震后形变和岩石圈流变学结构

岩石圈流变学结构是控制不同构造环境下岩石圈形变的关键因素之一. 随着空间大地测量观测技术的发展, 基于空间大地测量数据的震后形变研究对揭示断裂带内的力学性质和区域性岩石圈流变学结构已成为可能. 该文首先基于岩石力学的摩擦和流变学实验, 对余滑和分布式韧性流的构造物理背景进行了分别阐述, 并介绍了震后形变数值模拟中本构关系和数值模型的发展. 数值模型主要有解析、 半解析和纯数值3类, 涉及的本构关系包括基于速率-状态摩擦准则的余滑以及分布式韧性流中常用的线性流变学模型(麦克斯韦尔体和标准线性固体)和瞬态流变学模型(宏观经验性的伯格斯(Burgers)体和微观幂律流变律). 然后以美国南加州1992年Landers M_W7.3地震和1999年Hector Mine M_W7.1地震震后形变研究为例, 介绍了震后形变的研究进展. 最后回顾了大陆岩石圈流变学结构的研究进展, 并以震后形变研究中的流变学结构(“三明治模型”和“焦糖布丁模型”)存在的争议为例, 说明了岩石圈流变学结构研究所具有的挑战性.      

震后短期和长期形变模拟——以1960年智利Mw9.5地震为例

以1960年5月智利瓦尔迪维亚(Valdivia)Mw9.5地震为例分析震后不同时期的形变,实现了以Burgers体为粘弹介质模型来模拟震后粘弹松弛效应有限元数值模拟.计算结果表明,该粘弹介质模型可以模拟地震引起的瞬时同震弹性响应及震后粘弹松弛的短期和长期响应.由1960智利Mw9.5地震震后模拟的应变率显示以Burgers体为粘弹介质模型可以解决Maxwell体在模拟震后短期和长期形变不协调问题.     

The loading problem for a linear viscoelastic earth: I. Compressible,non-gravitating models

Summary A Legendre mode solution is given for deformation of a solid isotropic linear viscoelastic sphere under applied surface stresses. Under the simplifying assumptions that the sphere is elastic in compression and standard linear solid in shear two relaxation times appear; one the creep relaxation time of the material, the other depending on mode. It is shown formally how to reduce the case of a layered viscoelastic sphere to an equivalent unlayered one.     

联合GPS和GRACE观测研究日本MW9.0地震震后变形机制

利用GPS和GRACE观测数据研究了日本M_W9.0地震的震后变形特征.GPS观测显示,区域震后位移呈现随指数函数变化特征,变化速率符合大森公式的衰减特性;近五年的震后水平位移累积已达到东向60~165 cm,南向20~65 cm的量值,距震中较远站点已超过同震变化量,且震后变形仍然持续.GRACE观测到显著的震后重力变化,地震破裂两侧的重力变化总体均呈上升趋势,但海洋侧的变化速率较快.联合震后余滑和黏弹性位错理论对震后变形进行了模拟,探索了GPS和GRACE观测的综合应用方法.研究发现,综合考虑震后余滑和黏滞性松弛效应可以对日本地震的震后变形做出较合理的解释,震后初期余滑起主要作用,1至2年以后逐渐减弱,黏滞性松弛作用逐渐增强.在震后变形模拟和区域黏滞性结构反演中形成GPS和GRACE观测结合应用的方法,先基于震后GPS形变估算区域黏滞性结构,而后利用GRACE观测修正深部的黏滞系数,并综合利用这两种观测微调浅层黏滞系数,最终确定区域黏滞性结构.基于该方法反演了日本震源区的地幔黏滞性结构,地震断层破裂两侧的流变参数存在差异,大陆侧的地幔顶层黏滞系数在1.0×10¹⁹ Pa·s量级,而海洋侧的则略小于大陆的,在6.0×10¹⁸ Pa·s量级.     

