Inhomogeneous Harmonic Plane Waves in Viscoelastic Anisotropic Media

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.     

Grid travel-time tracing: Second-order method for the first arrivals in smooth media

A new computational scheme for calculating the first-arrival travel times on a rectangular grid of points is proposed. The new proposed method is of second-order accuracy. This means that the error of the calculated travel time is proportional to the second power of the grid spacing. The method should be sufficiently accurate for all applications in smooth seismic models. On the other hand, the method is not, in its present form, proposed for models with structural interfaces which make the method unstable and generate travel-time errors of the first order. Equations are also presented for the appropriate evaluation of the errors of calculated travel times to check their accuracy, and the proposed method is compared with other numerical methods. The method is developed, described and demonstrated in 2-D, but may also be extended to 3-D models and to general models with structural interfaces.     

Estimation of azimuth and slowness of tele-seismic signals recorded by a local seismic network

Introduction The azimuth and slowness are two major features of seismic signals. The accurate estimation of them is quite important for both phase identification and event location. Generally, there are two types of seismic stations, i.e. 3-component stations (3C) and arrays. To estimate the two direc-tional parameters, the polarization analysis (Jurkevics, 1988) is commonly used for 3C stations and the frequency-wavenumber spectrum analysis ( f-k) (Capon, 1969; Kvaerna, Doornbos, 1986) is …     

Finite-amplitude mountain waves in a compressible atmosphere including the effects of dissipation

Abstract

Adiabatic, two-dimensional, steady-state finite-amplitude, hydrostatic gravity waves produced by flow over a ridge are considered. Nonlinear self advection steepens the wave until the streamlines attain a vertical slope at a critical height z_c. The height z_c , where this occurs, depends on the ridge crest height and adiabatic expansion of the atmosphere. Dissipation is introduced in order to balance nonlinear self advection, and to maintain a marginal state above z_c. The approach is to assume that the wave is inviscid except in a thin layer, small compared to a vertical wavelength, where dissipation cannot be neglected. The solutions in each region are matched to obtain a continuous solution for the streamline displacement δ. Solutions are presented for different values of the nondimensional dissipation parameter β. Eddy viscosity coefficients and the thickness of the dissipative layer are expressed as functions of β, and their magnitudes are compared to other theoretical evaluations and to values inferred from radar measurements of the stratosphere.

The Fourier spectrum of the solution for z ≫ z_c is shown to decay exponentially at large vertical wave numbers n. In comparison, a spectral decay law n ^?-8/3 characterizes the marginal state of the wave at z = z_c .     

Free and forced shallow-water oscillations in a rotating channel of parabolic cross-section

Free and forced oscillations of shallow water in an infinitely long rotating channel of parabolic cross-section are analyzed. The pure cross-channel oscillations ofChrystal (1905) and solutions for zero rotation first discussed byProudman (1925) andHidaka (1932) are special asymptotic solutions for the free modes of this model. However, for increasingly large, along-shore wave number, our solutions donot uniformly approach those ofReid (1958) andBall (1967) for a single shore-line and semi-infinite ocean. A method of computing eigen frequencies and eigen functions for the general problem is described, and a sufficient number of these are exhibited graphically to permit visualization of the transitions between the asymptotic regions.The forced problem consists of an incoming wave-train or surge generated at the center of the channel. Amplitude and transports near the shore are computed for a wide range of dimensionless incoming-wave frequencies and rotational frequencies.     

A reduced model for nonlinear dispersive waves in a rotating environment

Abstract

The simplest model for geophysical flows is one layer of a constant density fluid with a free surface, where the fluid motions occur on a scale in which the Coriolis force is significant. In the linear shallow water limit, there are non-dispersive Kelvin waves, localized near a boundary or near the equator, and a large family of dispersive waves. We study weakly nonlinear and finite depth corrections to these waves, and derive a reduced system of equations governing the flow. For this system we find approximate solitary Kelvin waves, both for waves traveling along a boundary and along the equator. These waves induce jets perpendicular to their direction of propagation, which may have a role in mixing. We also derive an equivalent reduced system for the evolution of perturbations to a mean geostrophic flow.     

Ray path-length-dependent slowness model

By introducing a new parameter, slowness deviation, a ray-path-length-dependent slowness model has been previously developed. Synthetic tests indicate that for a horizontal layered slowness structure, the new model gives a good estimate of the weighted average slowness of a ray when the rays considered cover a small range of take-off angles. When the rays considered cover a large range of take-off angles, the new model gives good estimates of the weighted average slowness for the long rays, but large errors still remain for the short rays.     

