裸眼井中弹性波传播的非对称模式的数值研究

本文从数值上研究了裸眼井中弹性波传播的非对称模式,给出了合成微地震图和导波（弯曲波）的频散曲线,发现在“硬”地层和“软”地层的井中,导波都是高度频散的,其最大相速度等于地层的横波速度,其截止频率低于对称模式的伪瑞利波的截止频率;在低频（2-3kHz）和长源距（3-4m）的条件下,由非对称的声源（如声偶极子）所产生的微地震图中,初至信号是以横波速度传播的,而以纵波速度传播的信号被抑制。本文的结果对研制横波速度测井仪是有意义的。     

Acoustic reflection logging for open and cased holes

In the present work, the waveforms of reflected wave sonic log for open and cased boreholes are calculated. Calculations are performed for a borehole containing an acoustic multipole source (monopole, dipole, or quadrupole). A reflected wave is more efficiently excited at resonant frequencies. These frequencies for all source types are close to the frequencies of oscillations of a fluid column located in an absolutely rigid hollow cylinder. It is shown that the acoustic reverberation is controlled by the acoustic impedance of the rock Z = V_p ρ_s for fixed parameters of the borehole fluid, where V_p is the compressional wave velocity in the rock, and ρ_s is the rock density. This result is correct for all types of acoustic sources (monopole, dipole, or quadrupole). Methods of the waveform processing for determining parameters characterizing the reflected wave are discussed.     

Energy of acoustic signals in a borehole

In the present article, the dependencies of the acoustic signal total energy and the energies of the wave packets of different types of the waves on the elastic parameters and permeability of rocks have been studied. We have considered traditional logging tools containing acoustical monopole source. Calculations were performed in a frequency range of dozens of kilohertz, typical for acoustic well logging. It was shown that in a typical high-velocity formation (v_s > v_f, where v_s and v_f are the velocities of the shear wave in the rock and of the compressional wave in the borehole fluid, respectively), the pseudo-Rayleigh waves, whose elastic properties depend mainly on the shear modulus of the rock, contributed significant energy to the total signal energy in the borehole. The energies of different wave packets depend on the permeability in different ways. The greatest sensitivity to permeability change has been shown by the acoustic signal total energy and the energy of the low-velocity part of the pseudo-Rayleigh wave packet. The theoretical analysis was illustrated by real sonic log data.     

长源距声波测井资料分析处理

本文对长源距声波测井记录的波列特征进行分析,综述时域及频域处理信号的方法.阐明首波检测法、波形相似相关法、直接相位法的特点.讨论“软”、“硬”地层的不同特点,研究相应纵波、横波、管波的特征及其提取方法.并对“软”地层中管波速度反演横渡速度的模型进行了讨论.     

低速地层裸眼井中弹性波的传播

本文在文献[4]的基础上分析了低速地层（地层横波速度低于井内流体速度）裸眼井中由点源激发的弹性波的传播。指出在这种情况下井内传播的波仅有共振纵波、斯通利波和衰减的反射波,共振横波和伪瑞利波将不再出现。由数值计算得出了相速度和群速度频散曲线,给出了势函数的振幅表达式和反射波随井轴的衰减规律。     

声波测井中首波与次首波的理论研究

本文讨论了裸眼井中由点状声源激发的首波与次首波问题,认为:首波与次首波分别是以地层纵波速度V_c和地层横波速度V_s传播的几何衰减波。同时给出了泄漏波的解析式,而泄漏纵波和泄漏横波的截止频率分别为远场处的首波与次首波的传播特征频率。     

SECONDARY SHEAR WAVES FROM SOURCE BOREHOLES1

Previous studies of radiation from point sources in fluid-filled boreholes have most often been based on far-field, stationary phase analysis. In these papers, the explicit contribution of the borehole itself acting as a waveguide has not been properly considered, with a few exceptions. In general, these studies accurately describe S-wave radiation in high-velocity rocks such as granites and limestones and P-wave radiation in most rocks, and experiments have confirmed this. However, tube waves directly influence the external wavefield and in fact create a shear-wave ‘wake’ outside the borehole due to constructive interference of tube-wave emission if a velocity condition is met. This constructive interference or wake is generated when the tube-wave velocity is greater than the shear-wave velocity. When this happens, a tube-wave complex pole invalidates the mathematical assumptions for stationary phase analysis and the stationary phase predictions do not agree with experimentally derived radiation patterns. Shales at shallow depths and other soft sediments characteristically have tube-wave velocities greater than shear-wave velocities. Because the tube-wave is of relatively high amplitude compared to body waves generated directly by the source, these secondary shear waves can be the highest amplitude arrivals on receiver arrays. The shape and properties of these secondary shear waves are calculated and shown to have identical properties to Mach waves of aerodynamics and seismology. For instance, these waves are geometrically conical and the aperture of the cone and the moveout velocity can be calculated. This paper also demonstrates the important effect that casing has on the Mach waves and provides predictions about when these waves are likely to be observed. Finally, evidence of Mach waves in data sets is examined and it is shown how these waves have been confused with receiver borehole tube waves. It is possible, though rare, that the tube-wave velocity of the borehole is greater than the compressional-wave velocity of the surrounding medium. In this case secondary compressional or compressional Mach waves would be generated although this problem is not addressed here.     

