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1.
郭飚 《国际地震动态》2010,(3):46-48,22
大陆动力学已经成为当今固体地球物理各领域研究的主导方向。大陆动力学涉及问题非常广泛,但核心问题是大陆形变及其动力学。地震各向异性是地球动力学过程的指示器,根据地震各向异性的研究结果,可以推断上地幔物质的流动或变形,有助于了解地球内部的应力状态和地球的演化过程。  相似文献   

2.
Several problems for nonlinear localized wave processes are analysed. Wave solutions of the kink type, concentrated in the vicinity of some curve l, are considered. Both the solution and the curve l are unknown. It is shown that the determination of l may be realized without knowledge of the solution. For one class of problems, a variational principle for finding l, similar to the Fermat principle, is obtained. Types of waves are found which exist due to the inhomogeneity of the medium or due to the initial front curvature only.  相似文献   

3.
Hermite-Gaussian beams in a 3D elastic inhomogeneous medium are obtained as high-frequency asymptotic solutions of equations of motion concentrated in a vicinity of P- and S-wave rays. Equations of motion are transformed into the parabolic equation (Schroedinger equation) in this case. Explicit expressions for a complete set of linearly independent solutions of a parabolic equation are derived. The method of creation and anihilation operators known from quantum mechanics are used in the derivation.  相似文献   

4.
In viscoelastic media, the slowness vector p of plane waves is complex-valued, p = P + iA. The real-valued vectors P and A are usually called the propagation and the attenuation vector, repectively. For P and A nonparallel, the plane wave is called inhomogeneousThree basic approaches to the determination of the slowness vector of an inhomogeneous plane wave propagating in a homogeneous viscoelastic anisotropic medium are discussed. They differ in the specification of the mathematical form of the slowness vector p. We speak of directional specification, componental specification and mixed specification of the slowness vector. Individual specifications lead to the eigenvalue problems for 3 × 3 or 6 × 6 complex-valued matrices.In the directional specification of the slowness vector, the real-valued unit vectors N and M in the direction of P and A are assumed to be known. This has been the most common specification of the slowness vector used in the seismological literature. In the componental specification, the real-valued unit vectors N and M are not known in advance. Instead, the complex-valued vactorial component p of slowness vector p into an arbitrary plane with unit normal n is assumed to be known. Finally, the mixed specification is a special case of the componental specification with p purely imaginary. In the mixed specification, plane represents the plane of constant phase, so that N = ±n. Consequently, unit vector N is known, similarly as in the directional specification. Instead of unit vector M, however, the vectorial component d of the attenuation vector in the plane of constant phase is known.The simplest, most straightforward and transparent algorithms to determine the phase velocities and slowness vectors of inhomogeneous plane waves propagating in viscoelastic anisotropic media are obtained, if the mixed specification of the slowness vector is used. These algorithms are based on the solution of a conventional eigenvalue problem for 6 × 6 complex-valued matrices. The derived equations are quite general and universal. They can be used both for homogeneous and inhomogeneous plane waves, propagating in elastic or viscoelastic, isotropic or anisotropic media. Contrary to the mixed specififcation, the directional specification can hardly be used to determine the slowness vector of inhomogeneous plane waves propagating in viscoelastic anisotropic media. Although the procedure is based on 3 × 3 complex-valued matrices, it yields a cumbersome system of two coupled equations.  相似文献   

