不同参数对地震干涉实现VSP向SWP波场重构的影响

地震干涉是近几年勘探地球物理领域研究的一个热点方向,它是波场重构的有力工具.然而,地震干涉往往引入虚假同相轴,影响波场重构的质量.为进一步分析虚假同相轴产生的原因并改善波场重构的质量,本文基于稳相分析,详细探讨子波主频、激发炮数、检波器埋深、检波器间距和地层倾角五个因素对波场重构的影响.模型结果表明,震检排列方式和地层倾角等因素通过改变有限震检范围内稳相点的位置来影响波场重构的质量.将垂直地震剖面VSP中的下行直达波与下行反射波进行地震干涉处理,可有效重构来自高陡反射面的下行反射波,将传统的VSP转化为单井地震剖面SWP.直接利用重构SWP波场进行成像,不仅扩大传统VSP的成像范围,而且避免常规勘探面临的静校正和近地表速度建模问题,为高陡构造成像提供一种新方法.     

STEEP DIP FINITE-DIFFERENCE MIGRATION*

A method is presented to derive approximate versions of the wave equation which allow finite-difference migration for very steep dips (> 50°). It is shown that for conventional finite-difference schemes, in addition to the dip limitation, the maximum acceptable frequency should be specified. A finite-difference migration technique is proposed in the frequency domain. It is derived that finite-difference wave field extrapolation in the frequency domain consists of a space-variant convolution procedure for each frequency component, the space-variance being defined by the lateral variation in the velocity. Finally it is shown that with finite-difference migration, particle velocity data can be easily obtained from pressure data.     

High-order kernels for Riemannian wavefield extrapolation

Riemannian wavefield extrapolation is a technique for one‐way extrapolation of acoustic waves. Riemannian wavefield extrapolation generalizes wavefield extrapolation by downward continuation by considering coordinate systems different from conventional Cartesian ones. Coordinate systems can conform with the extrapolated wavefield, with the velocity model or with the acquisition geometry. When coordinate systems conform with the propagated wavefield, extrapolation can be done accurately using low‐order kernels. However, in complex media or in cases where the coordinate systems do not conform with the propagating wavefields, low order kernels are not accurate enough and need to be replaced by more accurate, higher‐order kernels. Since Riemannian wavefield extrapolation is based on factorization of an acoustic wave‐equation, higher‐order kernels can be constructed using methods analogous to the one employed for factorization of the acoustic wave‐equation in Cartesian coordinates. Thus, we can construct space‐domain finite‐differences as well as mixed‐domain techniques for extrapolation. High‐order Riemannian wavefield extrapolation kernels improve the accuracy of extrapolation, particularly when the Riemannian coordinate systems does not closely match the general direction of wave propagation.     

Effect of seepage on flow and bedforms dynamics

This study, using an experimental approach, focuses on the effect of downward seepage on a threshold alluvial channel morphology and corresponding turbulent flow characteristics. In all the experiments, we observed that the streamwise time‐averaged velocities and Reynolds shear stresses were increased under the influence of downward seepage. Scales of eddy length and eddy turnover time were significantly increased with the application of downward seepage, leading to sediment transport and initiation of bedforms along the channel length. As the amount of seepage discharge increased, eddy length and turnover time were further increased, causing the development of larger bedforms. It was revealed that the geometry of bedforms was linked with the size of eddies. In this work, statistics of bedform dynamics are presented in terms of multi‐scalar bedforms in the presence of seepage. These multi‐scalar ubiquitous bedforms cast a potential impact on flow turbulence as well as stream bed morphology in channels. We used wavelet to analyse temporally lagged spatial bed elevation profiles that were obtained from a set of laboratory experiments and synchronized the wavelet coefficients with bed elevation fluctuations at different length scales. A spatial cross‐correlation analysis, based on the wavelet coefficients, was performed on these bed elevation datasets to observe the effect of downward seepage on the dynamic behaviour of bedforms at different length scales. It was found that celerity of bedforms reduced with increase in seepage percentage. Bedform celerity was best approximated by a probability density function such as Rayleigh distribution under varying downward seepage. Further, statistical analysis of physical parameters of bedforms ascertained that the reduction in bedform celerity was a result of increased bedform size. Copyright © 2017 John Wiley & Sons, Ltd.     

WAVE FIELD EXTRAPOLATION TECHNIQUES FOR INHOMOGENEOUS MEDIA WHICH INCLUDE CRITICAL ANGLE EVENTS. PART I: METHODS USING THE ONE-WAY WAVE EQUATIONS*

Part I of this series starts with a brief review of the fundamental principles underlying wave field extrapolation. Next, the total wave field is split into downgoing and upgoing waves, described by a set of coupled one-way wave equations. In cases of limited propagation angles and weak inhomogeneities these one-way wave equations can be decoupled, describing primary waves only. For large propagation angles (up to and including 90°) an alternative choice of sub-division into downgoing and upgoing waves is presented. It is shown that this approach is well suited for modeling as well as migration and inversion schemes for seismic data which include critical angle events.     