孔、裂隙并存地层中的声波测井理论及多极子声场特征

在油、气储层的勘探和开发中观察到的一个现象是储层岩石中普遍存在孔隙和裂隙.随着近年来孔、裂隙介质弹性波动理论的进展,我们可以将此理论应用于测井技术,以此来指导从声波测井中测量孔、裂隙地层的声学参数.本文计算了孔、裂隙地层里充流体井眼中的多极子声场,分析了声场随裂隙介质的两个主要参数(即裂隙密度和裂隙纵横比)的变化特征.井孔声场的数值计算表明裂隙密度可以大幅度地降低井中声波纵、横波的波速和振幅.随着裂隙密度的增加,在测井频段内也可以看到纵、横波速的频散现象(这种频散在孔隙地层中一般是观察不到的).本文还研究了多极子模式波 (即单极的Stoneley波、伪瑞利波以及偶极的弯曲波)随裂隙参数的变化特征.结果表明,这些模式波的振幅激发和速度频散都受裂隙密度的影响.裂隙密度越高影响越大.此外,裂隙还对模式波的传播造成较大的衰减.相对裂隙密度而言,裂隙纵横比是一个频率控制参数,它控制裂隙对声场影响的频率区间.本文的分析结果对裂缝、孔隙型地层的声波测井具有指导意义.     

Field velocity resistivity probe for estimating stiffness and void ratio

Elastic and electromagnetic waves are commonly used to investigate various soil characteristics. The goal of this study is to estimate the elastic moduli and the void ratio based on both the compressional and shear wave velocities, and the electrical resistivity measured by field velocity resistivity probe (FVRP). The compressional and shear waves are measured by piezoelectric disk elements and bender elements installed at the end of the FVRP frame tip. The electrical resistivity is determined by the electrical resistivity probe installed at the tip of the FVRP frame. The FVRP tests are carried out in a clay–sand mixture prepared in a calibration chamber and in silty sand to silty clay soils in the field. The elastic waves and electrical resistivity are measured at every 1 cm. The field tests are carried out at a depth of 6–20 m, at 10 cm intervals, at the Southern coastal area of the Korean peninsula. The measured data are converted into the constraint and shear moduli based on the elastic waves. Void ratios are evaluated based on the elastic wave velocities and the electrical resistivity, and these void ratios match the volumetric void ratio well. This study suggests that the FVRP may effectively determine the elastic moduli and void ratio.     

Dispersion and radial depth of investigation of borehole modes

Sonic techniques in geophysical prospecting involve elastic wave velocity measurements that are performed by placing acoustic transmitters and receivers in a fluid‐filled borehole. The signals recorded at the receivers are processed to obtain compressional‐ and shear‐wave velocities in the surrounding formation. These velocities are generally used in seismic surveys for the time‐to‐depth conversion and other formation parameters, such as porosity and lithology. Depending upon the type of transmitter used (e.g. monopole or dipole) and as a result of eccentering, it is possible to excite axisymmetric (n= 0) , flexural (n= 1) and quadrupole (n= 2) families of modes propagating along the borehole. We present a study of various propagating and leaky modes that includes their dispersion and attenuation characteristics caused by radiation into the surrounding formation. A knowledge of propagation characteristics of borehole modes helps in a proper selection of transmitter bandwidth for suppressing unwanted modes that create problems in the inversion for the compressional‐ and shear‐wave velocities from the dispersive arrivals. It also helps in the design of a transmitter for a preferential excitation of a given mode in order to reduce interference with drill‐collar or drilling noise for sonic measurements‐while‐drilling. Computational results for the axisymmetric family of modes in a fast formation with a shear‐wave velocity of 2032 m/s show the existence of Stoneley, pseudo‐Rayleigh and anharmonic cut‐off modes. In a slow formation with a shear‐wave velocity of 508 m/s, we find the existence of the Stoneley mode and the first leaky compressional mode which cuts in at approximately the same normalized frequency ωa/V_S= 2.5 (a is the borehole radius) as that of the fast formation. The corresponding modes among the flexural family include the lowest‐order flexural and anharmonic cut‐off modes. For both the fast and slow formations, the first anharmonic mode cuts in at a normalized frequency ωa/V_S= 1.5 approximately. Cut‐off frequencies of anharmonic modes are inversely proportional to the borehole radius in the absence of any tool. The borehole quadrupole mode can also be used for estimating formation shear slownesses. The radial depth of investigation with a quadrupole mode is marginally less than that of a flexural mode because of its higher frequency of excitation.     