Research on the Result of Calibration for the Location of the Seismic Array in Shanghai

The paper proposes the calibration theory and methods for the Shanghai seismic array and analyzes the calibration results. As a result, the calibration results for the seismic array based on 2 typical earthquakes have been drawn; the difference of calibration results between Hokkaido and Honshu region in Japan is investigated. And calibration results of different directions, different epicenter distances and different magnitudes are probed into. The result shows that the location of earthquakes on the Shanghai seismic array is greatly improved.     

火山岩、白云岩储层基质孔隙度计算方法分析(英文)

火山岩、风化壳白云岩等缝洞储层基质孔隙度计算是测井评价亟需解决的难题之一.本文首先将全直径流纹岩声波实验公式(2005年,李宁)与国内外常用的基质孔隙度计算公式进行了细致的对比;进而就该公式在中基性火山岩、风化壳白云岩等缝洞储层中的适用性进行了深入讨论,并以岩心分析资料为基础,详细给出了该公式与其它公式在计算上述储层基质孔隙度时的误筹分布.误差统计结果表明该公式具有更高的精度.通过中国东部和西部三家油田70口井的实际应用验证,在孔隙度从1.5%到15%范围内,该公式不仅适用于酸性火山岩储层,而且适用于中基性火山岩、风化壳白云岩等缝洞储层基质孔隙度的评价.同时,该公式能够最大限度地减小扩径、岩石蚀变等复杂地质条件对计算结果的影响,实用性更强.     

Surface‐wave inversion for a P‐velocity profile with a constant depth gradient of the squared slowness

Surface waves are often used to estimate a near‐surface shear‐velocity profile. The inverse problem is solved for the locally one‐dimensional problem of a set of homogeneous horizontal elastic layers. The result is a set of shear velocities, one for each layer. To obtain a P‐wave velocity profile, the P‐guided waves should be included in the inversion scheme. As an alternative to a multi‐layered model, we consider a simple smooth acoustic constant‐density velocity model, which has a negative constant vertical depth gradient of the squared P‐wave slowness and is bounded by a free surface at the top and a homogeneous half‐space at the bottom. The exact solution involves Airy functions and provides an analytical expression for the dispersion equation. If the ratio is sufficiently small, the dispersion curves can be picked from the seismic data and inverted for the continuous P‐wave velocity profile. The potential advantages of our model are its low computational cost and the fact that the result can serve as a smooth starting model for full‐waveform inversion. For the latter, a smooth initial model is often preferred over a rough one. We test the inversion approach on synthetic elastic data computed for a single‐layer P‐wave model and on field data, both with a small ratio. We find that a single‐layer model can recover either the shallow or deeper part of the profile but not both, when compared with the result of a multi‐layer inversion that we use as a reference. An extension of our analytic model to two layers above a homogeneous half‐space, each with a constant vertical gradient of the squared P‐wave slowness and connected in a continuous manner, improves the fit of the picked dispersion curves. The resulting profile resembles a smooth approximation of the multi‐layered one but contains, of course, less detail. As it turns out, our method does not degrade as gracefully as, for instance, diving‐wave tomography, and we can only hope to fit a subset of the dispersion curves. Therefore, the applicability of the method is limited to cases where the ratio is small and the profile is sufficiently simple. A further extension of the two‐layer model to more layers, each with a constant depth gradient of the squared slowness, might improve the fit of the modal structure but at an increased cost.     

Generation of baroclinic topographic waves by a tropical cyclone impacting a low-latitude continental shelf

Numerical model experiments have been performed to analyze the low-latitude baroclinic continental shelf response to a tropical cyclone. The theory of coastally trapped waves suggests that, provided appropriate slope, latitude, stratification and wind stress, bottom-intensified topographic Rossby waves can be generated by the storm. Based on a scale analysis, the Nicaragua Shelf is chosen to study propagating topographic waves excited by a storm, and a model domain is configured with simplified but similar geometry. The model is forced with wind stress representative of a hurricane translating slowly over the region at 6 km h⁻¹. Scale analysis leads to the assumption that baroclinic Kelvin wave modes have minimal effect on the low-frequency wave motions along the slope, and coastal-trapped waves are restricted to topographic Rossby waves. Analysis of the simulated motions suggests that the shallow part of the continental slope is under the influence of barotropic topographic wave motions and at the deeper part of the slope baroclinic topographic Rossby waves dominate the low-frequency motions. Numerical solutions are in a good agreement with theoretical scale analysis. Characteristics of the simulated baroclinic waves are calculated based on linear theory of bottom-intensified topographic Rossby waves. Simulated waves have periods ranging from 153 to 203 h. The length scale of the waves is from 59 to 87 km. Analysis of energy fluxes for a fixed volume on the slope reveals predominantly along-isobath energy propagation in the direction of the group velocity of a topographic Rossby wave. Another model experiment forced with a faster translating hurricane demonstrates that fast moving tropical cyclones do not excite energetic baroclinic topographic Rossby waves. Instead, robust inertial oscillations are identified over the slope.     