5.
Fermat's variational principle states that the signal propagates from point S to R along a curve which renders Fermat's functional (l) stationary. Fermat's functional (l) depends on curves l which connect points S and R, and represents the travel times from S to R along l. In seismology, it is mostly expressed by the integral (l) = (x k,x k ')du, taken along curve l, where (x k,x k ') is the relevant Lagrangian, x k are coordinates, u is a parameter used to specify the position of points along l, and x k ' = dx k÷du. If Lagrangian (x k,x k ') is a homogeneous function of the first degree in x k ', Fermat's principle is valid for arbitrary monotonic parameter u. We than speak of the first-degree Lagrangian (1)(x k,x k '). It is shown that the conventional Legendre transform cannot be applied to the first-degree Lagrangian (1)(x k,x k ') to derive the relevant Hamiltonian (1)(x k,p k), and Hamiltonian ray equations. The reason is that the Hessian determinant of the transform vanishes identically for first-degree Lagrangians (1)(x k,x k '). The Lagrangians must be modified so that the Hessian determinant is different from zero. A modification to overcome this difficulty is proposed in this article, and is based on second-degree Lagrangians (2). Parameter u along the curves is taken to correspond to travel time , and the second-degree Lagrangian (2)(x k, k ) is then introduced by the relation (2)(x k, k ) = [(1)(x k, k )]2, with k = dx k÷d. The second-degree Lagrangian (2)(x k, k ) yields the same Euler/Lagrange equations for rays as the first-degree Lagrangian (1)(x k, k ). The relevant Hessian determinant, however, does not vanish identically. Consequently, the Legendre transform can then be used to compute Hamiltonian (2)(x k,p k) from Lagrangian (2)(x k, k ), and vice versa, and the Hamiltonian canonical equations can be derived from the Euler-Lagrange equations. Both (2)(x k, k ) and (2)(x k,p k) can be expressed in terms of the wave propagation metric tensor g ij(x k, k ), which depends not only on position x k, but also on the direction of vector k . It is defined in a Finsler space, in which the distance is measured by the travel time. It is shown that the standard form of the Hamiltonian, derived from the elastodynamic equation and representing the eikonal equation, which has been broadly used in the seismic ray method, corresponds to the second-degree Lagrangian (2)(x k, k ), not to the first-degree Lagrangian (1)(x k, k ). It is also shown that relations (2)(x k, k ) = ; and (2)(x k,p k) = are valid at any point of the ray and that they represent the group velocity surface and the slowness surface, respectively. All procedures and derived equations are valid for general anisotropic inhomogeneous media, and for general curvilinear coordinates x i. To make certain procedures and equations more transparent and objective, the simpler cases of isotropic and ellipsoidally anisotropic media are briefly discussed as special cases.  相似文献   

6.
The TOPEX/POSEIDON (T/P) satellite altimeter data from January 1, 1993 to January 3, 2001 (cycles 11–305) was used for investigating the long-term variations of the geoidal geopotential W 0 and the geopotential scale factor R 0 = GM÷W 0 (GM is the adopted geocentric gravitational constant). The mean values over the whole period covered are W 0 = (62 636 856.161 ± 0.002) m2s-2, R 0 = (6 363 672.5448 ± 0.0002) m. The actual accuracy is limited by the altimeter calibration error (2–3 cm) and it is conservatively estimated to be about ± 0.5 m2s-2 (± 5 cm). The differences between the yearly mean sea surface (MSS) levels came out as follows: 1993–1994: –(1.2 ± 0.7) mm, 1994–1995: (0.5 ± 0.7) mm, 1995–1996: (0.5 ± 0.7) mm, 1996–1997: (0.1 ± 0.7) mm, 1997–1998: –(0.5 ± 0.7) mm, 1998–1999: (0.0 ± 0.7) mm and 1999–2000: (0.6 ± 0.7) mm. The corresponding rate of change in the MSS level (or R 0) during the whole period of 1993–2000 is (0.02 ± 0.07) mm÷y. The value W 0 was found to be quite stable, it depends only on the adopted GM, and the volume enclosed by surface W = W 0. W 0 can also uniquely define the reference (geoidal) surface that is required for a number of applications, including World Height System and General Relativity in precise time keeping and time definitions, that is why W 0 is considered to be suitable for adoption as a primary astrogeodetic parameter. Furthermore, W 0 provides a scale parameter for the Earth that is independent of the tidal reference system. After adopting a value for W 0, the semi-major axis a of the Earth's general ellipsoid can easily be derived. However, an a priori condition should be posed first. Two conditions have been examined, namely an ellipsoid with the corresponding geopotential which fits best W 0 in the least squares sense and an ellipsoid which has the global geopotential average equal to W 0. It is demonstrated that both a-values are practically equal to the value obtained by the Pizzetti's theory of the level ellipsoid: a = (6 378 136.7 ± 0.05) m.  相似文献   

