Stoneley wave generation by an external seismic point source in an infinite fluid-filled borehole embedded in a transversely isotropic formation: Basic relationships

The method of integral transformations is used to obtain a long-wave solution to the problem of tube wave excitation by an external point source in an infinite fluid-filled borehole embedded in a transversely isotropic formation. The external field that occurs in the formation gives rise to waves in the borehole fluid. The waves generated in the borehole include the lowest mode of the Stoneley wave (tube wave), which is the borehole eigenmode, and the qP-and qSV-waves. It is shown that the Stoneley wave is determined by the contributions of two poles in the complex plane of horizontal slowness. According to the asymptotic solution, the Stoneley wave can be described by one of three different waveforms depending on the relationship between the elastic parameters of the surrounding anisotropic formation and the borehole fluid. An analysis of the results of calculations shows that the shape and polarity of the Stoneley wave strongly depend on the sign of the nonellipticity parameter of the elastic medium, which offers a possibility of estimating the anisotropy of the borehole environment from observations of the waveform of the Stoneley wave.     

Excitation of a tube wave in a borehole by an external isotropic point source

The excitation of a tube wave in an infinite fluid-filled borehole by an external isotropic point source is considered. The solution to the problem is obtained in the form of a double integral with respect to the ray parameter (slowness) and frequency. The integral with respect to the slowness is transformed to a contour integral in the complex slowness plane and then reduced to the integral over the edges of the cut of the vertical slowness function and the semiresidues at the poles. An asymptotic expression for the wave field in the borehole is obtained with allowance for the radiation condition at infinity. It is shown that, when a longitudinal spherical wave is incident on the borehole, only one low-frequency Stoneley wave is excited and not two, as was assumed earlier [1].     

Borehole guided waves in a non-Newtonian (Maxwell) fluid-saturated porous medium

<正>The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian (Maxwell) fluid-saturated porous formation with a permeable wall is investigated.The influence of non-Newtonian effects on acoustic guided waves such as Stoneley waves,pseudo-Rayleigh waves,flexural waves,and screw waves propagations in a fluid-filled borehole is demonstrated based on the generalized Biot-Tsiklauri model by calculating their velocity dispersion and attenuation coefficients.The corresponding acoustic waveforms illustrate their properties in time domain.The results are also compared with those based on generalized Biot's theory.The results show that the influence of non-Newtonian effect on acoustic guided wave,especially on the attenuation coefficient of guided wave propagation in borehole is noticeable.     

利用井中偶极弯曲波反演渗透率的影响因素及灵敏度分析

本文以各向同性饱和流体孔隙介质充液井孔中声场传播理论为基础,系统考察了影响偶极弯曲波特征的主要因素,分析了快慢地层条件下弯曲波衰减和速度对不同参数的敏感度,对比结果表明,弯曲波的速度基本不受地层渗透率的影响,其衰减对渗透率的敏感性要远高于速度。弯曲波中心频率会随着波的衰减而发生偏移,说明利用弯曲波衰减和频移特征联合反演地层渗透率是可行的。通过对比快慢地层下的弯曲波衰减和速度灵敏度曲线,发现在慢速地层中反演渗透率的结果要好于快速地层。同时,本文也指出在低孔低渗储层中,还可以考虑利用弯曲波衰减识别气层。     

Determination of crack orientation in the vicinity of a borehole by vertical seismoacoustic profiling

Excitation of a Stoneley wave in a single fluid-filled crack of small wave size in a borehole under an external seismic wave incident on it at an arbitrary angle is considered. On the basis of the solution obtained, the feasibility of solving the inverse problem of reconstructing the crack orientation from the data of vertical seismoacoustic profiling by hydrophones with the use of minimal input data is demonstrated.     