Local Determination of Weak Anisotropy Parameters from Walkaway VSP qP-Wave Data in the Java Sea Region

We apply the inversion scheme of Zheng and Peník (2002) to the walkaway VSP data of Horne and Leaney (2000) collected in the Java Sea region. The goal is a local determination of parameters of the medium surrounding the borehole receiver array. The inversion scheme is based on linearized equations expressing qP-wave slowness and polarization vectors in terms of weak anisotropy (WA) parameters. It thus represents an alternative approach to Horne and Leaney (2000), who based their procedure on inversion of the Christoffel equation using a global optimization method. The presented inversion scheme is independent of structural complexities in the overburden and of the orientation of the borehole. The inverson formula is local, and has therefore potential to separate effects of anisotropy from effects of inhomogeneity. The data used are components of the slowness vector along the receiver array and polarization vectors. The inversion is performed without any assumptions concerning the remaining components of the slowness vector. The inversion is made (a) assuming arbitrary anisotropy, i.e., without any assumptions about symmetry of the medium, (b) assuming transverse isotropy with a vertical axis of symmetry and (c) assuming isotropy of the medium. Inverted are the raw data as well as data, in which weighting is used to reduce the effect of outliers. It is found that the WA parameters _z, ₁₅ and ₃₅ are considerably more stable than the parameters _x and _x. The latter two parameters are also found to be strongly correlated. Weaker correlation is also found between the mentioned two parameters and _z. The results of inversion show clearly that the studied medium is not isotropic. They also seem to indicate that the studied medium does not possess the VTI symmetry.     

A Fast Method of Computing Group-Velocity Partial Derivatives for Love Waves Propagating in a Layer on a Half-Space

The dispersion relation for Love waves in a layer on a half-space is modified by introducing the wave number and its square instead of the phase velocity. The implicit function theorem is then used to derive the analytical formulae for the group velocity and for the phase- and group-velocity partial derivatives with respect to the parameters of the medium. The formulae are compared with those obtained by Novotný (1971) where the traditional formulation of the dispersion relation was used.     

Solitary waves in a compressible fluid

Evolution equations for long nonlinear internal waves in a compressible fluid are derived, with the aim of comparing these equations with their counterparts in an incompressible fluid. Both the Korteweg-de Vries equation, and the deep fluid equation are discussed, for both dry and moist atmospheres. It is shown that the effects of compressibility, or non-Boussinesq terms, are generally small, but measurable, and are manifested mainly in the nonlinear term of the evolution equation. For the case of a moist atmosphere the effect of a gain in energy by latent heat release is compared with the energy lost by radiation damping.     

Monitoring of seismic events from a specific source region using a single regional array: A case study

In the monitoring of earthquakes and nuclear explosions using a sparse worldwide network of seismic stations, it is frequently necessary to make reliable location estimates using a single seismic array. It is also desirable to screen out routine industrial explosions automatically in order that analyst resources are not wasted upon detections which can, with a high level of confidence, be associated with such a source. The Kovdor mine on the Kola Peninsula of NW Russia is the site of frequent industrial blasts which are well recorded by the ARCES regional seismic array at a distance of approximately 300 km. We describe here an automatic procedure for identifying signals which are likely to result from blasts at the Kovdor mine and, wherever possible, for obtaining single array locations for such events. Carefully calibrated processing parameters were chosen using measurements from confirmed events at the mine over a one-year period for which the operators supplied Ground Truth information. Phase arrival times are estimated using an autoregressive method and slowness and azimuth are estimated using broadband f{-}k analysis in fixed frequency bands and time-windows fixed relative to the initial P-onset time. We demonstrate the improvement to slowness estimates resulting from the use of fixed frequency bands. Events can be located using a single array if, in addition to the P-phase, at least one secondary phase is found with both an acceptable slowness estimate and valid onset-time estimate. We evaluate the on-line system over a twelve month period; every event known to have occured at the mine is detected by the process and 32 out of 53 confirmed events were located automatically. The remaining events were classified as “very likely” Kovdor events and were subsequently located by an analyst. The false alarm rate is low; only 84 very likely Kovdor events were identified during the whole of 2003 and none of these were subsequently located at a large distance from the mine. The location accuracy achieved automatically by the single-array process is remarkably good, and is comparable to that obtained interactively by an experienced analyst using two-array observations. The greatest problem encountered in the single array location procedure is the difficulty in determining arrival times for secondary phases, given the weak Sn phase and the complexity of the P-coda. The method described here could be applied to a wide range of locations and sources for which the monitoring of seismic activity is desirable. The effectiveness will depend upon the distance between source and receiver, the nature of the seismic sources and the level of regional seismicity.     