7.
曹颖  黄江培  付虹 《中国地震》2018,34(4):652-666
联合小湾水库库区及其附近11249个地震的P波绝对到时、相对到时数据,利用双差地震层析成像方法反演得到小湾水库蓄水后2008年12月16日~2011年6月30日和2011年7月1日~2016年12月31日2个时间段内库区及其附近的地震重定位结果和三维P波速度结构。结果表明,蓄水后黑惠江段和小湾水库回水澜沧江段地震的增多与水库蓄水有关。由于水体渗透导致孔隙压变化,并随着时间的推移孔隙压变化朝着更深的部位扩散,地震震源深度也随之向深部扩散,进而导致介质变化和P波速度降低。蓄水回水至澜沧江保山段后该区域地震增多,P波速度下降,库水渗透作用为主控因素,该区域地下一定深度的地质构造有利于库水的快速渗透。初步判定2015年10月30日云南昌宁M_S5.1地震余震序列是与蓄水有关的柯街断裂上的构造地震。同时,也存在着与蓄水相关性不大的属于构造地震的活动,如云南施甸一带历来地震多发,施甸2010年6月1日M_L4.8、2012年9月11日M_S4.7地震序列均属于构造地震,与水库蓄水无关。  相似文献   

8.
—Love wave dispersion in a vertically inhomogeneous multilayered medium is studied by a combination of analytical and numerical methods for arbitrary variation of rigidity and density with depth. The problem is reduced to a boundary value problem for a differential equation and solved numerically. The method compares favourably with other methods in use. Simple particular cases are considered and interesting results are exhibited graphically.  相似文献   

9.
利用国家测震台网数据备份中心提供的2009年1月至2015年11月的地震波形数据,选取震级范围为ML1.8~6.7,震中距小于800km的1 820个地震事件的16 156条Pg波到时数据,对鄂尔多斯西南缘P波三维Q值分布特征进行了研究。结果表明:鄂尔多斯西南缘一系列呈"L"型分布的断裂带上,Q值呈现出比较低的水平;而其两侧地区,Q值相对较高,且分布存在较大差异。研究区内呈现低Q值状态的海原地区和天水—礼县地区存在明显的低阻—低速层,而高Q值的渭源—定西—通渭—西吉地区则在地壳内缺失低阻层。另外,存在明显高热流的渭河盆地和天水—礼县地区,Q值都明显偏低,而其周围地区则Q值较高。沿临潼—长安—富城—蒲城断裂走向,有一条比较显著的垂直形变梯度带和重力变化等值线,水平形变沿此断裂方向呈现条带状变化特征,而该区低Q值的状态反映了Q值分布与地壳大面积的垂直、水平形变及重力变化等存在一定联系。  相似文献   

10.
A recurrence procedure is outlined for constructing asymptotic series for surface wave field in a half-space with weak lateral heterogeneity. Both horizontal variations of the elastic parameters and of the wave field are assumed small on the distances comparable with the wavelength. This is equivalent to the condition that the frequency is large. The Surface Wave Asymptotic Ray Theory (SWART) is an analog of the asymptotic ray theory (ART) for body waves. However the case of surface waves presents additional difficulty: the rate of amplitude variation is different in vertical and horizontal directions. In vertical direction it is proportional to the large parameter . To overcome this difficulty the transformation equalizing vertical and horizontal coordinated is suggested, Z = z. In the coordinates x,y,Z the wave field is represented as an asymptotic series in inverse powers of . The amplitudes of successive terms of the series are determined from a recurrent system of equations. Attention is paid to similarity and difference of the procedures for constructing the ray series in SWART and ART. Applications of SWART to interpretation of seismological observations are discussed.  相似文献   

11.
Cheng  Jiwei  Zhang  Feng  Li  Xiangyang 《Surveys in Geophysics》2022,43(5):1395-1433
Surveys in Geophysics - Shales represent strongly intrinsic vertical transverse isotropy (VTI) property or polar anisotropy. The presence of vertically aligned fractures makes shale exhibit...  相似文献   

