声电效应测井电声比及其与地层渗透率的关系

基于流体饱和孔隙介质中声波-电磁场耦合效应的测井方法具有潜在的应用价值.本文从Pride动电耦合波方程组入手,推导了伴随斯通利波的井孔电场与声压比值(电声比)的频率域表达式.结果表明,在较低频率条件下,电声比幅角的正切值与渗透率呈反比.在此基础上,提出了利用低频的声电效应测井全波反演地层渗透率的方法.针对砂岩地层,从计...     

声电效应测井的有限差分模拟

本文研究声电效应测井波场的有限差分模拟算法.忽略井外地层中诱导电磁场对孔隙弹性波的影响,将求解动电耦合波方程组的问题解耦,先计算孔隙弹性波,再计算其诱导电磁场.基于轴对称柱坐标系下的速度-应力交错网格,采用时域有限差分计算井孔流体声波和井外地层孔隙弹性波.将电磁场近似看作似稳场,基于轴对称柱坐标系下的5点式有限差分网格,求解不同时刻的电位Poisson方程,计算诱导电场.结果表明:本文算法可准确模拟频率6.0 kHz的声电效应测井全波;在声波测井频率范围内,电导率、动电耦合系数和动态渗透率的低频近似对伴随电磁场的计算影响不大;地层水平界面导致伴随反射斯通利波的电场和显著的界面电磁波,后者对于探测地层界面具有潜在的应用价值.     

Dependence of borehole shear‐horizontal‐wave seismoelectric response on soil textures

The phenomenon of acoustic waves inducing electric fields in porous media is called the seismoelectric effect. Earlier investigators proposed the usage of seismoelectric effect for well logging. Soil texture has a strong influence on the coupled wave fields during shallow surface explorations. In this article, we study the borehole pure shear‐horizontal wave and the coupling transverse‐electric field (acoustic–electrical coupling wave fields) in the partially saturated soil. Combined with related theories, we expand the formation parameters to partially saturated forms and discuss the influence of soil texture conditions on the seismoelectric wave fields. The results show that the elastic and electrical properties of porous media are sensitive to water saturation. The compositions of the acoustic and electric fields for different soil textures do not change, but the waveforms differ. We also use the secant integral method to simulate the interface‐converted electromagnetic waves. The results show that interface response strength is greatly influenced by soil texture. In addition, considering the sensitivity of the inducing electric field to fluid salinity, we also simulate the time‐domain waveforms of electric field for different pore fluid salinity levels. The results show that as the salinity increases, the electric field amplitude decreases monotonically. The above conclusions have certain significance for the application of borehole shear wave and its coupled electric fields for resource exploration, saturation assessment and groundwater pollution monitoring.     

裸眼井声波全波测井中纵波和斯通利波的数值研究

本文利用射线展开理论、割线积分技术及留数定理,研究了裸眼井声波全波测井中纵波和斯通利波的性质。下面简要说明数值计算方法。 计算方法 考虑在无限大均匀地层中,有一充满流体的深井。在井轴上放一点状声源,则在井轴上离声源距离为z处的声压为     

Seismoelectric measurements in a porous quartz‐sand sample with anisotropic permeability

Seismoelectric coupling coefficients are difficult to predict theoretically because they depend on a large numbers of rock properties, including porosity, permeability, tortuosity, etc. The dependence of the coupling coefficient on rock properties such as permeability requires experimental data. In this study, we carry out a set of laboratory measurements to determine the dependence of seismoelectric coupling coefficient on permeability. We use both an artificial porous “sandstone” sample, with cracks, built using quartz‐sand and Berea sandstone samples. The artificial sample is a cube with 39% porosity. Its permeability levels are anisotropic: 14.7 D, 13.8 D, and 8.3 D in the x‐, y‐, and z‐directions, respectively. Seismoelectric measurements are performed in a water tank in the frequency range of 20 kHz–90 kHz. A piezoelectric P‐wave source is used to generate an acoustic wave that propagates through the sample from the three different (x, y, and z) directions. The amplitudes of the seismoelectric signal induced by the acoustic waves vary with the direction. The highest signal is in the direction of the highest permeability, and the lowest signal is in the direction of the lowest permeability. Since the porosity of the sample is constant, the results directly show the dependence of seismoelectric coefficients on permeability. Seismoelectric measurements with natural rocks are performed using Berea sandstone 500 and 100 samples. Because the Berea samples are nearly isotropic in permeability, the amplitudes of the seismoelectric signals induced in the different directions are the same within the measurement error. Because the permeability of Berea 500 is higher than that of Berea 100, the amplitude of the seismoelectric signals induced in Berea 500 is higher than those in Berea 100. To determine the relative contributions of porosity and permeability on seismoelectric conversion, we carried out an analysis, using Pride (1994) formulation and Kozeny–Carman relationship; the normalized amplitudes of seismoelectric coupling coefficients in three directions are calculated and compared with the experimental results. The results show that the seismoelectric conversion is related to permeability in the frequency range of measurements. This is an encouraging result since it opens the possibility of determining the permeability of a formation from seismoelectric measurements.     

