Practical VTI approximations: a systematic anatomy

Transverse isotropy (TI) with a vertical symmetry axis (VTI) often provides an appropriate earth model for prestack imaging of steep-dip reflection seismic data. Exact P-wave and SV-wave phase velocities in VTI media are described by complicated equations requiring four independent parameters. Estimating appropriate multiparameter earth models can be difficult and time-consuming, so it is often useful to replace the exact VTI equations with simpler approximations requiring fewer parameters. The accuracy limits of different previously published VTI approximations are not always clear, nor is it always obvious how these different approximations relate to each other. Here I present a systematic framework for deriving a variety of useful VTI approximations. I develop first a sequence of well-defined approximations to the exact P-wave and SV-wave phase velocities. In doing so, I show how the useful but physically questionable heuristic of setting shear velocities identically to zero can be replaced with a more precise and quantifiable approximation. The key here to deriving accurate approximations is to replace the stiffness a₁₃ with an appropriate factorization in terms of velocity parameters. Two different specific parameter choices lead to the P-wave approximations of Alkhalifah (Geophysics 63 (1998) 623) and Schoenberg and de Hoop (Geophysics 65 (2000) 919), but there are actually an infinite number of reasonable parametrizations possible. Further approximations then lead to a variety of other useful phase velocity expressions, including those of Thomsen (Geophysics 51 (1986) 1954), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Harlan (Stanford Exploration Project Report 89 (1995) 145), and Stopin (Stopin, A., 2001. Comparison of v(θ) equations in TI medium. 9th International Workshop on Seismic Anisotropy). Each P-wave phase velocity approximation derived this way can be paired naturally with a corresponding SV-wave approximation. Each P-wave or SV-wave phase velocity approximation can then be converted into an equivalent dispersion relation in terms of horizontal and vertical slownesses. A simple heuristic substitution also allows each phase velocity approximation to be converted into an explicit group velocity approximation. From these, in turn, travel time or moveout approximations can also be derived. The group velocity and travel time approximations derived this way include ones previously used by Byun et al. (Geophysics 54 (1989) 1564), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Tsvankin and Thomsen (Geophysics 59 (1994) 1290), Harlan (89 (1995) 145), and Zhang and Uren (Zhang, F. and Uren, N., 2001. Approximate explicit ray velocity functions and travel times for P-waves in TI media. 71st Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts, 106–109).     

Seismic evidence for deep low-velocity anomalies in the transition zone beneath West Antarctica

We present a three-dimensional (3D) SV-wave velocity model of the upper mantle beneath the Antarctic plate constrained by fundamental and higher mode Rayleigh waves recorded at regional distances. The good agreement between our results and previous surface wave studies in the uppermost 200 km of the mantle confirms that despite strong differences in data processing, modern surface wave tomographic techniques allow to produce consistent velocity models, even at regional scale. At greater depths the higher mode information present in our data set allows us to improve the resolution compared to previous regional surface wave studies in Antarctica that were all restricted to the analysis of the fundamental mode. This paper is therefore mostly devoted to the discussion of the deeper part of the model. Our seismic model displays broad domains of anomalously low seismic velocities in the asthenosphere. Moreover, we show that some of these broad, low-velocity regions can be more deeply rooted. The most remarkable new features of our model are vertical low-velocity structures extending from the asthenosphere down to the transition zone beneath the volcanic region of Marie Byrd Land, West Antarctica and a portion of the Pacific-Antarctic Ridge close to the Balleny Islands hotspot. A deep low-velocity anomaly may also exist beneath the Ross Sea hotspot. These vertical structures cannot be explained by vertical smearing of shallow seismic anomalies and synthetic tests show that they are compatible with a structure narrower than 200 km which would have been horizontally smoothed by the tomographic inversion. These deep low-velocity anomalies may favor the existence of several distinct mantle plumes, instead of a large single one, as the origin of volcanism in and around West Antarctica. These hypothetical deep plumes could feed large regions of low seismic velocities in the asthenosphere.     

A hybrid indirect boundary element—discrete wave number method applied to simulate the seismic response of stratified alluvial valleys

A hybrid indirect boundary element – discrete wavenumber method is presented and applied to model the ground motion on stratified alluvial valleys under incident plane SH waves from an elastic half-space. The method is based on the single-layer integral representation for diffracted waves. Refracted waves in the horizontally stratified region can be expressed as a linear superposition of solutions for a set of discrete wavenumbers. These solutions are obtained in terms of the Thomson–Haskell propagators formalism. Boundary conditions of continuity of displacements and tractions along the common boundary between the half-space and the stratified region lead to a system of equations for the sources strengths and the coefficients of the plane wave expansion. Although the regions share the boundary, the discretization schemes are different for both sides: for the exterior region, it is based on the numerical and analytical integration of exact Green's functions for displacements and tractions whereas for the layered part, a collocation approach is used. In order to validate this approach results are compared for well-known cases studied in the literature. A homogeneous trapezoidal valley and a parabolic stratified valley were studied and excellent agreement with previous computations was found. An example is given for a stratified inclusion model of an alluvial deposit with an irregular interface with the half-space. Results are displayed in both frequency and time domains. These results show the significant influence of lateral heterogeneity and the emergence of locally generated surface waves in the seismic response of alluvial valleys.     