12.
--The new eigenfunction expansion formula based upon the method of separation of variables is derived. The method gives the exact transport equation and the generalized eikonal equation without the need of asymptotic series expansions. The generalized eikonal equation extends the classical eikonal equation to a rapidly varying medium. It governs the wave propagation with dispersive phase velocity depending upon the amplitude. Both equations are separated by making use of conventional phase-ray coordinates. The solution is expressed in terms of the elementary Sturm-Liouville eigenfunctions or modes for the vibrating string. The generalized eikonal equation is solved by employing the modified Hamiltonian formalism. This results in frequency-dependent phase-ray trajectories associated with the energy flux vector field.  相似文献   

13.
Seismic amplitude variation with offset and azimuth (AVOaz) inversion is well known as a popular and pragmatic tool utilized to estimate fracture parameters. A single set of vertical fractures aligned along a preferred horizontal direction embedded in a horizontally layered medium can be considered as an effective long-wavelength orthorhombic medium. Estimation of Thomsen’s weak-anisotropy (WA) parameters and fracture weaknesses plays an important role in characterizing the orthorhombic anisotropy in a weakly anisotropic medium. Our goal is to demonstrate an orthorhombic anisotropic AVOaz inversion approach to describe the orthorhombic anisotropy utilizing the observable wide-azimuth seismic reflection data in a fractured reservoir with the assumption of orthorhombic symmetry. Combining Thomsen’s WA theory and linear-slip model, we first derive a perturbation in stiffness matrix of a weakly anisotropic medium with orthorhombic symmetry under the assumption of small WA parameters and fracture weaknesses. Using the perturbation matrix and scattering function, we then derive an expression for linearized PP-wave reflection coefficient in terms of P- and S-wave moduli, density, Thomsen’s WA parameters, and fracture weaknesses in such an orthorhombic medium, which avoids the complicated nonlinear relationship between the orthorhombic anisotropy and azimuthal seismic reflection data. Incorporating azimuthal seismic data and Bayesian inversion theory, the maximum a posteriori solutions of Thomsen’s WA parameters and fracture weaknesses in a weakly anisotropic medium with orthorhombic symmetry are reasonably estimated with the constraints of Cauchy a priori probability distribution and smooth initial models of model parameters to enhance the inversion resolution and the nonlinear iteratively reweighted least squares strategy. The synthetic examples containing a moderate noise demonstrate the feasibility of the derived orthorhombic anisotropic AVOaz inversion method, and the real data illustrate the inversion stabilities of orthorhombic anisotropy in a fractured reservoir.  相似文献   

14.
A system of three ordinary non-linear first order differential equations is proposed for the computation of the geometrical spreading of the wave front of a seismic body wave in a three-dimensional medium. The variables of the system are the parameters which provide a second order approximation of the wave front.  相似文献   

15.
杨峰 《地震》2020,40(4):33-48
选取黑龙江、吉林、辽宁、内蒙古区域地震台网,以及NECESSArray流动台阵记录的223个远震事件的波形资料,采用多道互相关方法得到了22569个P波相对走时数据,并计算了相应的走时灵敏度核,应用有限频率层析成像反演得到中国东北地区上地幔600 km以上的P波三维速度结构模型,利用检测板评估了反演结果的分辨率。结果表明,松辽盆地下方80~200 km的深度上呈主体的低速异常,与这一地区上地幔浅部的高地温值和低密度的特征相互对应,可能暗示了部分熔融的地幔。南北重力梯度带两侧的速度结构明显不同,这一差异可以延伸到200 km以下,表明在中国东北地区南北重力梯度带有可能是一条上地幔内部结构的变化带,或是深部结构的分界线。长白山火山区下呈大范围的低速异常,并可从上地幔浅部延伸到地幔转换带中,推测此低速异常可能反映了地幔转换带内上涌的热物质,上涌的原因则主要是受到太平洋板块俯冲运动的作用。  相似文献   