动电测井实验研究Ⅰ:渗透率的评价

本文针对流体饱和孔隙介质的动电效应,在砂岩模型井中开展了动电测井实验研究.记录到渗透率不同模型中单极源动电测井的全波波形,清晰地观测到了伴随纵波、横波和斯通利波的动电转换信号,给出了本文实验条件下,动电测井全波中各分波的幅度,并通过电声比的大小说明了各分波的动电转换能力.实验结果表明:孔隙介质动电效应与渗透率密切相关,动电信号的幅度随着地层渗透率的增大而增加,在高渗透率地层中记录动电信号的幅度较大,这一特性可用于地层渗透率的井下动电评估.本文实验结果还验证了动电测井的可行性,同时指出:与声波测井相比,动电测井信号对地层渗透率更加敏感,这为渗透率等地层参数的井下动电测量奠定了实验基础.     

Analytical expressions for the borehole seismic signatures excited by an explosive source buried in an elastic half‐space

Borehole guided waves that are excited by explosive sources outside of the borehole are important for interpreting borehole seismic surveys and for rock property inversion workflows. Borehole seismograms are typically modelled using numerical methods of wave propagation. In order to benchmark such numerical algorithms and partially to interpret the results of modelling, an analytical methodology is presented here to compute synthetic seismograms. The specific setup is a wavefield emanating from a monopole point source embedded within a homogeneous elastic medium that interacts with a fluid‐filled borehole and a free surface. The methodology assumes that the wavelength of the seismic signal is much larger than the borehole radius. In this paper, it is supposed that there is no poroelastic coupling between the formation and the borehole. The total wavefield solution consists of P, PP, and PS body waves; the surface Rayleigh wave; and the low‐frequency guided Stoneley wave (often referred as the tube wave) within the borehole. In its turn, the tube wave consists of the partial responses generated by the incident P‐wave and the reflected PP and PS body waves at the borehole mouth and by the Rayleigh wave, as well as the Stoneley wave eigenmode. The Mach tube wave, which is a conic tube wave, additionally appears in the Mach cone in a slow formation with the tube‐wave velocity greater than the shear one. The conditions of appearance of the Mach wave in a slow formation are formulated. It is shown that the amplitude of the Mach tube wave strongly depends on Poisson's ratio of the slow surrounding formation. The amplitude of the Mach tube wave exponentially decreases when the source depth grows for weakly compressible elastic media with Poisson's ratio close to 0.5 (i.e., saturated clays and saturated clay soils). Asymptotic expressions are also provided to compute the wavefield amplitudes for different combinations of source depth and source‐well offset. These expressions allow an approximate solution of the wavefield to be computed much faster (within several seconds) than directly computing the implicit integrals arising from the analytical formulation.     