Attenuation of a Stoneley wave and higher Lamb modes due to the scattering by two-dimensional irregularities of the walls of a fluid-filled borehole

Attenuation of Stoneley waves and higher Lamb modes propagating along an irregular surface of a fluid-filled borehole is investigated. This problem generalizes the problem on the attenuation of Rayleigh waves by an irregular surface of an empty borehole [10]. The technique used to evaluate the attenuation coefficient is based on the perturbation method (surface irregularity heights are considered to be small in comparison with the wavelength) and the mean field method. As a result, an expression is obtained for the partial coefficients of the eigenmode attenuation due to the scattering of eigenmodes by the irregularities of the borehole walls into the same or other eigenmodes, as well as into the bulk longitudinal and transverse waves. The frequency-dependent behavior of the partial attenuation coefficients of both Stoneley waves and higher modes is analyzed against the ratio between the irregularity correlation length and the borehole radius for different correlation functions of irregularities.     

Theoretical simulation of electroacoustic borehole logging in a fluid-saturated porous formation

Electroacoustic (E-A) logging describes the acoustic response to an electromagnetic (EM) source in a fluid-filled borehole surrounded by a porous medium. The E-A response is simulated by two different methods in this paper. In the coupled method, the EM field and the acoustic field are modeled using Pride's model, which couples Maxwell's equations and Biot's equations. In the uncoupled method, the EM field is uninfluenced by the converted acoustic field, resulting in separate acoustic formulation with an electrokinetic source term derived from the primary EM field. The difference of the transient full waveforms between the above two methods is remarkably small for all examples, thus confirming the validity of using the computationally simpler uncoupled method. It is shown from the simulated waveforms that an EM-accompanying acoustic field is coupled to the EM field and appears with an apparent phase velocity of the EM wave in the formation. Acoustic waves with the conventional acoustic velocities are also seen in the converted full waveforms. For the sandstone models used in this paper, when permeability is less than 1 Darcy, the E-A Stoneley wave amplitude increases with porosity, which is different from that in conventional acoustic-to-acoustic logging.     

Properties of surface waves in an elastic cylinder filled with a liquid

The properties of harmonic surface waves in an elastic cylinder filled with a liquid are studied. The case of elastic material for which the shear wave velocity is higher than the sound velocity in a liquid is considered. The wave motion is described based on the complete system of equations of the dynamic theory of elasticity and the equation of motion of an ideal compressible liquid. The asymptotic analysis of the dispersion equation in the region of large wave numbers and qualitative analysis of the dispersion spectrum showed that in such a waveguiding system there exist two surface waves, the Stoneley and the Rayleigh waves. The lowest normal wave forms the Stoneley wave on the internal surface of the cylinder. In this waveguide phase, velocities of all normal waves, except for the lowest one, have the velocity of sound in the liquid as their limit. Therefore, the Rayleigh wave on the external surface of the cylinder is formed by all normal waves in the range of frequencies and wave numbers in which phase velocities of normal waves of the composite waveguide and the lowest normal wave of the elastic hollow cylinder coincide.     

A numerical investigation of the acoustic mode waves in a deviated borehole penetrating a transversely isotropic formation

A 2.5-dimensional method in frequency wave-number domain is developed to investigate the mode waves in a deviated borehole penetrating a transversely isotropic formation. The phase velocity dispersion characteristics of the fast and slow flexural mode waves excited by a dipole source are computed accurately at various deviation angles for both hard and soft formations. The sensitivities of the flexural mode waves to all elastic constants in a transversely isotropic formation are calculated. Numerical results show that, for a soft formation, the fast flexural mode wave is dominated by c66 at high deviation angles and low frequencies, while the slow flexural mode wave is dominated by c44 at the same conditions. Waveforms in time domain are also presented to support the conclusions.     

横向各向同性地层快速各向异性反演方法

斯通利波的频散特性常用于反演横向各向同性地层的各向异性。该文重点对斯通利波频散曲线随井孔和地层弹性模量相关参数的变化规律进行了探讨,提出了频散曲线的快速插值计算方法,经过误差分析验证了插值频散计算的可行性。据此提出了通过对参数大间隔取值建立理论频散数值表,插值计算不同各向异性参数的频散曲线,对比波形频散快速反演横向各向同性地层各向异性的方法。基于实轴积分法计算的横向各向同性地层井孔声场分别进行了插值频散快速反演和传统方法反演,对比结果证实了该文提出的快速反演方法的准确高效性,并且对数据加噪后验证了快速反演方法的抗噪性。     

