一种模拟非均匀介质中弹性波传播新的k-space方法          下载免费PDF全文

黄继伟  刘洪 《地球物理学报》2020,63(8):3091-3104

传统的伪谱(PS)方法,采用傅里叶变换(FT)计算空间导数具有很高的精度,每个波长仅需要两个采样点,而时间导数采用有限差分(FD)近似因而精度较低.当采用大时间步长时,由于时空精度不平衡,PS法存在不稳定性问题.原始的k-space方法可以有效地克服这些问题但是却无法适用于非均匀介质.为了提高原始k-space方法模拟非均匀介质波动方程的精度,我们提出了一种新的k-space算子族.它是用非均匀介质的变速度代替原k-space算子中的常数补偿速度构造得到,引入低秩近似可以高效求解.我们将构造的新的k-space算子应用于耦合的二阶位移波动方程,而不是交错网格一阶速度应力波动方程,使模拟弹性波的计算存储量减少.我们从数学上证明了基于二阶波动方程的k-space方法与基于一阶波动方程的k-space方法是等价的.数值模拟实验表明,与传统的PS、交错网格PS和原始的k-space方法相比,我们的新方法可以在时间和空间步长较大的均匀和非均匀介质中,为弹性波的传播提供更精确的数值解.在保持稳定性和精度的同时,采用较大的时空采样间隔,可以大大降低数值模拟的计算成本.  相似文献   

A nearly analytic symplectic partitioned Runge–Kutta method based on a locally one-dimensional technique for solving two-dimensional acoustic wave equations     

Chol Sim  Chunyou Sun  Nam Yun 《Geophysical Prospecting》2020,68(4):1253-1269

In this paper, we develop a new nearly analytic symplectic partitioned Runge–Kutta method based on locally one-dimensional technique for numerically solving two-dimensional acoustic wave equations. We first split two-dimensional acoustic wave equation into the local one-dimensional equations and transform each of the split equations into a Hamiltonian system. Then, we use both a nearly analytic discrete operator and a central difference operator to approximate the high-order spatial differential operators, which implies the symmetry of the discretized spatial differential operators, and we employ the partitioned second-order symplectic Runge–Kutta method to numerically solve the resulted semi-discrete Hamiltonian ordinary differential equations, which results in fully discretized scheme is symplectic unlike conventional nearly analytic symplectic partitioned Runge–Kutta methods. Theoretical analyses show that the nearly analytic symplectic partitioned Runge–Kutta method based on locally one-dimensional technique exhibits great higher stability limits and less numerical dispersion than the nearly analytic symplectic partitioned Runge–Kutta method. Numerical experiments are conducted to verify advantages of the nearly analytic symplectic partitioned Runge–Kutta method based on locally one-dimensional technique, such as their computational efficiency, stability, numerical dispersion and long-term calculation capability.  相似文献   

南海东北部内潮的模态结构和传播     

刘倩  谢晓辉  尚晓东  陈桂英  汪宏 《海洋学报(英文版)》2019,38(9):12-23

The evolution of energy, energy flux and modal structure of the internal tides(ITs) in the northeastern South China Sea is examined using the measurements at two moorings along a cross-slope section from the deep continental slope to the shallow continental shelf. The energy of both diurnal and semidiurnal ITs clearly shows a～14-day spring-neap cycle, but their phases lag that of barotropic tides, indicating that ITs are not generated on the continental slope. Observations of internal tidal energy flux suggest that they may be generated at the Luzon Strait and propagate west-northwest to the continental slope in the northwestern SCS. Because the continental slope is critical-supercritical with respect to diurnal ITs, about 4.6 kJ/m~2 of the incident energy and 8.7 kW/m of energy flux of diurnal ITs are reduced from the continental slope to the continental shelf. In contrast, the semidiurnal internal tides enter the shelf because of the sub-critical topography with respect to semidiurnal ITs.From the continental slope to the shelf, the vertical structure of diurnal ITs shows significant variation, with dominant Mode 1 on the deep slope and dominant higher modes on the shelf. On the contrary, the vertical structure of the semidiurnal ITs is stable, with dominant Mode 1.  相似文献   

Experimental investigation on a cabin-suspended catamaran in terms of motion reduction and wave energy harvesting by means of a semi-active motion control system     