含有倾斜薄裂缝孔隙地层中的井孔声场

应用三维交错网格应力-速度有限差分方法,数值模拟了含有倾斜裂缝孔隙介质地层中点声源所激发的井孔声场问题.为满足薄裂缝计算需求,开发了不均匀网格有限差分算法,提高了计算精度及计算速度.利用将孔隙介质方程参数取为流体极限的办法来处理裂缝中的流体,实现了流体-孔隙介质界面处的差分方程统一,使界面处的计算更加灵活方便.在验证了方法正确性的基础上,分别考察了单裂缝宽度、裂缝带宽度、裂缝倾斜角度以及孔隙介质渗透率等参数的变化对井轴上阵列波形的影响并进行了分析.结果表明,声波经过裂缝时可能产生反射横波及斯通利波,后者随裂缝宽度的减小而减小,而前者随裂缝宽度的改变,变化不大,在裂缝很小(20μm)时依然存在;裂缝带的宽度、密度越大,反射斯通利波越强;当裂缝(裂缝带)倾斜时,反射横波消失,但反射斯通利波受裂缝倾斜角度的影响较小;渗透率的改变对斯通利波的衰减影响较为明显.     

Two‐dimensional waveform inversion of multi‐component data in acoustic‐elastic coupled media

In order to account for the effects of elastic wave propagation in marine seismic data, we develop a waveform inversion algorithm for acoustic‐elastic media based on a frequency‐domain finite‐element modelling technique. In our algorithm we minimize residuals using the conjugate gradient method, which back‐propagates the errors using reverse time migration without directly computing the partial derivative wavefields. Unlike a purely acoustic or purely elastic inversion algorithm, the Green's function matrix for our acoustic‐elastic algorithm is asymmetric. We are nonetheless able to achieve computational efficiency using modern numerical methods. Numerical examples show that our coupled inversion algorithm produces better velocity models than a purely acoustic inversion algorithm in a wide variety of cases, including both single‐ and multi‐component data and low‐cut filtered data. We also show that our algorithm performs at least equally well on real field data gathered in the Korean continental shelf.     

矿化度界面对震电测井波场的影响

震电测井的现场试验中测得电磁首波幅值大于伴随电场幅值,这种情况在前人的理论模拟和模型井测量中从未出现.本文研究矿化度界面对震电测井波场的影响,基于Pride方程和边界连续条件模拟了震电测井波场,其中井外孔隙地层可以视为均匀的或者是径向分层的.计算结果表明:对于均匀孔隙地层,当井内流体矿化度大于井外地层孔隙流体矿化度时,电磁首波幅值可以比伴随斯通利波的电场幅值还大;井内流体矿化度与井外地层孔隙流体矿化度的比值越大,电磁首波相对伴随斯通利波的电场的幅值越大.对于径向分层地层,当井内流体矿化度大于内层地层的孔隙流体矿化度时,电磁首波幅值可以比伴随斯通利波的电场幅值还大;当外层地层矿化度小于内层地层矿化度时,电磁首波幅值可以比伴随斯通利波的电场幅值还大;增加内层地层厚度,电场全波幅值减小,电磁首波相对伴随电场的幅值减小.本文的模拟结果表明,震电测井中确实会出现电磁首波幅值比伴随电场幅值还大的情况,这对于解释震电测井的测量结果具有指导意义.     

Correlation‐based reflection waveform inversion by one‐way wave equations

Reflection full waveform inversion can update subsurface velocity structure of the deeper part, but tends to get stuck in the local minima associated with the waveform misfit function. These local minima cause cycle skipping if the initial background velocity model is far from the true model. Since conventional reflection full waveform inversion using two‐way wave equation in time domain is computationally expensive and consumes a large amount of memory, we implement a correlation‐based reflection waveform inversion using one‐way wave equations to retrieve the background velocity. In this method, one‐way wave equations are used for the seismic wave forward modelling, migration/de‐migration and the gradient computation of objective function in frequency domain. Compared with the method using two‐way wave equation, the proposed method benefits from the lower computational cost of one‐way wave equations without significant accuracy reduction in the cases without steep dips. It also largely reduces the memory requirement by an order of magnitude than implementation using two‐way wave equation both for two‐ and three‐dimensional situations. Through numerical analysis, we also find that one‐way wave equations can better construct the low wavenumber reflection wavepath without producing high‐amplitude short‐wavelength components near the image points in the reflection full waveform inversion gradient. Synthetic test and real data application show that the proposed method efficiently updates the background velocity model.     