黏弹性介质中瑞雷波有限差分数值模拟与波场分析

瑞雷面波经常被用来反演地表浅层横波速度,受到越来越广泛的关注。对瑞雷波的研究一般都基于完全弹性介质,而实际地层更接近黏弹性介质,对黏弹性介质中的瑞雷面波进行模拟更具实际意义。本文采用广义标准线性体模型来描述黏弹性介质,并采用交错网格有限差分法对考虑水平自由表面的黏弹介质进行正演模拟,再与弹性介质中的结果进行对比分析。首先采用非线性最优化算法根据期望常数品质因子直接求取松弛时间来拟合常Q模型,并给出广义标准线性固体的具体算例,实施自由表面条件时采用声学-弹性边界近似法,通过剪切模量不变来考虑自由表面上、下横向应力保持连续的条件。对于非自由表面,采用非分裂的多轴卷积完全匹配层来吸收波场。然后对几种典型的数值模型进行正演模拟计算,数值解与解析解的对比验证了本文方法的准确性与有效性,正演结果的对比表明波场尤其是面波频散会受黏弹性影响,因此有必要在面波勘探中考虑黏弹性因素。      

Viscoelastic relaxation of the upper mantle and afterslip following the 2014 MW8.1 Iquique earthquake

An improved understanding of postseismic crustal deformation following large subduction earthquakes may help to better understand the rheological properties of upper mantle and the slip behavior of subduction interface. Here we construct a three-dimensional viscoelastic finite element model to study the postseismic deformation of the 2014 M_W8.1 Iquique, Chile earthquake. Elastic units in the model include the subducting slab, continental and oceanic lithospheres. Rheological units include the mantle wedge, the oceanic asthenosphere and upper mantle. We use a 2 ​km thick weak shear zone attached to the subduction fault to simulate the time-dependent stress-driven afterslip. The viscoelastic relaxation in the rheological units is represented by the Burgers rheology. We carry out grid-searches on the shear zone viscosity, thickness and viscosity of the asthenosphere, and they are determined to be 10¹⁷ ​Pa ​s, 110 ​km and 2 ​× ​10¹⁸ ​Pa ​s, respectively. The stress-driven afterlsip within the first two years is up to ~47 ​cm and becomes negligible after two years (no more than 5 ​cm/yr). Our results suggest that a thin, low-viscosity oceanic asthenosphere together with a weak shear zone attached to the fault are required to better reproduce the observed postseismic deformation.     

The dynamical equations of polar wander and the global characteristics of the lithosphere as extracted from rotational data

The initial value problem describing the linear responses of the spin axis of a layered viscoelastic planet from surface loading is studied by means of Laplace transform techniques. A complete solution of polar motion requires the usage of two classes of eigenspectra: one arising from viscoelastic relaxation of the mantle due to surface forcing, the other involving the gradual readjustment of the spin axis as a consequence of mantle viscoelasticity. Our analytical 4-layer model comprising an elastic lithosphere, a two-layer, adiabatically stratified, viscoelastic mantle and an inviscid core has been incorporated into this formalism in which rotational deformation and isostatic relaxation are taken into account for all times. From employing both sets of rotational data, polar variations from the 70 years of data from the International Latitude Service (I.L.S.) and the non-tidal deceleration of the length of the day (l.o.d.) an estimate of the globally averaged lithosphere of between 130 and 200 km is obtained from the long wavelength flexural mode due to the degree-two harmonic. This range of values may have strong implications on the mode of continental evolution.     