Electroseismic waves excited by vertical magnetic dipole in borenole

Acoustic and electromagnetic fields are coupled in a fluid saturated porous medium due to seismoelectric effect. Seismoelectric well logging method has been proposed to detect deep target formation utilizing such effect. Because of uncoupling of SH waves with P-SV waves, a simple and forthright way to get shear waves information is possible, especially for soft or slow formation whose shear wave velocity is lower than the velocity of borehole fluid. We consider the wave fields excited by a vertical magnetic dipole (VMD) source. Two methods are used to simulate, one is the coupled method based on Pride model and the other is the uncoupled method. For two methods, the frequency wavenumber domain representations of the acoustic field and associated seismoelectric field are formulated. The full waveforms of acoustic waves and electromagnetic wave induced SH waves excited by VMD source in the time domain propagation in borehole are simulated and analyzed.     

外表面应力自由的充液有限壁厚井孔中的声场及其频散曲线的“平台”特征

为了开发一种新型标准刻度井,对外表面应力自由的充液有限壁厚井孔中的声场进行了更加深入的研究,计算分析了这种圆柱形封闭声波导结构中的声场和多阶对称模式波的频散特性。结果表明:充液有限壁厚井孔中高阶对称模式波的相速度频散曲线在一定频率范围内出现“平台”现象;当声源激发主频大于5 kHz且慢度时间相关法(STC)的窗长取4到5个周期时,得到全波波形中的“首波”速度与高阶模式波相速度频散曲线上的“平台”区域速度接近,该“平台”区域的速度与有限壁厚管材的纵波速度相差百分比随管材泊松比增加呈指数型上升;通过选择合适的管材材料以及改变其几何尺寸,可在一定频率范围内控制对称模式波相速度频散曲线的“平台”宽度、位置及平稳度。这一研究可为建立行业标准的声速刻度井提供新思路。      

孔隙地层井壁上的声波首波及其诱导电磁场的原因

声波测井时孔隙地层中的声波首波平行于井轴沿井壁传播，它既有轴向位移分量，又有垂直于井壁的位移分量.这种以快纵波速度传播的波, 不仅含有由快、慢纵波势给出的梯度场,而且还含有由横波势给出的旋度场.慢纵波势的梯度是渗流位移首波的主要构成成分, 也是声电效应测井响应中存在伴随声波首波电场的主要原因.首波包含有旋度位移场，是存在伴随声波首波磁场的原因. 关键词： 孔隙介质 声波首波 诱导电磁场 测井     

Analysis of noncircular fluid-filled boreholes in elastic formations using a perturbation model

This paper presents a perturbation model to obtain flexural mode dispersions of noncircular fluid-filled boreholes in homogeneous elastic formations. The perturbation model is based on Hamilton's principle with a modified procedure for the reference state selection in order to handle the directional sensitivity of the flexural modes. The accuracy of the perturbation model has been confirmed by comparison to boundary integral solutions. Numerical results confirm that for a fast formation, even modes, and for a slow formation, odd modes are more sensitive to changes in the borehole elongation and azimuth. Even though the focus of this work is on elliptical boreholes and breakouts, the formulation is valid for any kind of noncircular borehole.     

圆弧片状声源向地层中辐射声场的有限差分模拟

提出了一种可用于随钻声波测井的非对称的圆弧片状声源,旨在发展一种能够在钻井过程中精确确定反射体位置的三维反射声波远探测方法。研究了在复杂的井孔条件(钻铤偏心、各向异性和不规则井孔形状)下,该声源向地层中辐射的声场的特征,进一步分析了不同井况条件对三维随钻远探测声波测井的影响。数值模拟结果表明,在圆形井孔、钻铤居中条件下,无论快速地层还是慢速地层,圆弧片状声源均能够向地层中定向辐射声波信号,其辐射指向性图主瓣3 dB角宽窄,旁瓣级低,方位分辨率较高,适用于随钻三维反射成像测井;井壁粗糙程度、地层各向异性等因素对声场特征影响不大,说明该方法适用于粗糙井壁和各向异性地层情况;钻铤偏心和井壁一侧的破坏对辐射声场的影响较大。对本文的模型而言,在破坏深度小于3 cm或者偏心距离小于2 cm时,声场仍有较好的方位特征,该方法仍然适用。而当破坏深度大于6 cm,声场指向性图出现多个幅值较大的角瓣,可能无法利用其确定反射体的方位。本文的研究结果为三维随钻反射声波仪的设计和研发提供了必备的理论基础。      