ADI plus interpolation: accurate finite-difference solution to 3D paraxial wave equation

An accurate finite-difference solution is developed for the paraxial wave equation in 3D seismic migration. The conventional alternating-direction-implicit (ADI) scheme used in migration causes errors, because the variables in the migration problem are complex-valued, not real-valued, and the imaginary part of the higher-order spatial derivatives cannot be ignored. The accuracy of the 3D paraxial extrapolator is preserved by (i) retaining these higher-order terms so that it does not produce the apparent azimuthal anisotropy in conventional migration, and (ii) filtering the non-physical evanescent waves during the downward extrapolation. The implementation of the accurate solution consists of two steps: firstly, the application of ADI to solve two tridiagonal systems sequentially, and secondly, an interpolation between the extrapolated wavefields of successive extrapolation levels. The method is computationally efficient as it uses the ADI scheme and, in addition, couples the correction for azimuthal anisotropy and the suppression of evanescent waves into a single operation, the interpolation step.     

TOWARDS OPTIMUM ONE-WAY WAVE PROPAGATION1

Numerical wavefield extrapolation represents the backbone of any algorithm for depth migration pre- or post-stack. For such depth imaging techniques to yield reliable and interpretable results, the underlying wavefield extrapolation algorithm must propagate the waves through inhomogeneous media with a minimum of numerically induced distortion, over a range of frequencies and angles of propagation. A review of finite-difference (FD) approximations to the acoustic one-way wave equation in the space-frequency domain is presented. A straightforward generalization of the conventional FD formulation leads to an algorithm where the wavefield is continued downwards with space-variant symmetric convolutional operators. The operators can be precomputed and made accessible in tables such that the ratio between the temporal frequency and the local velocity is used to determine the correct operator at each grid point during the downward continuation. Convolutional operators are designed to fit the desired dispersion relation over a range of frequencies and angles of propagation such that the resulting numerical distortion is minimized. The optimization is constrained to ensure that evanescent energy and waves propagating at angles higher than the maximum design angle are attenuated in each extrapolation step. The resulting operators may be viewed as optimally truncated and bandlimited spatial versions of the familiar phase shift operator. They are unconditionally stable and can be applied explicitly. This results in a simple wave propagation algorithm, eminently suited for implementation on pipelined computers and on large parallel computing systems.     

基于波场垂向和水平方向外推的高陡构造偏移

常规的单程波波动方程偏移成像方法对大角度的高陡构造偏移成像存在内在的限制.根据波动方程在各个空间方向的数学特性和高陡构造反射地震波的传播特征,通过把地震波分解为垂向的上下行波、水平方向的前后行波和左右行波,提出基于波场垂向外推和水平方向外推相结合的单程波波动方程高陡构造偏移成像方法,即用波场垂向外推的单程波波动方程偏移成像方法解决中低角度平缓构造的偏移成像,用波场水平方向外推的单程波波动方程偏移成像方法解决中高角度陡倾构造的偏移成像.这种基于波场垂向和水平方向外推相结合的高陡构造偏移成像方法是常规单程波波动方程叠前深度偏移成像方法的补充和改进,它相对基于全波方程的逆时偏移具有计算效率上的优势.     

FULL WAVE EQUATION DOWNWARD CONTINUATION OF SEISMIC REFLECTION DATA*

A new method for suppressing multiple reflections in seismograms is developed. It is based on a downward continuation procedure which uses the full acoustic wave equation (hyperbolic form) as a downward continuation operator. We demonstrate that the downward continuation of the recorded wave field maps a reflectivity function without multiply reflected events. The method is applied successfully to individual traces of plane-wave decomposed (slant-stacked) synthetic and field data.     

VHF radar observed characteristics of convectively generated gravity waves during wet and dry spells of Indian summer monsoon

A powerful VHF radar observed characteristics of Convectively generated Gravity Waves (CGW) excited during the wet and dry spells of Indian summer monsoon over a tropical station Gadanki (13.5°N, 79.2°E) are discussed. The characteristics of gravity waves in the lower stratosphere during these two spells are discussed in terms of their wavelet spectra along with height–time sections of vertical velocity. A total of 31 events are analyzed and in more than 50% of the events, the lower stratospheric gravity wave amplitudes were found to be relatively large in dry spell compared to that in the wet spell. The wavelet analysis of lower stratospheric vertical velocities showed a dominant periodicity of about ～20–40 min in wet spell and ～10–20 min in dry spell. The analysis also indicates that wet spell is found to be more conducive for the generation of gravity waves. However, the propagation of these waves into the stratosphere is found to be more efficient in dry spell of monsoon. The strengthening/weakening of the tropical easterly jet during wet/dry spell of monsoon is found to be the main reason for the inhibited/enhanced wave activity in the lower stratosphere during wet/dry spell. The present analysis also suggests that the static stability of the mid- and upper-troposphere during these two spells have implications in the observed frequency of the CGW. Thus, the present analyses brought out for the first time the features of CGW during two distinctive regimes of convective systems and emphasized the importance of prevailing background conditions in exciting/filtering them.     

