A new form of generalized Boussinesq equations for varying water depth

A new set of equations of motion for wave propagation in water with varying depth is derived in this study. The equations expressed by the velocity potentials and the wave surface elevations include first-order non-linearity of waves and have the same dispersion characteristic to the extended Boussinesq equations. Compared to the extended Boussinesq equations, the equations have only two unknown scalars and do not contain spatial derivatives with an order higher than 2. The wave equations are solved by a finite element method. Fourth-order predictor–corrector method is applied in the time integration and a damping layer is applied at the open boundary for absorbing the outgoing waves. The model is applied to several examples of wave propagation in variable water depth. The computational results are compared with experimental data and other numerical results available in literature. The comparison demonstrates that the new form of the equations is capable of calculating wave transformation from relative deep water to shallow water.     

A new approach for predicting the extreme response of structures

In this article a method to estimate the mean upcrossing intensity, μ(u), of a stochastic process is proposed. It is assumed that the stochastic process is a sum of a Gaussian process and a second-order correction term. The method is based on the two-dimensional Saddlepoint approximation. The accuracy of the method is tested on processes having analytical solutions for μ(u). Numerical examples are given where the stochastic process represents (i) the horizontal response of a floating offshore structure in a Gaussian sea, and (ii) the response of a structure subjected to a Gaussian wind velocity process. In addition, the estimates are compared to empirical upcrossing intensities of simulated responses. For case (ii), the obtained μ(u) estimates are compared to estimates obtained by numerical integration.     

Boussinesq-type modelling using an unstructured finite element technique

A model for solving the two-dimensional enhanced Boussinesq equations is presented. The model equations are discretised in space using an unstructured finite element technique. The standard Galerkin method with mixed interpolation is applied. The time discretisation is performed using an explicit three-step Taylor–Galerkin method. The model is extended to the surf and swash zone by inclusion of wave breaking and a moving boundary at the shoreline. Breaking is treated by an existing surface roller model, but a new procedure for the detection of the roller thickness is devised. The model is verified using four test cases and the results are compared with experimental data and results from an existing finite difference Boussinesq model.     

Probing mid-mantle heterogeneity using PKP coda waves

We investigate the utility of PKP coda waves for studying weak scattering from small-scale heterogeneity in the mid-mantle. Coda waves are potentially a useful probe of heterogeneity in the mid-mantle because they are not preferentially scattered near the CMB, as PKP precursors are, but are sensitive to scattering at all depths. PKP coda waves have not been used for this purpose historically because of interference with other late-arriving energy due to near-surface resonance and scattering. Any study of deep mantle scattering using coda waves requires the removal of near-surface effects from the data. We have analyzed 3624 recordings of PKP precursors and coda made by stations in the Incorporated Research Institutions for Seismology (IRIS) Global Seismographic Network (GSN). To study the range and time dependence of the scattered waves, we binned and stacked envelopes of the recordings. We have considered precursors that arrive within a 20 s window before PKP and coda waves in a 60 s window after PKP. The PKP scattered waves increase in amplitude rapidly with range as predicted by scattering theory. At ranges below 125°, we predict and observe essentially no scattered energy preceding PKP. Coda amplitudes at these ranges are independent of range and provide an estimate of energy due to near-surface effects that we can expect at all ranges. We use the average coda amplitude at ranges from 120 to 125° to correct coda amplitudes at other ranges. PKP coda waves show a strong dependence on time and range and are clearly influenced by scattering in the lower mantle. PKP coda waves, however, do not provide a tighter constraint on the vertical distribution of mantle heterogeneity than is provided by precursors. This is due, in part, to relatively large scatter in coda amplitudes as revealed by a resampling analysis. Modeling using Rayleigh–Born scattering theory and an exponential autocorrelation function shows that PKP coda amplitudes are not highly sensitive to the vertical distribution of heterogeneity in the mantle. To illustrate this we consider single-scattering in two extreme models of mantle heterogeneity. One allows heterogeneity just at the CMB; the other includes heterogeneity throughout the mantle. The amplitudes of precursors are tightly constrained by our stack and support our earlier conclusion that small-scale heterogeneity is uniformly distributed throughout the lower mantle. The best-fit model includes 8 km scale length heterogeneity with an rms velocity contrast throughout the mantle of 1%.     