Estimation of hydro-fracture parameters by analysis of tube waves at vertical seismic profiling

The problem on tube wave excitation in a well intersected by a finite-size fluid-filled crack under action of external seismic wave is considered. This situation appears at vertical seismic profiling (VSP) in the presence of hydro-fracture intersecting the borehole. A heterogeneous integral-differential equation for the fluid pressure field in fracture is derived in the long-wave approximation by the fracture opening. Stitching of the solution for pressure in fracture with that for tube waves in a well allows to calculate the amplitude and shape of generated tube waves. Numerical computations that under action of the external seismic field the crack edges excite a strongly dispersive mode of a thin fluid layer which can be used for estimation of linear fracture size on the basis of VSP technique.     

O HeкotopБix cboИctbax плaжmehhoгo boлhoboДa

Electromagnetic wave propagation in a circular waveguide with an axially-placed discharge tube is discussed. Fundamental properties of slow and fast waves are derived from the dispersion formula and a simple oscilloscopic method for the identification of these two waves is demonstrated. The electron density is obtained from the measured phase velocity by numerical calculation of dispersion equation (for real plasma permittivity). Collision frequency is then found from the attenuation factor.     

孔隙地层震电测井波场分波分析

由于孔道的双电层结构和流体-固体耦合运动, 弹性波在孔隙地层中传播时会引起电磁场. 前人提出了基于这种耦合效应的震电测井方法, 但对井中震电波的特性缺少细致的分析. 本文对孔隙地层充流体井孔中点声源激发的震电耦合波的分波进行分析, 证明了井孔流体电磁波波数不是井内震电波场支点, 计算了地层电磁波支点、横波支点和快纵波支点对应的侧面波. 在利用辐角原理求出震电波场函数的复极点之后, 针对典型砂岩地层计算了震电波场模式波(包括泄漏模式)的频散曲线和声压、电场激发曲线. 计算了各个侧面波和模式波的电场激发强度与声压激发强度的比值(电声激发比), 发现纵波的电声激发比相对于横波和模式波更高, 而Stoneley波电声激发比的辐角对渗透率敏感, 其敏感性会随频率增大而增加, 随孔隙度增大而降低.     

倾斜地层下的井孔声场分析及声速校正图版制作

理解声波在倾斜井孔下的传播规律,对于准确获得目的层真速度有着至关重要的作用。通过有限差分和几何声学分析方法对比了倾斜地层下纵横波首波速度的变化规律,旨在建立倾斜地层下的声速校正图版。研究结果表明,当倾斜地层速度"上低下高"时,从全波中得到的声波速度不再是地层的真实速度,均大于目的层真速度。尤其是当地层界面倾角大于45°时,即便是源距超过了4 m,仍对首波速度有影响,必须对其校正。相反,当倾斜地层速度"上高下低"时,任何源距和地层倾角下的视速度值都接近目的层真速度,可以不予校正。根据以上分析,建立了倾斜地层下的声速校正图版,并指出下层速度的变化对于校正图版有着较大影响,源距的变化对于图版影响很小,在不同源距下可以使用同一个图版。      

Features of radiation of the surface Stoneley wave by a harmonic force acting at the gas-solid interface

The solution is found for the problem of radiation of the surface Stoneley wave by a point harmonic force acting normally to the interface between uniform solid and gaseous half-spaces. We consider the case where the sound velocity in the gas is less than the Rayleigh-wave velocity on the surface of the solid. Expressions for the partial powers of the Stoneley wave radiated into the solid and the gas are obtained. The dependences of these powers on the parameters of the contacting media are analyzed. It is shown that if the velocities of the compressional and shear waves in the solid are significantly greater than the sound velocity in the gas, then almost all power of the Stoneley wave is concentrated in the gas. If the velocity of the Rayleigh wave in the solid half-space is close to the sound velocity in the gas, then the Stoneley-wave power radiated into the solid can be greater than the power radiated in the gas. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 4, pp. 304–313, April 2008.