16.
Diffraction and anelasticity problems involving decaying, “evanescent” or “inhomogeneous” waves can be studied and modelled using the notion of “complex rays”. The wavefront or “eikonal” equation for such waves is in general complex and leads to rays in complex position-slowness space. Initial conditions must be specified in that domain: for example, even for a wave originating in a perfectly elastic region, the ray to a real receiver in a neighbouring anelastic region generally departs from a complex point on the initial-values surface. Complex ray theory is the formal extension of the usual Hamilton equations to complex domains. Liouville's phase-space-incompressibility theorem and Fermat's stationary-time principle are formally unchanged. However, an infinity of paths exists between two fixed points in complex space all of which give the same final slowness, travel time, amplitude, etc. This does not contradict the fact that for a given receiver position there is a unique point on the initial-values surface from which this infinite complex ray family emanates.In perfectly elastic media complex rays are associated with, for example, evanescent waves in the shadow of a caustic. More generally, caustics in anelastic media may lie just outside the real coordinate subspace and one must trace complex rays around the complex caustic in order to obtain accurate waveforms nearby or the turning waves at greater distances into the lit region. The complex extension of the Maslov method for computing such waveforms is described. It uses the complex extension of the Legendre transformation and the extra freedom of complex rays makes pseudocaustics avoidable. There is no need to introduce a Maslov/KMAH index to account for caustics in the geometrical ray approximation, the complex amplitude being generally continuous. Other singular ray problems, such as the strong coupling around acoustic axes in anisotropic media, may also be addressed using complex rays.Complex rays are insightful and practical for simple models (e.g. homogeneous layers). For more complicated numerical work, though, it would be desirable to confine attention to real position coordinates. Furthermore, anelasticity implies dispersion so that complex rays are generally frequency dependent. The concept of group velocity as the velocity of a spatial or temporal maximum of a narrow-band wave packet does lead to real ray/Hamilton equations. However, envelope-maximum tracking does not itself yield enough information to compute synthetic seismogramsFor anelasticity which is weak in certain precise senses, one can set up a theory of real, dispersive wave-packet tracking suitable for synthetic seismogram calculations in linearly visco-elastic media. The seismologically-accepiable constant-Q rheology of Liu et al. (1976), for example, satisfies the requirements of this wave-packet theory, which is adapted from electromagnetics and presented as a reasonable physical and mathematical basis for ray modelling in inhomogeneous, anisotropic, anelastic media. Dispersion means that one may need to do more work than for elastic media. However, one can envisage perturbation analyses based on the ray theory presented here, as well as extensions like Maslov's which are based on the Hamiltonian properties.  相似文献   

17.
Diffraction and anelasticity problems involving decaying, evanescent or inhomogeneous waves can be studied and modelled using the notion of complex rays. The wavefront or eikonal equation for such waves is in general complex and leads to rays in complex position-slowness space. Initial conditions must be specified in that domain: for example, even for a wave originating in a perfectly elastic region, the ray to a real receiver in a neighbouring anelastic region generally departs from a complex point on the initial-values surface. Complex ray theory is the formal extension of the usual Hamilton equations to complex domains. Liouville's phase-space-incompressibility theorem and Fermat's stationary-time principle are formally unchanged. However, an infinity of paths exists between two fixed points in complex space all of which give the same final slowness, travel time, amplitude, etc. This does not contradict the fact that for a given receiver position there is a unique point on the initial-values surface from which this infinite complex ray family emanates. In perfectly elastic media complex rays are associated with, for example, evanescent waves in the shadow of a caustic. More generally, caustics in anelastic media may lie just outside the real coordinate subspace and one must trace complex rays around the complex caustic in order to obtain accurate waveforms nearby or the turning waves at greater distances into the lit region. The complex extension of the Maslov method for computing such waveforms is described. It uses the complex extension of the Legendre transformation and the extra freedom of complex rays makes pseudocaustics avoidable. There is no need to introduce a Maslov/KMAH index to account for caustics in the geometrical ray approximation, the complex amplitude being generally continuous. Other singular ray problems, such as the strong coupling around acoustic axes in anisotropic media, may also be addressed using complex rays. Complex rays are insightful and practical for simple models (e.g. homogeneous layers). For more complicated numerical work, though, it would be desirable to confine attention to real position coordinates. Furthermore, anelasticity implies dispersion so that complex rays are generally frequency dependent. The concept of group velocity as the velocity of a spatial or temporal maximum of a narrow-band wave packet does lead to real ray/Hamilton equations. However, envelope-maximum tracking does not itself yield enough information to compute synthetic seismograms. For anelasticity which is weak in certain precise senses, one can set up a theory of real, dispersive wave-packet tracking suitable for synthetic seismogram calculations in linearly visco-elastic media. The seismologically-accepiable constant-Q rheology of Liu et al. (1976), for example, satisfies the requirements of this wave-packet theory, which is adapted from electromagnetics and presented as a reasonable physical and mathematical basis for ray modelling in inhomogeneous, anisotropic, anelastic media. Dispersion means that one may need to do more work than for elastic media. However, one can envisage perturbation analyses based on the ray theory presented here, as well as extensions like Maslov's which are based on the Hamiltonian properties.  相似文献   