大地测量约束下的阿尔泰山岩石圈流变结构

本文根据大地测量数据得到过去50年左右阿尔泰山富蕴区域形变场，破裂带中段的相对位移最大，平均速率达6mm/a，总体上表现为沿断裂的走滑运动特征．该形变场可以用1931年富蕴8级地震的震后黏弹性松弛模型进行模拟，反演得到下地壳黏滞系数为1.6×10¹⁹～7.9×10¹⁹Pa·s，上地幔黏滞系数为16×1018～63×1019Pa·s，与华北、Nevada等地区利用震后变形资料推算的黏度基本一致．根据该地区最佳黏弹性分层模型，最近五十年由于岩石圈下部应力松弛引起的地震破裂带两侧最大水平速率约为4mm/a． 我们的研究表明：大陆7～8级大震在几十年后仍可能有可观的地表变形，GPS监测得到的现今变形场可能包含震后变形成分．     

MS8.0汶川地震对MS7.0芦山地震成核失稳的影响

依据速率-状态依赖性摩擦本构关系,并结合中下地壳和上地幔的黏弹性松弛效应,以震后库仑破裂应力变化和同震动态库仑破裂应力变化的计算为基础,模拟了两种应力变化对芦山地震断层的失稳发震时间的影响,研究了2008年M_S8.0汶川地震与2013年M_S7.0芦山地震之间的触发关系.计算得到,汶川地震在芦山地震震源断层面上产生的动态应力变化的峰值为0.127 MPa;此外,经过近5年中下地壳和上地幔的黏弹性松弛效应,芦山地震震源断层面上受到的震后应力变化值为0.025 MPa.结果表明,芦山地震的震源断层在应力积累逐渐接近临界状态的某一特定时期内,受到了汶川地震产生的动态应力变化、静态应力变化以及黏弹性松弛效应造成应力变化的共同触发作用,且动态应力的延迟触发作用可能更为显著.最后对芦山地震之后研究区域的应力变化场进行了初步探讨.     

地壳、上地幔变形属性的判别

基于Ｍａｘｗｅｌｌ和Ｋｅｌｖｉｎ流变模型，以延续时间与松弛期的比值，即松弛数，作为衡量指标，对地壳、上地幔不同层次的变形属性进行了判别。结果表明，除软流圈地幔主要为粘性流动外，其上各层的情况是：在漫长的地质过程中，不仅岩石圈地幔和下地壳属于粘性，上地壳也有可能处于粘性流动状态；在延续数十年的情况下，上地壳以及岩石圈地幔都可能呈弹性状态；延续时间介乎二者，通常上地壳为弹性，下地壳和岩石圈地幔为粘性或滞弹粘性。此外，还结合变形属性的判别，就岩石圈地幔的流动和板内的驱动力远程传递等问题进行了讨论     

2011年日本MW9.0地震震后形变机制与震源区总体构造特征

本文利用较为完备的球体位错理论,结合4.5年的震后位移数据,优化了2011年日本M_W9.0地震震源区岩石圈弹性层厚度与地幔黏滞性因子,更新了该强震断层余滑时空演化过程.首先,基于日本列岛215个均匀分布的GPS连续观测站震前2年与震后4.5年的观测数据,提取了2011年日本M_W9.0地震引起的震后位移时空变化;接着,依据断层余滑衰减相对较快的特点,利用黏弹性球体位错理论对震后3~4.5年的GPS观测数据进行反复拟合,确定2011年日本M_W9.0地震震源区地幔黏滞性系数和岩石圈弹性层厚度的最优解分别为6×10¹⁸ Pa·s和30 km;然后,从震后3年内GPS观测数据中剔除地幔黏滞性松弛效应,获取了断层余滑对应的震后位移场;最后,利用基于球体位错理论的反演算法,反演了2011年日本M_W9.0地震断层余滑的时空演化过程.结果表明,2011年日本M_W9.0地震引起的断层余滑在震后半年内变化显著,震后2年主震区域余滑基本停止,断层的两端存在一定的余滑效应,断层余滑的累计矩震级达到8.59;地震后4年,地幔黏滞性松弛效应对震后位移场的贡献在总体上超过断层余滑的贡献.     