The 21 May 2003 Tsunami in the Western Mediterranean Sea: Statistical and Wavelet Analyses

We report the statistical and wavelet analyses of the 21 May 2003 tsunami produced by an M _w 6.8–6.9 thrust earthquake in the western Mediterranean Sea using 19 tide gauge records. The largest trough-to-crest wave height was 196 cm recorded at the Sant Antoni station in the lee of the incoming tsunami wave. Except at one station, the first wave was not the largest wave at all the analyzed stations, and the largest wave arrived several hours after the first arrival. In addition, the tsunami waves persisted for more than 1 day at most stations. As the spectra of coastal tide gauge stations are strongly influenced by topographic features, special care was taken here while interpreting the results of spectral and wavelet analysis. Our wavelet analysis shows that only a peak at around 23 min is persistent for long duration, and other peaks at 14, 30, 45, and 60 min appeared at short durations. The 23-min signal is possibly associated with the width of the source fault whereas the fault length contributed to the 45-min signal. Based on these dominant periods, the tsunami source dimensions are estimated as 95 km × 45 km. The statistical and wavelet analyses performed here provide some new insights into the characteristics of the tsunami that was generated and propagated in the western Mediterranean basin.     

Studies in diffusion,IV. Pressure dependence of Ar diffusion in phlogopite mica

Radiogenic Ar diffusion from phlogopite mica has been measured at 900° and 1080°C at 15 kbars pressure, using a Griggs-type hot creep tester operated at hydrostatic pressure, and followed by standard mass spectrometric analysis. The diffusion coefficients fall within the uncertainty of the diffusion results reported by Giletti (1974) at 1 kbar at 900° and on extrapolation of that Arrhenius plot to 1080°C. That linear plot is given by D₀ = 0.75 and Q = 57.9kcal/g-atom Ar. In the observed temperature range, the effect of pressure up to 15 kbars is not significant. A second Ar diffusion, which employed Ca(OH)₂-CaO as a water buffer, was run at 1 atm H₂O pressure and 550°C for 781 days. The resulting diffusion coefficient agrees, within the uncertainty, with the extrapolation of the earlier curve. This result, and both earlier ones at 600°, are similar in that they fall below the curve. Consequently, despite the agreement within the uncertainty, it is possible that diffusion of Ar from phlogopite below 650°C is somewhat slower than given by the above equation parameters.     

First results of warm mesospheric temperature over Gadanki (13.5°N, 79.2°E) during the sudden stratospheric warming of 2009

Rayleigh lidar observations at Gadanki (13.5°N, 79.2°E) show an enhancement of the nightly mean temperature by 10–15 K at altitudes 70–80 km and of gravity wave potential energy at 60–70 km during the 2009 major stratospheric warming event. An enhanced quasi-16-day wave activity is observed at 50–70 km in the wavelet spectrum of TIMED–SABER temperatures, possibly due to the absence of a critical level in the low-latitude stratosphere because of less westward winds caused by this warming event. The observed low-latitude mesospheric warming could be due to wave breaking, as waves are damped at 80 km.     

位场向下延拓的波数域迭代法及其收敛性

提出了位场向下延拓的波数域迭代法. 对水平面上的位场观测值进行Fourier变换,得到其波谱. 根据第一类Fredholm积分方程的空间域迭代解法,推导出计算向下延拓水平面上位场波谱的波数域迭代公式. 在波数域中进行迭代,一直进行到相继两次迭代近似解的差值最大绝对值小于给定的精度,或迭代达到给定的最大迭代次数. 对这种迭代近似解进行Fourier逆变换,得到向下延拓的位场. 数值计算结果表明：与空间域迭代法比较,这种波数域迭代法简单、快速,并有同样好的向下延拓效果. 本文还证明了这种迭代法是收敛的,并给出了它的收敛特性和滤波特性.     