18.
杨峰 《地震》2019,39(1):58-71
利用区域固定台站和华北科学探测台阵记录的10 461个近震事件的183 909个Pg波绝对走时和495 753个相对走时数据,采用双差地震层析成像获得华北北部(37.5°~41.5°N,111.5°~119.5°E)范围内的地壳三维P波速度结构模型。结果表明:研究区内各主要构造单元具有明显不同的速度结构特征,速度异常的走向与区域构造的走向一致,浅层速度图像很好地反映了地表地质和岩性的变化;重定位后的大部分地震集中在0~20km的深度上,主要位于低速区的内部或高速和低速区的交界部位;三河—平谷和唐山地震震源区中、下地壳的低速异常可能是流体的显示。结合前人成果和本文模型所揭示的深、浅结构,我们认为太平洋板块在中国东部之下的俯冲和滞留引起板块脱水、软流圈物质上涌等一系列过程,软流圈热物质到达上地幔顶部并沿超壳断裂上侵进入地壳,致使上地幔顶部和下地壳中的含水矿物发生脱水作用产生流体,流体继续上移造成中、上地壳发震层的弱化,从而导致大地震的发生。因此华北北部地区的强震活动,以及地壳结构的非均匀性应是与太平洋板块俯冲、滞留引起的深部过程密切相关的。  相似文献   

19.
太行山断裂带东南缘地壳三维P波速度结构成像   总被引:1,自引:0,他引:1       下载免费PDF全文
应用多年地震台网观测数据,使用多震相走时成像方法获得了太行山断裂带东南缘地壳的三维P波速度结构模型。结果表明:速度结构图像在浅部较好地反映了地表地形、地质构造的特征,深部显示地壳速度具有明显的横向变化特征。12km深度以上显示研究区北部太行山隆起区地壳主要呈现为高速区,南部沉降区为低速区,而12km深度以下具有反转的特点。整体显示速度异常的走向大致与邻近活动断裂走向一致。垂直速度剖面显示研究区地壳具有分层特征,上地壳厚约10km,速度横向变化较小;中、下地壳的界面呈现局部上隆或凹陷状,横向起伏变化较大。通过分析速度、断裂与中强地震发生的关系推测研究区具备发生中强震的深部孕震条件。  相似文献   

20.
杨峰 《地震》2021,41(3):42-58
利用区域固定台站和中国地震科学探测台阵记录的7349个近震事件的60471个Pg波绝对走时和196465个相对走时数据,采用双差地震层析成像获得滇西北地区(25°~28.2°N,99.5°~101.5°E)横向分辨率为0.2°的中、上地壳的三维P波速度模型,重点分析了区域内各主要断裂带及其邻区的速度结构特征.结果表明:金沙江—红河断裂带北段15 km以上的P波速度较低,重定位后中、小地震的震中主要位于低速异常的内部,且震源深度在断裂带两侧相似;推测金沙江—红河断裂带作为川滇菱形块体西南边界的剪切控制作用已弱化,分界能力局部减弱,并且断裂带下方主体的低速异常可能为跨越断裂的动力传递提供条件.丽江—小金河断裂带(西南段)两侧存在大范围的P波低速异常,推测此低速体可能是青藏高原东南向挤出的物质,而程海断裂带以东从近地表至25 km深处明显的P波高速异常体则可能会阻挡高原物质东南向的逃逸.  相似文献   

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