《Applied Ocean Research》2019

A novel concept catamaran equipped with a suspended cabin, named Wave Harmonizer Type 4 (WHzer-4), is proposed and evaluated. The mass-spring-mass system is constructed by mounting four sets of suspensions in-between the cabin and the twin-hull. Two sets of dual motor/generators (M/Gs) are attached on the center beam of the cabin's deck fore and aft. Each shaft-end of the dual M/Gs is connected to the twin-hull through a rack-pinion gear unit. In this way the vertical relative motion between the cabin and the twin-hull can be transferred into the rotational motion of the M/Gs, and vice versa. A semi-active motion control system, which contains a proportional-integral (PI) controller, is designed and applied to each of the dual M/Gs for the aim of absorbing wave energy under the condition of suppressing the local vertical velocity of the cabin as much as possible. A 1/5 scale model ship with a length of 1.6 m is built, and a forced-oscillation bench test is implemented to validate the performance of the control system. Then, a series of towing tank tests is carried out in regular head waves. The heave and pitch responses of the cabin, those of the twin-hull and the corresponding wave energy capture width ratio (CWR) at five control scenarios and two reference scenarios are investigated. Discussion on the results of the tank test shows that the motion reduction of the cabin and the wave energy harvesting can be achieved simultaneously at a few wave conditions. However, at other conditions, although noticeable amount of wave energy is harvested, motion reduction of the heave and pitch of the cabin could not be obtained at the same time. It is suggested that varying the gain settings of the PI controllers according to the location of the controllers may improve the effectiveness of the proposed control system.  相似文献   

Hydrodynamic performance of a T-shaped floating breakwater     

《Applied Ocean Research》2019

The comprehensive utilization of floating breakwaters, specially acting as a supporting structure for offshore marine renewable energy explorations, has received more and more attention recently. Based on linear water-wave theory, the hydrodynamic performance of a T-shaped floating breakwater is semi-analytically investigated through the matched eigenfunction expansion method (MEEM). Auxiliary functions, to speed up the convergence and improve the accuracy in the numerical computations, are introduced to represent the singular behavior of fluid field near the lower salient corners of the structure. The effects of the height and installation position of the vertical screen on the reflection and transmission coefficients, dynamic response and wave forces are examined. It is found that the presence of the screen shifts the resonance frequency of RAO for both surge and pitch modes to the low-frequency area, while has no effect on heave mode. The identical added masses, damping and transmission coefficients can be obtained in the cases where the screen holds the same distance away from the longitudinal central axis of the upper box-type structure. Moreover, a relatively small pitch response can be achieved in a wide wave–frequency range, when the breakwater is Γ-shaped.  相似文献   

Modelling of viscoacoustic wave propagation in transversely isotropic media using decoupled fractional Laplacians     

Zhihao Qiao  Chengyu Sun  Jie Tang 《Geophysical Prospecting》2020,68(8):2400-2418

A new wave equation is derived for modelling viscoacoustic wave propagation in transversely isotropic media under acoustic transverse isotropy approximation. The formulas expressed by fractional Laplacian operators can well model the constant-Q (i.e. frequency-independent quality factor) attenuation, anisotropic attenuation, decoupled amplitude loss and velocity dispersion behaviours. The proposed viscoacoustic anisotropic equation can keep consistent velocity and attenuation anisotropy effects with that of qP-wave in the constant-Q viscoelastic anisotropic theory. For numerical simulations, the staggered-grid pseudo-spectral method is implemented to solve the velocity–stress formulation of wave equation in the time domain. The constant fractional-order Laplacian approximation method is used to cope with spatial variable-order fractional Laplacians for efficient modelling in heterogeneous velocity and Q media. Simulation results for a homogeneous model show the decoupling of velocity dispersion and amplitude loss effects of the constant-Q equation, and illustrate the influence of anisotropic attenuation on seismic wavefields. The modelling example of a layered model illustrates the accuracy of the constant fractional-order Laplacian approximation method. Finally, the Hess vertical transversely isotropic model is used to validate the applicability of the formulation and algorithm for heterogeneous media.  相似文献   