Simulation of full-waveform log in saturated cracked formations using Hudson's approach

We study the propagation of elastic waves that are generated in a fluid‐filled borehole surrounded by a cracked transversely isotropic medium. In the model studied the anisotropy and borehole axes coincide. To obtain the effective elastic moduli of a cracked medium we have applied Hudson's theory that enables the determination of the overall properties as a function of the crack orientation in relation to the symmetry axis of the anisotropic medium. This theory takes into account the hydrodynamic mechanism of the elastic‐wave attenuation caused by fluid filtration from the cracks into a porous matrix. We have simulated the full waveforms generated by an impulse source of finite length placed on the borehole axis. The kinematic and dynamic parameters of the compressional, shear and Stoneley waves as functions of the matrix permeability, crack orientation and porosity were studied. The modelling results demonstrated the influence of the crack‐system parameters (orientation and porosity) on the velocities and amplitudes of all wave types. The horizontally orientated cracks result in maximal decrease of the elastic‐wave parameters (velocities and amplitudes). Based on the fact that the shear‐ and Stoneley‐wave velocities in a transversely isotropic medium are determined by different shear moduli, we demonstrate the feasibility of the acoustic log to identify formations with close to horizontal crack orientations.     

Joint elastic‐electrical properties of reservoir sandstones and their relationships with petrophysical parameters

We measured in the laboratory ultrasonic compressional and shear‐wave velocity and attenuation (0.7–1.0 MHz) and low‐frequency (2 Hz) electrical resistivity on 63 sandstone samples with a wide range of petrophysical properties to study the influence of reservoir porosity, permeability and clay content on the joint elastic‐electrical properties of reservoir sandstones. P‐ and S‐wave velocities were found to be linearly correlated with apparent electrical formation factor on a semi‐logarithmic scale for both clean and clay‐rich sandstones; P‐ and S‐wave attenuations showed a bell‐shaped correlation (partial for S‐waves) with apparent electrical formation factor. The joint elastic‐electrical properties provide a way to discriminate between sandstones with similar porosities but with different clay contents. The laboratory results can be used to estimate sandstone reservoir permeability from seismic velocity and apparent formation factor obtained from co‐located seismic and controlled source electromagnetic surveys.     

声波测井中的纵波和横波

充流体井中声传播理论是声波测井的理论基础。Blot（1952）绘出了充流体井中简正模式和斯通利波的频散曲线,White等（1968）首先计算了合成全波列波形,Peterson（1974）和余寿绵（1984）导出了简正模式和斯通利波的振幅表达式。余寿绵还预言纵波和横波是一种共振现象,为沿轴向传播存在特征频率的不衰减波。但是,现行理论认为纵     

Effects of petrophysical parameters on attenuation and dispersion of seismic waves in the simplified poroelastic theory: Comparison between the Biot's theory and viscosity‐extended theory

The simplified macro‐equations of porous elastic media are presented based on Hickey's theory upon ignoring effects of thermomechanical coupling and fluctuations of porosity and density induced by passing waves. The macro‐equations with definite physical parameters predict two types of compressional waves (P wave) and two types of shear waves (S wave). The first types of P and S waves, similar to the fast P wave and S wave in Biot's theory, propagate with fast velocity and have relatively weak dispersion and attenuation, while the second types of waves behave as diffusive modes due to their distinct dispersion and strong attenuation. The second S wave resulting from the bulk and shear viscous loss within pore fluid is slower than the second P wave but with strong attenuation at lower frequencies. Based on the simplified porous elastic equations, the effects of petrophysical parameters (permeability, porosity, coupling density and fluid viscosity) on the velocity dispersion and attenuation of P and S waves are studied in brine‐saturated sandstone compared with the results of Biot's theory. The results show that the dispersion and attenuation of P waves in simplified theory are stronger than those of Biot's theory and appear at slightly lower frequencies because of the existence of bulk and shear viscous loss within pore fluid. The properties of the first S wave are almost consistent with the S wave in Biot's theory, while the second S wave not included in Biot's theory even dies off around its source due to its extremely strong attenuation. The permeability and porosity have an obvious impact on the velocity dispersion and attenuation of both P and S waves. Higher permeabilities make the peaks of attenuation shift towards lower frequencies. Higher porosities correspond to higher dispersion and attenuation. Moreover, the inertial coupling between fluid and solid induces weak velocity dispersion and attenuation of both P and S waves at higher frequencies, whereas the fluid viscosity dominates the dispersion and attenuation in a macroscopic porous medium. Besides, the heavy oil sand is used to investigate the influence of high viscous fluid on the dispersion and attenuation of both P and S waves. The dispersion and attenuation in heavy oil sand are stronger than those in brine‐saturated sandstone due to the considerable shear viscosity of heavy oil. Seismic properties are strongly influenced by the fluid viscosity; thus, viscosity should be included in fluid properties to explain solid–fluid combination behaviour properly.     