频率域有限差分数值模拟地震波衰减和震电效应特征

地震波在地下含流体孔隙介质中传播时,会引起中观尺度的"局域流",进而产生地震波震电效应.基于Biot(1941)固结理论的准静态方程,在频率域中采用空间有限差分方法,正演模拟虚岩石物理岩样的地震波衰减和震电效应.与时间域虚岩石物理方法相比,该方法既可以直接求取任一频率下的地震波衰减和电势,便于应用于实际岩样的预测分析,也避免了讨论岩样外表面施加的力源函数表达式及时间剖分稳定性条件等问题.首先利用周期性层状介质模型验证了本文所描述方法的有效性,并进一步求取分析了周期性层状介质两种不同特征单元的渗流电流密度及电势,数值模拟结果表明由中观尺度"局域流"引起的震电效应电势振幅数量级在实验室测量范围之内,随后,分析研究了四种不同高渗介质占比值的地震衰减及震电效应特征.最后,将本文提出的震电效应数值计算方法推广至二维,并求取了二维斑块饱和模型的地震波衰减、速度频散、电势的振幅和相位角数值结果.     

Anisotropic permeability in fractured reservoirs from frequency‐dependent seismic Amplitude Versus Angle and Azimuth data

Attempts have previously been made to predict anisotropic permeability in fractured reservoirs from seismic Amplitude Versus Angle and Azimuth data on the basis of a consistent permeability‐stiffness model and the anisotropic Gassmann relations of Brown and Korringa. However, these attempts were not very successful, mainly because the effective stiffness tensor of a fractured porous medium under saturated (drained) conditions is much less sensitive to the aperture of the fractures than the corresponding permeability tensor. We here show that one can obtain information about the fracture aperture as well as the fracture density and orientation (which determines the effective permeability) from frequency‐dependent seismic Amplitude Versus Angle and Azimuth data. Our workflow is based on a unified stiffness‐permeability model, which takes into account seismic attenuation by wave‐induced fluid flow. Synthetic seismic Amplitude Versus Angle and Azimuth data are generated by using a combination of a dynamic effective medium theory with Rüger's approximations for PP reflection coefficients in Horizontally Transversely Isotropic media. A Monte Carlo method is used to perform a Bayesian inversion of these synthetic seismic Amplitude Versus Angle and Azimuth data with respect to the parameters of the fractures. An effective permeability model is then used to construct the corresponding probability density functions for the different components of the effective permeability constants. The results suggest that an improved characterization of fractured reservoirs can indeed be obtained from frequency‐dependent seismic Amplitude Versus Angle and Azimuth data, provided that a dynamic effective medium model is used in the inversion process and a priori information about the fracture length is available.     

Modelling and straight‐ray tomographic imaging studies of cross‐hole radio‐frequency electromagnetic data for mineral exploration

Radio‐frequency electromagnetic tomography (or radio imaging method) employs radio‐frequency (typically 0.1–10 MHz) electromagnetic wave propagation to delineate the distribution of electric properties between two boreholes. Currently, the straight‐ray imaging method is the primary imaging method for the radio imaging method data acquired for mineral exploration. We carried out synthetic studies using three‐dimensional finite‐element modelling implemented in COMSOL Multiphysics to study the electromagnetic field characteristics and to assess the capability of the straight‐ray imaging method using amplitude and phase data separately. We studied four sets of experiments with models of interest in the mining setting. In the first two experiments, we studied models with perfect conductors in homogeneous backgrounds, which show that the characteristics of the electromagnetic fields depend mainly on the wavelength. When the borehole separations are less than one wavelength, induction effects occur; conductors with simple geometries can be recovered acceptably with amplitude data but are incorrectly imaged on the phase tomogram. When the borehole separations are longer than two wavelengths, radiation effects play a major role. In this case, phase tomography provides images with acceptable quality, whereas amplitude tomography does not provide satisfactory results. The third experiment shows that imaging with both original and reciprocal datasets is somewhat helpful in improving the imaging quality by reducing the impact of noise. In the last experiment, we studied models with conductive zones extended into the borehole plane with different lengths, which were not accurately recovered with amplitude tomography. The experiment implies that it is difficult to determine the extent of a mineralised zone that has been intersected by one of the boreholes. Due to the large variation of the wavelength in the radio‐frequency range, we suggest investigating the local electric properties to select an operating frequency prior to a survey. We conclude that straight‐ray tomography with either amplitude or phase data cannot provide high‐quality imaging results. We suggest using more general methods based on full electromagnetic modelling to interpret the data. In circumstances when computational time is critical, we suggest saving time by using either induction methods for borehole separations less than one wavelength or wave‐based methods (only radiation fields are considered) for borehole separation larger than two wavelengths.     