Attenuation of body waves in Southeastern Sicily (Italy)

The attenuation of P- and S-waves in Southeastern Sicily was estimated by applying two different methods in time and frequency domains. We analyzed waveforms from about 290 local events (0.6≤M_L≤4.6) recorded at a three-component digital network.By applying the pulse broadening method to the first P-wave pulse, we found an average Q_p value of ca. 140. The application of the frequency decay method provided a Q_p value of ca. 120, in the low-frequency band (3-9 Hz). Conversely, in the high frequency range (16-27 Hz) the average Q_p is significantly larger (ca. 640). The frequency decay method was also applied to S-waves spectra. In the low frequency range (2-5 Hz) the estimated average Q_s is ca. 190. As for Q_p, also Q_s, in the high frequency range (16-27 Hz), is larger (ca. 700). These results evidenced a frequency dependence of both the quality factors Q_p and Q_s, as commonly observed in tectonically active zones characterized by high degree of heterogeneity.     

Magnetic activity inside the auroral zones and field-aligned currents

Big perturbations of the magnetic field (amplitudes larger than 250 nT) are simply detected by subtracting the values of a model from the measurements of CHAMP satellite. Taking a full year of CHAMP data and organizing them in four subsets of three months length (spring, summer, autumn, winter), it is found that: (a) the two domains where such big perturbations mainly exist are limited, in both hemispheres, by a parallel of high latitude of the corrected geomagnetic coordinates system; (b) a conspicuous seasonal (annual) variation affects the density of the perturbations and is opposite in the two hemispheres. We hold that these perturbations are linked to the midday magnetic activity within the auroral zone, long ago described by one of us (Mayaud, 1956). The source of the perturbations observed at the satellite altitude would be field-aligned currents resulting from the penetration of the solar wind into the magnetospheric cusps. To cite this article: J.-L. Le Mouël et al., C. R. Geoscience 335 (2003).     

Estimating palaeowind strength from beach deposits

Abstract The geological record of past wind conditions is well expressed in the coarse gravel, cobble and boulder beach deposits of Quaternary palaeolakes in the Great Basin of the western USA and elsewhere. This paper describes a technique, using the particle‐size distribution of beach deposits, to reconstruct palaeowind conditions when the lakes were present. The beach particle technique (BPT) is first developed using coarse beach deposits from the 1986–87 highstand of the Great Salt Lake in Utah, combined with instrumental wind records from the same time period. Next, the BPT is used to test the hypothesis that wind conditions were more severe than at present during the last highstand of Lake Lahontan (≈ 13 ka), which only lasted a decade or two at most. The largest 50 beach clasts were measured at nine beach sites located along the north, west and south sides of Antelope Island in the Great Salt Lake, all of which formed in 1986–87. At these sites, the largest clast sizes range from 10 to 28 cm (b‐axis), and fetch lengths range from 25 to 55 km. Nearshore wave height was calculated by assuming that the critical threshold velocity required to move the largest clasts represents a minimum estimate of the breaking wave velocity, which is controlled by wave height. Shoaling transformations are undertaken to estimate deep‐water wave heights and, ultimately, wind velocity. Wind estimates for the nine sites, using the BPT, range from 6·5 to 17·4 m s^?1, which is in reasonable agreement with the instrumental record from Salt Lake City Airport. The same technique was applied to eight late Pleistocene beaches surrounding the Carson Sink sub‐basin of Lake Lahontan, Nevada. Using the BPT, estimated winds for the eight sites range from 9·7 to 27·1 m s^?1. The strongest winds were calculated for a cobble/boulder beach with a fetch of 25 km. Instrumental wind records for the 1992–99 period indicate that wind events of 9–12 m s^?1 are common and that the strongest significant wind event (≥ 9 m s^?1 for ≥ 3 h) reached an average velocity of 15·5 m s^?1. Based on this preliminary comparison, it appears that the late Pleistocene western Great Basin was a windier place than at present, at least for a brief time.     

斜底面上的表面波理论

考察了任意倾斜底面上的Kelvin波问题，并用线性化的控制方程分别研究了相应于垂直刚壁的和无限倾斜底面上的表面波频散关系。文中还对任意斜坡上的浅水表面波做了尺度分析，并把决定其频散关系的特征值问题简化为该斜坡上气压扰动的常微分方程，且用数值方法进行了求解。     

Reflection and transmission of seismic waves at an interface betwen two saturated soils

ＲｅｆｌｅｃｔｉｏｎａｎｄｔｒａｎｓｍｉｓｉｏｎｏｆｓｅｉｓｍｉｃｗａｖｅｓａｔａｎｉｎｔｅｒｆａｃｅｂｅｔｗｅｎｔｗｏｓａｔｕｒａｔｅｄｓｏｉｌｓＪＵＮＹＡＮＧ（杨峻）ＳＨＩＭＩＮＧＷＵ（吴世明）ＺｈｅｊｉａｎｇＵｎｉｖｅｒｓｉｔｙ，Ｈａｎｇｚ...     

第22太阳活动周峰年的ULF波观测与研究

本文介绍第２２太阳活动周峰年期间利用ＵＬＦ波的观测和分析，对磁层近地空间电磁环境的研究，文中列举了这峰年期间地磁脉动的主要成果。有些成果是国际上首次提出和发表的，目前，地磁脉动的观测和研究已经成为监测近地空间电磁环境的重要手段。     

线性和非线性风应力对海-气耦合波的影响

在略去Ｒｅｙｌｅｉｇｈ摩擦和Ｎｅｗｔｏｎ冷却的条件下，采用定常的线性大气模式和半地转近似的非线性海洋模式，讨论了线性和非线性风应力对海－气耦合Ｒｏｓｓｂｙ波的影响，结果表明，当耦合波处于非线性不稳定的情况下，线性和非线性风应力均可产生孤立波，不同之处在于，非线性风应力所产笺波图像具有间断特点，波能的急剧聚集有可能使波的性质发生变化。