垂向不均匀介质中波传播特点的研究

本文由波传播问题的变分原理导出了垂向不均匀介质中的弹性波波动方程及纵波和横波波动方程。在不同的假设条件下得到了纵、横波波动方程的几种简化形式,其中包括地震勘探中常用的变系数波动方程。利用有限单元法,求得了垂向不均匀介质中波动方程的数值解。通过数值结果对纵、横波之间的耦合程度以及介质的不均匀性对波的衰减作用进行了讨论。     

The frequency content and attenuation of seismic wavelets along the surface of different types of soil

Summary An experimental investigation was conducted over 6 widely different types of soil in order to gain some reliable information on the wave propagation properties relevant to seismic prospecting. The elastic constants of the surface layers were also found from the compressional and Rayleigh wave velocities. While the predominant frequencies of the compressional and Rayleigh waves both decrease with distance from the source, they are in most cases of the same order of magnitude. The amplitude of the particle velocity for the compressional wave was found to decrease inversely as the square of the distance, while that for the Rayleigh wave decreased more slowly; wide variations occur between different localities. The significance of these results to seismic prospecting instrumentation is discussed.     

解耦纵横波反射波走时反演

基于常规弹性波动方程的反射波走时反演结合走时和反射波信息可以有效的摄取模型参数中的低波数成分,然而纵横波之间的耦合效应以及纵横波速度对波场的敏感性差异,导致反演的非线性问题增强.为此本文研究了基于解耦波动方程的反射波走时反演,并提出改进的时移互相关目标函数,分别隐式计入射波场快照与反传波场快照的时移量,很大程度的降低了纵波、横波之间的耦合关系,并提高纵横波速度低波数信息的反演质量.最后模型测试证明了本文方法的正确性.     

Laboratory measurements of guided‐wave propagation within a fluid‐saturated fracture

A fluid‐saturated flat channel between solids, such as a fracture, is known to support guided waves—sometimes called Krauklis waves. At low frequencies, Krauklis waves can have very low velocity and large attenuation and are very dispersive. Because they propagate primarily within the fluid channel formed by a fracture, Krauklis waves can potentially be used for geological fracture characterization in the field. Using an analogue fracture consisting of a pair of flat slender plates with a mediating fluid layer—a trilayer model—we conducted laboratory measurements of the velocity and attenuation of Krauklis waves. Unlike previous experiments using ultrasonic waves, these experiments used frequencies well below 1 kHz, resulting in extremely low velocity and large attenuation of the waves. The mechanical compliance of the fracture was varied by modifying the stiffness of the fluid seal of the physical fracture model, and proppant (fracture‐filling high‐permeability sand) was also introduced into the fracture to examine its impact on wave propagation. A theoretical frequency equation for the trilayer model was derived using the poroelastic linear‐slip interface model, and its solutions were compared to the experimental results.     

有薄疏松复盖层的弹性半空间中地震波的传播问题

本文将地表疏松风化层看作是附在弹性介貭上的一种有慣性而无弹性的薄层,当扰动在弹性介貭中传播吋,风化薄层跟随振动;討論了弹性半空間內点震源产生的地震波和疏松薄层对地震波反射的影响。     

Elastic interferometry for ocean bottom cable data: Theory and examples‡

Elastic imaging from ocean bottom cable (OBC) data can be challenging because it requires the prior estimation of both compressional‐wave (P‐wave) and shear‐wave (S‐wave) velocity fields. Seismic interferometry is an attractive technique for processing OBC data because it performs model‐independent redatuming; retrieving ‘pseudo‐sources’ at positions of the receivers. The purpose of this study is to investigate multicomponent applications of interferometry for processing OBC data. This translates into using interferometry to retrieve pseudo‐source data on the sea‐bed not only for multiple suppression but for obtaining P‐, converted P to S‐wave (PS‐wave) and possibly pure mode S‐waves. We discuss scattering‐based, elastic interferometry with synthetic and field OBC datasets. Conventional and scattering‐based interferometry integrands computed from a synthetic are compared to show that the latter yields little anti‐causal response. A four‐component (4C) pseudo‐source response retrieves pure‐mode S‐reflections as well at P‐ and PS‐reflections. Pseudo‐source responses observed in OBC data are related to P‐wave conversions at the seabed rather than to true horizontal or vertical point forces. From a Gulf of Mexico OBC data set, diagonal components from a nine‐component pseudo‐source response demonstrate that the P‐wave to S‐wave velocity ratio (V_P/V_S) at the sea‐bed is an important factor in the conversion of P to S for obtaining the pure‐mode S‐wave reflections.