随钻斯通利波测井反演地层渗透率的理论、方法及应用

针对孔隙渗透地层的随钻声波测井问题,用Biot-Rosenbaum孔隙弹性波测井理论推导了孔隙地层的随钻井孔声场表达式.据此考察了随钻条件下井中斯通利波的波形、相速度频散、衰减以及相速度对渗透率的灵敏度,并与电缆测井中的情况进行了对比.数值模拟结果表明,随钻条件下斯通利波对地层渗透率的灵敏度相对于电缆测井有明显增加,更有利于用来反演地层渗透率.为快捷有效地处理现场测井数据和反演计算,采用简化Biot-Rosenbaum理论和钻铤的等效模型,对随钻斯通利波的频移和时滞进行联合反演.结果表明,随钻斯通利波反演的渗透率与核磁渗透率和岩心覆压测试渗透率符合较好,并且与常规测井曲线所反映的储层性质具有较好的一致性,证明了利用随钻斯通利波评价地层渗透率的有效性.     

The influence of errors in the source wavelet on inversion‐based surface‐related multiple attenuation

We investigate the influence of source wavelet errors on inversion‐based, surface‐related multiple attenuation, in order to address how the inverted primary impulse response, estimated primaries, and predicted multiples are affected by the estimated wavelet. In theory, errors in estimated wavelet can lead to errors in the upgoing waves. Because of smoothness and the band‐limitedness characteristics of the estimated wavelet, errors in the upgoing waves are usually not white and random. Theoretical analysis and two synthetic examples demonstrate that (i) when the overall amplitude scalar of the estimated wavelet is underestimated, the inversion of the primary impulse response suffers from instability, which will distort the estimation of primaries, and (ii) when the wavelet is overestimated, the estimated primaries will simply mimic the recorded upgoing waves. Nevertheless, the quality of the estimated primaries in the region above the first‐order, water‐bottom multiples is independent of the estimated wavelet. Synthetic results illustrate that inversion‐based, surface‐related multiple attenuation with a known wavelet is stable, since slight inaccuracy in amplitude spectrum and/or phase spectrum of the given wavelet or the corresponding upgoing waves will not lead to considerable deviation in the waveforms of the inverted results from those of the references. Furthermore, shot‐to‐shot wavelet variations, with maximum amplitude difference of 5% and maximum phase difference of 10°, create just slight artefacts in both the inverted primary impulse response and the estimated primaries. Moreover, the sensitivity test of estimation of primaries by sparse inversion method involving wavelet estimation shows that this method can stably and alternately update the wavelet and the primary impulse response; however, different choices of the initial wavelet can lead to different final inverted results.     

Seismoelectric numerical simulation in 2D vertical transverse isotropic poroelastic medium

Seismoelectric coupling in an electric isotropic and elastic anisotropic medium is developed using a primary–secondary formulation. The anisotropy is of vertical transverse isotropic type and concerns only the poroelastic parameters. Based on our finite difference time domain algorithm, we solve the seismoelectric response to an explosive source. The seismic wavefields are computed as the primary field. The electric field is then obtained as a secondary field by solving the Poisson equation for the electric potential. To test our numerical algorithm, we compared our seismoelectric numerical results with analytical results obtained from Pride's equation. The comparison shows that the numerical solution gives a good approximation to the analytical solution. We then simulate the seismoelectric wavefields in different models. Simulated results show that four types of seismic waves are generated in anisotropic poroelastic medium. These are the fast and slow longitudinal waves and two separable transverse waves. All of these seismic waves generate coseismic electric fields in a homogenous anisotropic poroelastic medium. The tortuosity has an effect on the propagation of the slow longitudinal wave. The snapshot of the slow longitudinal wave has an oval shape when the tortuosity is anisotropic, whereas it has a circular shape when the tortuosity is isotropic. In terms of the Thomsen parameters, the radiation anisotropy of the fast longitudinal wave is more sensitive to the value of ε, while the radiation anisotropy of the transverse wave is more sensitive to the value of δ.     