利用同震和震后位移数据联合反演2011年日本MW9.0地震同震断层滑动

基于黏弹性球体位错理论, 联合陆地和海底同震GPS数据以及日本本岛330个陆地GPS站点5~10年的震后数据, 反演了日本M_W9.0地震的断层滑动模型, 提升了断层滑动分布在细节上的合理性。 首先, 基于日本本岛330个陆地GPS站点震前2年和震后10年的连续观测数据, 获取了日本M_W9.0地震震后5~10年的年平均位移, 该时段的位移几乎完全由地幔黏弹性松弛效应引起; 接着, 利用黏弹性球体位错理论对震后5~10年的位移进行反复拟合, 确定了日本M_W9.0地震震源及周边地区的地幔黏滞性系数最优解(9.0×10¹⁸ Pa·s)。 然后, 联合同震和震后位移数据, 引入黏弹性位错格林函数, 反演了2011年日本M_W9.0地震的断层滑动分布。 结果表明, 该地震同震破裂的最大值达到了62.72 m, 同震滑动的总地震矩为4.48×10²² Nm, 相应的矩震级为M_W9.03。 由于黏弹性松弛效应引起的震后位移中包含了同震破裂的信息, 基于黏弹性球体地震位错理论, 联合同震和震后位移数据反演断层同震破裂, 有效提高了日本M_W9.0地震断层滑动分布的可靠性。 最后, 本文提出的反演方法为同震观测结果缺乏的大地震震后科考提供了理论支撑: 在大地震发生之后, 即使在同震期间没有足够的观测数据, 也可以在震后通过对震源区的加密观测积累的震后数据, 使用本文提出的反演方法优化同震断层滑动模型。     

The Deformational Response of a Viscoelastic Solid Earth Model Coupled to a Thermomechanical Ice Sheet Model

We apply a coupled thermomechanical ice sheet—self-gravitating viscoelastic solid Earth model (SGVEM), allowing for the dynamic exchange of ice thickness and bedrock deformation, in order to investigate the effect of viscoelastic deformation on ice dynamics and vice versa. In a synthetic glaciation scenario, we investigate the interaction between the ice sheet and the solid Earth deformation, the glacial-isostatic adjustment (GIA), accounting for an atmospheric forcing depending on the ice sheet surface altitude. We compare the results from the coupled model to runs with the common elastic lithosphere/relaxing asthenosphere (ELRA) model, where the lithosphere is represented by a thin plate and the mantle relaxes with one characteristic relaxation time, as well as to a rigid Earth without any deformation. We find that the deformational behaviour of the SGVEM on ice dynamics (i.e. stored ice volume, ice thickness and velocity field) is comparable to the ELRA for an optimal choice of the parameters in steady state, but exhibits differences in the transient behaviour. Beyond the ice sheet, in the region of peripheral forebulge, the differences in the transient surface deformation between ELRA and SGVEM are substantial, demonstrating the inadequacy of the ELRA model for interpreting constraints on GIA in the periphery of the ice sheet, such as sea-level indicators and GPS uplift rates.     

Geophysical Finite-Element Simulation Tool (GeoFEST): Algorithms and Validation for Quasistatic Regional Faulted Crust Problems

GeoFEST (Geophysical Finite Element Simulation Tool) is a two- and three-dimensional finite element software package for the modeling of solid stress and strain in geophysical and other continuum domain applications. It is one of the featured high-performance applications of the NASA QuakeSim project. The program is targeted to be compiled and run on UNIX systems, and is running on diverse systems including sequential and message-passing parallel systems. Solution to the elliptical partial differential equations is obtained by finite element basis sampling, resulting in a sparse linear system primarily solved by conjugate gradient iteration to a tolerance level; on sequential systems a Crout factorization for the direct inversion of the linear system is also supported. The physics models supported include isotropic linear elasticity and both Newtonian and power-law viscoelasticity, via implicit quasi-static time stepping. In addition to triangular, quadrilateral, tetrahedral and hexahedral continuum elements, GeoFEST supports split-node faulting, body forces, and surface tractions. This software and related mesh refinement strategies have been validated on a variety of test cases with rigorous comparison to analytical solutions. These include a box-shaped domain with imposed motion on one surface, a pair of strike slip faults in stepover arrangement, and two community-agreed benchmark cases: a strike slip fault in an enclosing box, and a quarter-domain circular fault problem. Scientific applications of the code include the modeling of static and transient co- and post-seismic earth deformation, Earth response to glacial, atmospheric and hydrological loading, and other scenarios involving the bulk deformation of geologic media.     