薄层时频特征的正演模拟

基于正演模拟的薄层时频特征响应分析是薄层定性识别与厚度定量预测的基础与关键.本文基于波场延拓理论,利用深度域相移法对不同厚度薄层进行了正演模拟.采用广义S变换对零偏移距地震道的反射复合波进行瞬时频谱分析,发现当薄层顶底反射系数极性相反时,复合波的干涉作用具有升频降幅作用,而极性相同时具有升幅降频作用;理论推导和实验分析均证明主峰值频率与薄层双程旅行时间厚度存在定量解析关系,这为薄层厚度定量预测提供了重要的技术手段;由于峰值频率对反射系数大小与极性变化不敏感,因此,峰值频率方法与时域振幅方法相比更具稳定性.     

Nocturnal temperature changes over tropics during CAWSES-III campaign: Comparison with numerical models and satellite data

In the frame of the third CAWSES tidal campaign in June–August 2007, lidar and satellite data were collected and compared with numerical models. Continuous nocturnal middle atmospheric temperature measurements performed with a Rayleigh lidar located at La Reunion Island (20.8°S–55.5°E) were obtained for three subsequent nights. The results clearly show the presence of tidal components with a downward phase propagation. Comparisons with SABER satellite data show good agreement on tidal amplitude; however, some differences on the structures are reported probably due to the zonal nature of the retrieval provided by the SABER data. The observed tidal components are compared with two different numerical models such as the 2D global scale wave model and the 3D-GCM LMDz-REPROBUS. Both models reveal good agreement with temperature lidar patterns, while simulated tidal amplitudes are smaller by a factor of around 2–2.5 K.     

Evaluation of the effective cross-section of scattering in the lithosphere

The theory of scattering affirms that, when a wave enters a scattering volume, secondary waves develop having propagation directions which form various angles with the ray of the primary wave. The energy of the scattered wave depends on the effective cross-section of scattering from a unit volume in a unit solid angle. The seismic phase P′·P′ is produced mainly by the scattering of P′₁ in the uppermost layer of the Earth. If the epicentral distances of the observation point of P′·P′ vary between 30 and 70°, the corresponding angles of scattering of P′ vary between 22° and a few degrees. This relationship enables us to evaluate the effective cross-section of scattering as a function of the angle of scattering. The latest world-average estimates of this quantity, which are based on a large number of seismic data, are presented. The values obtained are in good agreement with those calculated for the Gaussian auto-correlation function of the fluctuating part of the refractive index if the correlation interval is close to 13 km. The lower limit of the fractional r.m.s. of velocity variation in the lithosphere is close to 1.6%.     

基于时空域自适应高阶有限差分的声波叠前逆时偏移

叠前逆时偏移在理论上是现行偏移方法中最为精确的一种成像方法,其实现过程中的核心步骤之一是波动方程的波场延拓,而波场延拓的本质是求解波动方程,所以精确、快速地求解波动方程对逆时偏移至关重要.本文采用一种基于时空域频散关系的有限差分方法来求解声波方程,分析其频散和稳定性,实现波场数值模拟,并将分析和模拟结果与传统有限差分法进行对比.分析结果和模型数值模拟结果都表明时空域有限差分法模拟精度更高、稳定性更好.将时空域高阶有限差分法应用到叠前逆时偏移波场延拓的方程求解中,然后再利用归一化互相关成像条件成像,理论模型数据偏移处理获得了精度更高的成像.同时,在逆时偏移波场延拓的实现中,采用自适应变长度的空间差分算子求解空间导数的有限差分策略,在不影响数值模拟和成像精度的前提下,有效地提高了计算效率.     

APPLICATION OF ELASTIC MODELLING IN PROCESSING AND INTERPRETATION OF VSP DATA: A CASE HISTORY1

Data from offshore Norway is used to study applications of elastic VSP modelling in detecting shear waves and observing the effects of successive mode conversion in field-recorded VSP data. The shear-wave velocities and densities from log data are used in conjunction with compressional wave velocities determined from surface seismic and log data in the VSP modelling. The time domain non-normal incidence elastic VSP modelling technique of Aminzadeh and Mendel is used as the modelling algorithm. Two surface seismograms are computed first. One is the vertical component and the other is the horizontal component for plane waves that have specified incident angles. A downward continuation method is then applied to generate seismograms at different depth points. The collection of these seismograms constitutes non-normal incidence VSPs. Both vertical and horizontal components of VSP data can be obtained by this procedure. In this paper non-normal incidence VSPs are generated for a 12.5° incident plane wave. The modelling results of layered earth systems of thin layers and thick layers are both compared with field data, and the effect of mode conversions in thin layers is observed. Several events in the field data can be explained by this elastic VSP modelling. Comparison of the model data and field data enabled a probable tube wave or out-of-plane event to be identified, the removal of which significantly improved the final VSP section. This study also shows how the VSP data helped the interpretation of the surface 3D data.