Spectral and Multiscale Signal-to-Noise Thresholding of Spherical Vector Fields

The basic concepts of spectral and multiscale selective reconstruction of (geophysically relevant) vector fields on the sphere from error-affected data is outlined in detail. The reconstruction mechanism is formulated under the assumption that spectral as well as multiscale approximation is well-representable in terms of only a certain number of expansion coefficients at the various resolution levels. It is shown that spectral denoising by means of orthogonal expansions in terms of vector spherical harmonics reflects global a priori information of the noise (e.g., in form of a covariance tensor field), whereas multiscale signal-to-noise thresholding can be performed under locally dependent noise information within a multiresolution analysis in terms of spherical vector wavelets. An application of the multiscale formalism to Earth's magnetic field determination is presented.     

我国月降水和气温网格点资料的处理和分析

用逐步搜索逼近法的客观分析技术计算出１９５１－１９９２年中国月降水量和月平均气温的格点资料，并利用图象识别原理对格点值和站点观测值进行了比较。     

Bragg reflection of water waves by multiple floating horizontal flexible membranes with submerged rectangular bars on the seabed

Bragg reflection of water waves by multiple floating horizontal flexible membranes is investigated based on the linear wave theory and the assumption of small membrane response. Under the floating horizontal membranes, periodical submerged rectangular bars are arranged on the flat seabed. The total reflection and transmission coefficients are obtained by using the eigenfunction expansion method and the wide spacing approximation. The calculated coefficients are validated with the results available in the literature, which shows that the present method is applicable. The characteristics of Bragg reflection are systematically investigated by changing various parameters including the height of the rectangular bars, the number, the tension, the spacing, and the length of the flexible membranes. The results can help designing multiple floating horizontal flexible membranes as effective floating breakwaters by taking advantage of Bragg reflection.     

Interaction of flexural gravity waves with shear current in shallow water

In the present study, the effect of shear current on the propagation of flexural gravity waves is analyzed under the assumptions of linearized shallow-water theory. Explicit expressions for the reflection and transmission coefficients associated with flexural gravity wave scattering by a step discontinuity in both water depth and current speed are derived. Further, trapping and scattering of flexural gravity waves by a jet-like shear current with a top-hat profile are examined and certain limiting conditions for the waves to exist are derived. The effects of change in water depth, current speed, incident wavelength and the angle of incidence on the group and phase velocities as well as on the reflection and transmission characteristics are analyzed through different numerical results.     

变参考慢度Born近似傅氏偏移

针对常规Born近似傅氏偏移方法对于剧烈横向变速介质不能精确成像的状况而提出了变参考慢度Born近似傅氏偏移，理论上解决了任意速度变化地质模型的偏移成像问题。此外，为进一步提高复杂地层的成像精度和波场延拓算子的稳定性，对散射波场的计算公式作了改进。将改进的方法运用于盐丘模型的正演和偏移试验，并与常规Born近似偏移方法相比较，可明显看出变参考慢度Born近似傅氏偏移方法在效果上要优于后者，其处理速度横向变化的能力大大增强。     

GNSS海面散射信号的海面风场遥感

首先介绍了GNSS-R海洋遥感的发展过程,简要叙述了利用GNSS信号进行海洋动力学遥感测量的基本原理;然后分析了接收机天线的部分参数对GNSS信号可见数量的影响;最后详细阐述了GNSS海面散射信号的理论模型,该模型是利用几何光学限制的基尔霍夫近似建立起来的,并根据理论模型进行了数值仿真试验。结果证实了通过散射信号功率波形来反演海面风场理论上的可行性。