Modeling transient and long-term postseismic deformation: A case study of 1995 M W9.5 Chile earthquake

In this paper, we firstly use finite element method (FEM) with Burgers model to simulate the postseismic viscoe-lastic relaxation taking 1960 Chile earthquake as an example. The postseismic deformation modeled with Burgers model includes co-seismic deformation, transient postseismic deformation and long-term postseismic deformation. So if we apply Burgers model to calculate postseismic deformation of 1960 Chile earthquake, there is no discrep-ancy phenomenon due to different durations of postseismic deformations that happens in Maxwell model.     

震后GPS观测数据揭示的日本M_W9.0地震周边地区地幔黏滞性结构垂向变化

本文利用大范围的震后GPS数据和黏弹性球形地球位错理论,定量研究了日本M_W9.0地震周边地区地幔黏滞性结构的垂向变化.首先结合陆地和海底的GPS观测数据,以及基于球形地球位错理论格林函数和贝叶斯反演方法,反演了该地震的同震滑动分布,发现其最大错动量高达59m.然后在均一地幔黏滞性结构的假设前提下,确定了震源周边地区地幔黏滞因子的最优解,发现依据该地幔黏滞因子获得的理论远场震后位移和GPS观测结果之间的均方根误差高达0.81cm,不能解释远场观测结果.为解决上述问题,本文对震中周边地区地幔黏滞性结构沿垂向方向进行分层,建立了一个随深度变化的地幔黏滞性构造模型,然后综合利用远近场的GPS数据对该地区地幔黏滞因子进行反演研究,结果表明,震源周边地区岩石圈弹性层厚度最优解为40km,40～220km深度的地幔黏滞因子最优解为6×10~(18)Pa·s,220～670km深度之间的地幔黏滞因子最优解为1.5×10~(19)Pa·s.上述地幔黏滞性构造使远场的均方根误差降为0.12cm,仅为利用均一地幔黏滞性构造所得均方根误差值的15%,大大提高了远场模拟结果的准确性.最后,观测值和模拟值之间的均方根误差分析表明,近场震后形变数据主要约束浅层的地幔黏滞性结构,而远场震后形变数据主要约束深部的地幔黏滞性结构.     

Semi-analytical Solution for Viscoelastic Relaxation in Eccentrically-nested Spheres Induced by Surface Toroidal Traction

A semi-analytical solution to the 2-D forward modelling of viscoelastic relaxation in a heterogeneous sphere induced by a surface toroidal force is derived. The model consists of a concentrically-nested elastic lithosphere, a viscoelastic mantle, and an eccentrically-nested viscoelastic core. Since numerical codes based on finite-element or spectral-finite-difference techniques for modelling viscoelastic relaxation in a spherical geometry in the presence of lateral viscosity variations are becoming more popular, reliable examples for testing and validating such codes are essential. The eccentrically-nested sphere solution has been tested by comparing it with two distinct results: The analytical solution for viscoelastic relaxation in concentrically-nested spheres and the time domain, spectral finite-element numerical solution for viscoelastic relaxation in eccentrically-nested spheres, with excellent agreement being obtained.     

