbance and then formulating the problem of open-loop vibration control of this system as a mathematical programming problem. The final step uses numerical optimization techniques to find the control forces. When these techniques are used, the amplitude of the system's steady state response is minimized. The discussion also shows that while this method effectively controls the vibration, it has a great deal of flexibility in accomplishing its stated purpose.     

On the thermal bending of a thin elastic simply supported rectangular plate resting on an elastic foundation

Pure and Applied Geophysics - Deflection and bending moments of a thin isotropic rectangular plate, having its edges simply supported and maintained at zero temperature, have been investigated in...     

A review on developments in the electrical structure of craton lithosphere

Cratons have a long history of evolution. In this paper, applications of the magnetotelluric method used in the study of craton lithosphere over the past 30 years were reviewed, examining case studies of cratons in North America, South America, Asia, Australia, and Africa. The nuclei of the Archean cratons, for example the Kalahari Craton and Rae Craton, are usually characterized by thick and highly resistive lithospheric roots. During or after the formation of the cratons, tectonothermal events, such as collision, mantle plume, and asthenosphere upwelling led to the formation of high-conductivity zones in the craton lithosphere, which could be attributed to the increased hydrogen content (of nominally anhydrous minerals), higher iron content, and formation of graphite films or sulfides along the grain boundary of minerals. These conductive zones are characterized by resistivity discontinuities in craton lithosphere. In particular, the conductive zones include (1) large-scale lithospheric mantle conductors beneath the Slave Craton, Gawler Craton, and central part of North China Craton(Trans-North China Orogen); (2) near-vertical high-conductivity zone associated with the fossil subduction zone beneath the Dharwar Craton and Slave Craton; and (3) regional lateral electrical discontinuities, such as a conductive anomaly under the Bushveld Complex of the Kaapvaal Craton. The eMoho refers to the electrical discontinuity in the crust-mantle boundary. In existing research, this has been detected under the condition of extremely high lithospheric resistivity with only a slight decrease in the lower crust, and in the case of a very thin conductive lower crust or the lack thereof. In the resistivity model, the unique “mushroom-like” lower crust-lithosphere mantle conductor and very thin lower crust layer of the North China Craton may represent lithosphere destruction and/or thinning. We also find that some of the cratons are still not well understood. Therefore, extensive three-dimensional inversion and joint interpretation of geochemical, geophysical, and geologic data are necessary to understand the tectonic evolutionary history of craton lithosphere.

     

Thinning and destruction of the cratonic lithosphere:A global perspective

It has been proposed that the North China Craton(NCC)was thinned up to a thickness of100 km during the Phanerozoic,and underwent an associated craton destruction.Evidently,it is an important topic worthy of future study to understanding the mechanism of cratonic destruction and its role played in the continental evolution.After synthesized the global cratons of India,Brazil,South Africa,Siberia,East Europe(Baltic)and North America,we found that lithospheric thinning is common in the cratonic evolution,but it is not always associated with craton destruction.Most cratons was thinned by thermal erosion of mantle plume or mantle upwelling,which,however,may not cause craton destruction.Based on the studies of the North American and North China Cratons,we suggest that oceanic subduction plays an important role in caton destruction.Fluids or melts released by dehydration of the subducted slabs metasomatize the mantle wedge above and trigger extensive partial melting.More importantly,the metasomatized mantle lost its original rigidity and make craton easier to be deformed and then to be destoyed.Therefore,we suggest that the widespread crust-derived granite and large-scale ductile deformation within the continental crust can be regarded as the petrological and structural indicators of craton destruction,respectively.     

Predictive instantaneous optimal control of elastic structures during earthquakes

A predictive instantaneous optimal control (PIOC) algorithm is proposed for controlling the seismic responses of elastic structures. This algorithm compensates for the time delay that happens in practical control applications by predicting the structural response over a period that equals the time delay, and by substituting the predicted response in the instantaneous optimal control (IOC) algorithm. The unique feature of this proposed PIOC algorithm is that it is simple and at the same time compensates for the time delay very effectively. Numerical examples of single degree of freedom structures are presented to compare the performance of PIOC and IOC systems for various time delay magnitudes. Results show that a time delay always causes degradation of control efficiency, but PIOC can greatly reduce this degradation compared to IOC. The effects of the structure's natural periods and the choice of control gains on the degradation induced by the time delay are also analyzed. Results show that shorter natural periods and larger control gains are both more sensitive and more serious to the degradation of control efficiency. Finally, a practical application of PIOC is performed on a six‐story moment‐resisting steel frame. It is demonstrated that PIOC contributes significantly to maintain stability in multiple degree of freedom structures, and at the same time PIOC has a satisfactory control performance. Copyright © 2003 John Wiley & Sons, Ltd.     

A comparative study of seismic tomography models of the Chinese continental lithosphere

The Chinese mainland is subject to complicated plate interactions that give rise to its complex structure and tectonics. While several seismic velocity models have been developed for the Chinese mainland, apparent discrepancies exist and, so far, little effort has been made to evaluate their reliability and consistency. Such evaluations are important not only for the application and interpretation of model results but also for future model improvement. To address this problem, here we compare five published shear-wave velocity models with a focus on model consistency. The five models were derived from different datasets and methods (i.e., body waves, surface waves from earthquakes, surface waves from noise interferometry, and full waves) and interpolated into uniform horizontal grids (0.5° × 0.5°) with vertical sampling points at 5 km, 10 km, and then 20 km intervals to a depth of 160 km below the surface, from which we constructed an averaged model (AM) as a common reference for comparative study. We compare both the absolute velocity values and perturbation patterns of these models. Our comparisons show that the models have large (> 4%) differences in absolute values, and these differences are independent of data coverage and model resolution. The perturbation patterns of the models also show large differences, although some of the models show a high degree of consistency within certain depth ranges. The observed inconsistencies may reflect limited model resolution but, more importantly, systematic differences in the datasets and methods employed. Thus, despite several seismic models being published for this region, there is significant room for improvement. In particular, the inconsistencies in both data and methodologies need to be resolved in future research. Finally, we constructed a merged model (ChinaM-S1.0) that incorporates the more robust features of the five published models. As the existing models are constrained by different datasets and methods, the merged model serves as a new type of reference model that incorporates the common features from the joint datasets and methods for the shear-wave velocity structure of the Chinese mainland lithosphere.     

鄂尔多斯块体北缘呼包鄂地区岩石圈各向异性初步研究

选取呼包鄂区域11个宽频带地震台站记录的156个远震事件,使用剪切波分裂软件,对所选远震波形数据进行处理,求取并分析震中距85°—110°范围内同时被各地震台站记录的远震震相SKS的各向异性参数,即快波偏振方向及慢波到时差,结果表明:呼包鄂区域地下深层介质存在各向异性,快波偏振优势方向为ESE,慢波延迟时间为0.87—...