上海地震台阵的地震定位方法

详细介绍了上海地震台阵数据处理软件系统中的地震定位方法，用台阵的聚束方法得到地震的方位角和视慢度，根据统计得到的视慢度－震中距表推算震中距。并结合了地震台网的定位方法，由单台记录的各类主要震相从J－B走时表得到震中距，然后进行地震定位。该定位方法可对近震、远震进行定位处理，并由深震相得到震源深度。     

Hydromagnetic waves in a differentially rotating,stratified spherical shell

Abstract

Investigations of an earlier paper (Friedlander 1987a) are extended to include the effect of an azimuthal shear flow on the small amplitude oscillations of a rotating, density stratified, electrically conducting, non-dissipative fluid in the geometry of a spherical shell. The basic state mean fields are taken to be arbitrary toroidal axisymmetric functions of space that are consistent with the constraint of the ‘‘magnetic thermal wind equation''. The problem is formulated to emphasize the similarities between the magnetic and the non-magnetic internal wave problem. Energy integrals are constructed and the stabilizing/destabilizing roles of the shears in the basic state functions are examined. Effects of curvature and sphericity are studied for the eigenvalue problem. This is given by a partial differential equation (P.D.E.) of mixed type with, in general, a complex pattern of turning surfaces delineating the hyperbolic and elliptic regimes. Further mathematical complexities arise from a distribution of the magnetic analogue of critical latitudes. The magnetic extension of Laplace's tidal equations are discussed. It is observed that the magnetic analogue of planetary waves may propagate to the east and to the west.     

Long waves due to a symmetrical wind stress on the surface of a rotating ocean

Abstract

The problem of unsteady long waves generated by any horizontal and symmetrically distributed, time-periodic surface wind on a rotating ocean is analysed for large times and distances. Uniform asymptotic estimates of the surface displacement in the unsteady state are obtained. The steady-state wave and velocity fields at any distance are also determined. Some characteristics of the unsteady and steady motions are described. Also noted are the features that distinguish the motion from its one-dimensional analogue for which a non-uniform analysis in the unsteady state along with a large-distance form of the surface elevation are already known.     

上海地震台阵标定及结果分析

阐述了台阵的地震定位原理和建立台阵标定数据库的必要性。说明了如何利用上海地震台网资料和上海地震台阵建成后的资料建立台阵标定数据库，最后，对上海台阵标定的结果进行了导致定位误差的横向速度变化的位置和范围的讨论。     

Trapped internal waves over undular topography in a partially mixed estuary

The flow of a stratified fluid over small-scale topographic features in an estuary may generate significant internal wave activity. Lee waves and upstream influence generated at isolated topographic features have received considerable attention during the past few decades. Field surveys of a partially mixed estuary, the Rotterdam Waterway, in 1987, also showed a plethora of internal wave activity generated by isolated topography, banks and groynes. Additionally it revealed a spectacular series of resonant internal waves trapped above low-amplitude bed waves. The internal waves reached amplitudes of 3–4 m in an estuary with a mean depth of 16 m. The waves were observed during the decreasing flood tide and are thought to make a significant contribution to turbulence production and mixing. However, while stationary linear and finite amplitude theories can be used to explain the presence of these waves, it is important to further investigate their time-dependent and non-linear behaviour. With the development of advanced non-hydrostatic models it now becomes possible to further investigate these waves through numerical experimentation. This is the focus of the work presented here. The non-hydrostatic finite element numerical model FINEL3D developed by Labeur was used in the experiments presented here. The model has been shown to work well in a number of stratified flow investigations. Here, we first show that the model reproduces the field data and for idealised stationary flow scenarios that the results are in agreement with the resonant response predicted by linear theory. Then we explore the effects of non-linearity and time dependence and consider the importance of resonant internal waves for turbulence production in stratified coastal environments.Responsible Editior: Hans Burchard