2010年马乌莱MW8.8地震震后形变三维黏弹性数值模拟

2010年智利马乌莱M_W8.8地震发生在纳斯卡板块与南美板块的板块边界处,引起了显著的同震和震后效应。GPS台网数据显示记录到的同震海向位移最大约5 m,垂向沉降最大约50 cm。在经过对俯冲效应、季节变化等效应的校正后,震后6年的海向最大位移约68 cm,垂向抬升最大约20 cm。马乌莱地震显著的震后形变对该区域的地下三维黏弹性结构有良好的约束。本文建立了智利中南部俯冲带区域的三维有限元模型,黏弹性的地幔楔及海洋地幔均使用伯格斯体材料,并在断层面上设置2 km厚的软弱层以模拟震后余滑。在与GPS台站震后位移数据进行比较后,模拟结果表明,大洋地幔顶部存在约120 km厚,黏度为1×1019 Pa·s的软流圈。模拟震后余滑效应的软弱层黏度为5×1017 Pa·s,其等效震后余滑的最大值在震后前两年接近2 m,且随着时间的增长而快速衰减。      

Current motion and short-term deformations in the Suez–Sinai area from GPS observations

We analyze observations from eight GPS campaigns carried out between 1997 and 2005 on a network of 13 sites in the Suez–Sinai area, where separation between the African and the Arabian plates takes place. This is the key area to understand if and in which way Sinai behaves like a sub-plate of the African plate and the role played by seismic and geodetic (long-term) deformation release.Our analysis shows that, on average, the Suez–Sinai area motion, in terms of ITRF00 velocities, matches the African plate motion defined by the NNR-NUVEL-1A model.The horizontal principal strain rate axes estimated separately in the Gulf of Suez area and in the northern Sinai vary from compression across the Gulf (−2.2 ± 1.2) × 10⁻⁸ year⁻¹ to NE extension (1.0 ± 1.5) × 10⁻⁸ year⁻¹ in the North, showing the presence of two distinct domains, so that in our opinion Sinai cannot be considered simply a unique rigid block.The analysis of GPS baseline length variations shows short-term deformations across the Gulf of Suez, reaching up a maximum value of more than 1 cm in 8 years.Since current geodynamical models do not predict significant tectonic deformation in this area, we work under the hypothesis that a contribute may be expected by post-seismic relaxation effects. Under this hypothesis, we compare the baselines length variations with the post-seismic relaxation field associated with five major local earthquakes occurred in the area, testing two different viscoelastic models. Our results show that the detected short-term deformations are better modeled for viscosity values of 10¹⁸ Pa s in the lower crust and 10²⁰ Pa s in the asthenosphere. However, since the modeled post-seismic effect results modest and a certain amount of the detected deformation is not accounted for, we think that an improved modeling should take into account the lateral heterogeneities of crust and upper mantle structures.     

Dynamic mechanisms of the post-seismic deformation following large events: Case study of the 1999 Chi-Chi earthquake in Taiwan of China

The mechanism of postseismic deformation related to strong earthquakes is important in geodynamics, and presumably afterslip or viscoelastic relaxation is responsible for the postsesimic deformation. The 1999 Chi-Chi, Taiwan of China, earthquake occurred in the region where GPS observation station is most densely deployed in the world. The unprecedented GPS data provides a unique opportunity to study the physical processes of postseismic deformation. Here we assume that the interactions of viscoelastic relaxation, afterslip, fault zone collapse, poroelastic rebound, flow of underground fluids, and all these combined contribute to the surface displacements following the main shock. In order to know the essence of the postseismic deformation after the strong event, fault zone collapse, poroelastic rebound, flow of underground fluids, and so on, are represented equivalently by the variations of the focal medium properties. Therefore, the viscoelastic relaxation, afterslip, and the variations of the equivalent focal medium properties are inverted by applying the GPS temporal series measurement data with viscoelastic finite element method. Both the afterslip rate distribution along the fault and the afterslip evolution with time are obtained by means of inversion. Also, the preliminary result suggests that viscosities of the lower crust and the upper mantle in Taiwan region is 2.7×10¹⁸ and 4.2×10²⁰ Pa·s, respectively. Moreover, the inversion results indicate that the afterslip contributing to postseismic deformation of 44.6% in 450 days after the Chi-Chi earthquake, with 34.7% caused by the viscous relaxation and 20.7% by other factors such as fault zone collapse, poroelastic rebound, and the flow of liquids.