An adaptive free‐surface expression for three‐dimensional finite‐difference frequency‐domain modelling of elastic wave

Finite‐difference frequency‐domain modelling of seismic wave propagation is attractive for its efficient solution of multisource problems, and this is crucial for full‐waveform inversion and seismic imaging, especially in the three‐dimensional seismic problem. However, implementing the free surface in the finite‐difference method is nontrivial. Based on an average medium method and the limit theorem, we present an adaptive free‐surface expression to describe the behaviour of wavefields at the free surface, and no extra work for the free‐surface boundary condition is needed. Essentially, the proposed free‐surface expression is a modification of density and constitutive relation at the free surface. In comparison with a direct difference approximate method of the free‐surface boundary condition, this adaptive free‐surface expression can produce more accurate and stable results for a broad range of Poisson's ratio. In addition, this expression has a good performance in handling the lateral variation of Poisson's ratio adaptively and without instability.     

随钻声波测井FDTD模拟及钻铤波传播特性研究

幅度大的钻铤波掩盖地层信号是困扰随钻声波测井技术的难题,认识钻铤波特性对于消除或有效降低钻铤波至关重要.记录岩石动电效应引起电磁场的随钻动电测井,被认为有望彻底解决钻铤波干扰问题.本文采用有限差分法,模拟不同钻铤、不同井孔结构的随钻声场,对比分析了单极源钻铤波的传播特性,阐明存在伴随钻铤波动电信号的原因.结果表明:钻铤声波在沿钻铤传播时向外部介质辐射能量,透过井壁进入地层的具有视钻铤波速度的声波,与地层纵横波一样可发生动电转化,因而可导致随钻动电测井时产生钻铤波速度的电磁信号.计算还表明,高频情况下,随钻声波测井钻铤波呈现两阶模式:具有低频截止频率的高阶钻铤波幅度较小,其速度略低于钻铤纵波速度;无截止频率的低阶钻铤波幅度较大,其波速在高频时甚至低于钻铤横波速度.这种频散特性和多阶模式特性,是径向多分层开波导结构的导波属性.     

2D acoustic‐elastic coupled waveform inversion in the Laplace domain

Although waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the time‐ and frequency‐domain waveform inversion algorithms still have critical limitations in their applications to field data. This may be attributed to the highly non‐linear objective function and the unreliable low‐frequency components. To overcome the weaknesses of conventional waveform inversion algorithms, the acoustic Laplace‐domain waveform inversion has been proposed. The Laplace‐domain waveform inversion has been known to provide a long‐wavelength velocity model even for field data, which may be because it employs the zero‐frequency component of the damped wavefield and a well‐behaved logarithmic objective function. However, its applications have been confined to 2D acoustic media. We extend the Laplace‐domain waveform inversion algorithm to a 2D acoustic‐elastic coupled medium, which is encountered in marine exploration environments. In 2D acoustic‐elastic coupled media, the Laplace‐domain pressures behave differently from those of 2D acoustic media, although the overall features are similar to each other. The main differences are that the pressure wavefields for acoustic‐elastic coupled media show negative values even for simple geological structures unlike in acoustic media, when the Laplace damping constant is small and the water depth is shallow. The negative values may result from more complicated wave propagation in elastic media and at fluid‐solid interfaces. Our Laplace‐domain waveform inversion algorithm is also based on the finite‐element method and logarithmic wavefields. To compute gradient direction, we apply the back‐propagation technique. Under the assumption that density is fixed, P‐ and S‐wave velocity models are inverted from the pressure data. We applied our inversion algorithm to the SEG/EAGE salt model and the numerical results showed that the Laplace‐domain waveform inversion successfully recovers the long‐wavelength structures of the P‐ and S‐wave velocity models from the noise‐free data. The models inverted by the Laplace‐domain waveform inversion were able to be successfully used as initial models in the subsequent frequency‐domain waveform inversion, which is performed to describe the short‐wavelength structures of the true models.