煤体静载破坏微震、电磁辐射及裂纹扩展特征研究     

艾迪昊  李成武  赵越超  李光耀 《岩土力学》2020,41(6):2043-2051

为研究型煤在单轴压缩破裂过程中产生的微震、电磁辐射信号与裂纹演化特征的对应关系，利用自主设计的低噪声静态加载试验系统，对0～0.25、0.25～0.5、0.5～1.0、1～2 mm共4种不同粒度的型煤进行了单轴压缩破坏试验，同步采集了煤样破坏过程中的微震、电磁辐射信号及破坏视频图像，提出了一种煤体裂纹快速提取方法并计算了型煤裂纹面积的变化规律。研究结果表明：型煤在单轴压缩过程中产生的微震、电磁辐射信号及裂纹面积在时域上具有良好的同步性。型煤破坏过程中裂纹面积随时间变化曲线可分为4个阶段。第1阶段为压实阶段，煤样所受应力值较小，其表面的裂纹面积以极为缓慢的速率增加。第2阶段为初始破裂阶段，随着应力的增加和内部弹性势能的积聚，型煤表面裂纹面积的增加速率较压实阶段有明显提高，伴随产生许多细小裂纹。第3阶段为加速破裂阶段，随着应力继续增加以及材料内部积聚弹性能的释放，试样变形过程加速，导致裂纹面积增速进一步增大。第4阶段为卸压阶段，试样的裂纹面积达到最大值，承载能力急剧降低，发生失稳破坏。  相似文献   

三峡库区龙门寨危岩体崩塌产生涌浪研究   总被引：1，自引：1，他引：0  

郑嘉豪  黄波林  张全  赵海林  冯万里  王健  陈小婷 《地质力学学报》2020,26(4):533-543

长江两岸高耸的危岩体对航道、沿岸居民带来巨大安全隐患。大宁河属于长江一级支流，龙门寨危岩体位于大宁河上，距离巫山县城仅1 km。利用FLOW-3D软件，模拟了145 m、175 m两种水位工况下龙门寨危岩体崩塌产生涌浪过程和涌浪传播过程。模拟结果表明，涌浪在145 m水位工况下最大浪高约为17.9 m，175 m水位工况下最大浪高约为11.6 m；在巫山县的五个码头处，两种水位工况最大涌浪爬高分别约为10.9 m、3.8 m；根据涌浪高度，对大宁河进行危险分区，145 m水位工况下极高危险区长度约4.4 km，很高危险区长度约1.9 km；175 m水位工况下极高危险区长度约3.0 km，很高危险区长度约1.0 km。研究结果有助于防控龙门寨危岩体潜在涌浪灾害危害，保障大宁河航道和巫山县码头安全，同时也为三峡库区滑坡涌浪灾害提供了预警依据。   相似文献   

Experimental investigation of tsunami bore impact pressure on a perforated seawall     

《Applied Ocean Research》2019

Catastrophic failures of many tsunami barriers along the affected coasts during the 2011 Tohoku earthquake tsunami has prompted extensive investigation into improving and revising design codes for tsunami defence structures. To date, researchers and coastal engineers are investigating to understand the failure mechanisms and to find solutions so that the structures merely remain intact in the extreme event such as tsunami. Thus, the present work is motivated to experimentally study tsunami-induced bore pressures exerted on vertical seawalls; a solid vertical wall and a porous vertical seawall that consisted of a perforated front wall and a solid rear wall. Bores with various heights and velocities were generated by using the dam-break method. A porous seawall with 20% porosity of perforated front wall was used in this study. Bore pressures exerted on the solid rear wall and chamber oscillations that occurred in the experiments were also discussed. The experimental results showed that multiple peak pressures were observed during bore run-up phase in the time series of bore impacts. A predictive equation to estimate the maximum bore pressure on a perforated seawall was developed using multiple regression analysis. The proposed equation was also compared with previous empirical formulas.  相似文献   

Wave refocusing for linear diffractor using the time-reversal principle     

Shemer Keydar  Evgeny Landa 《Geophysical Prospecting》2019,67(5):1345-1353

One of the problems encountered in a variety of near-surface investigations is detecting and mapping localized heterogeneities. The heterogeneities may be classified under two kinds of objects: (1) a point diffractor that can be considered as an approximation of a small quasi-isometric, such as small karstic cavities and caves; (2) a linear diffractor roughly approximating an elongated object, such as a tube or fault plane. The point and linear diffractors generate two types of seismic diffraction: tip and edge waves, respectively. During the last few decades, different methods were proposed by many researchers for detecting these heterogeneities utilizing seismic waves diffracted by them. An alternative method for detecting point diffractors using a time-reversal principle combined with focusing analysis is proposed in this study: we present an extension of the time-reversal method for linear diffractors. It consists of a coherent summation of seismic energy along edge-diffraction traveltimes. Real data examples show the feasibility and efficiency of the proposed method.  相似文献