Nature of the scattered seismic response from zones of random clusters of cavities and fractures in a massive rock

The scattering of elastic energy by random clusters of fractures and/or cavities in a massive rock is studied. The interpretation of the scattered seismic response reveals crucial information about the clusters of inhomogeneities (fractures/cavities), which may correspond to reservoirs. The study is based on a new two‐dimensional numerical‐modelling method that relaxes the constraints on the location and orientation of the inhomogeneities, accounts for inhomogeneities that have almost no volume but a finite surface area (fractures) and improves the accuracy of the calculation when the size of the inhomogeneities is comparable to the mesh size. It is shown that the nature of the seismic response of zones of diffuse fracturing and/or cavities is associated with the non‐uniformity of micro‐inhomogeneities in such zones; accumulations of these micro‐inhomogeneities are known as clusters. The relationship between the non‐uniformity of micro‐inhomogeneities and the strength of the seismic response has been established and measured. Considerable differences in the structure of the seismic response of zones of diffuse fracturing and diffuse cavities have been identified. Converted PS‐waves dominate in the scattered wavefield associated with fractures. This is explained, as the modelling results show, by a greater transparency of fluid‐filled fractures, which reduces the reflected energy of compressional waves. The wavefield associated with cavities is characterized by the predominance (in terms of strength) of compressional PP‐waves. The strength of converted PS‐waves in the scattered wavefields for both media is approximately the same. On the whole, according to the results of the modelling, the energy of the scattered response of fractured reservoirs is considerably less (about two times) than that of cavernous reservoirs.     

True amplitude imaging by inverse generalized Radon transform based on Gaussian beam decomposition of the acoustic Green's function

True amplitude migration is one of the most important procedures of seismic data processing. As a rule it is based on the decomposition of the velocity model of the medium into a known macrovelocity component and its sharp local perturbations to be determined. Under this decomposition the wavefield can be considered as the superposition of an incident and reflected/scattered waves. The single scattering approximation introduces the linear integral operator that connects the sharp local perturbations of the macrovelocity model with the multishot/multioffset data formed from reflected/scattered waves. We develop the pseudoinverse of this operator using the Gaussian beam based decomposition of acoustic Green's functions. The computation of this pseudoinverse operator is done pointwise by shooting Gaussian beams from the target area towards the acquisition system. The numerical implementation of the pseudoinverse operator was applied to the synthetic data Sigsbee2A. The results obtained demonstrate the high quality of the true amplitude images computed both in the smooth part of the model and under the salt body.     

Scattering and diffraction of earthquake motions in irregular elastic layers,I: Love and SH waves

We describe the wave propagation through an irregularly layered, elastic medium for incoming body (SH) and surface (Love) waves. As a result of irregular geometry, each layer generates additional waves by scattering and diffraction. These additional waves modify the input motions and locally may lead to larger motions and concentrations of stresses, strains, and rotations on or below the ground surface. For engineering design, and in particular for analyses of soil-structure interaction, it is important to understand the nature and the consequences of such motions.The scattering and diffraction of Love and SH waves by irregular layers will be investigated by the weighted-residuals method. The scattered and diffracted mode shapes and spectral amplification characteristics at different frequencies will be examined and discussed.     

Sensitivity of seismic waves to structure

We study how the perturbations of a generally heterogeneous isotropic or anisotropic structure manifest themselves in the wavefield, and which perturbations can be detected within a limited aperture and a limited frequency band. A short-duration broad-band incident wavefield with a smooth frequency spectrum is considered. In-finitesimally small perturbations of elastic moduli and density are decomposed into Gabor functions. The wavefield scattered by the perturbations is then composed of waves scattered by the individual Gabor functions. The scattered waves are estimated using the first-order Born approximation with the paraxial ray approximation. For each incident wave, each Gabor function generates at most 5 scattered waves, propagating in specific directions and having specific polarisations. A Gabor function corresponding to a low wavenumber may generate a single broad-band unconverted wave scattered in forward or narrow-angle directions. A Gabor function corresponding to a high wavenumber usually generates 0 to 5 narrow-band Gaussian packets scattered in wide angles, but may also occasionally generate a narrow-band P to S or S to P converted Gaussian packet scattered in a forward direction, or a broad-band S to P (and even S to S in a strongly anisotropic background) converted wave scattered in wide angles. In this paper, we concentrate on the Gaussian packets caused by narrow-band scattering. For a particular source, each Gaussian packet scattered by a Gabor function at a given spatial location is sensitive to just a single linear combination of 22 values of the elastic moduli and density corresponding to the Gabor function. This information about the Gabor function is lost if the scattered wave does not fall into the aperture covered by the receivers and into the legible frequency band.     

Model‐based attenuation for scattered dispersive waves

Coherent noise in land seismic data primarily consists in source‐generated surface‐wave modes. The component that is traditionally considered most relevant is the so‐called ground roll, consisting in surface‐wave modes propagating directly from sources to receivers. In many geological situations, near?surface heterogeneities and discontinuities, as well as topography irregularities, diffract the surface waves and generate secondary events, which can heavily contaminate records. The diffracted and converted surface waves are often called scattered noise and can be a severe problem particularly in areas with shallow or outcropping hard lithological formations. Conventional noise attenuation techniques are not effective with scattering: they can usually address the tails but not the apices of the scattered events. Large source and receiver arrays can attenuate scattering but only in exchange for a compromise to signal fidelity and resolution. We present a model?based technique for the scattering attenuation, based on the estimation of surface‐wave properties and on the prediction of surface waves with a complex path involving diffractions. The properties are estimated first, to produce surface?consistent volumes of the propagation properties. Then, for all gathers to filter, we integrate the contributions of all possible diffractors, building a scattering model. The estimated scattered wavefield is then subtracted from the data. The method can work in different domains and copes with aliased surface waves. The benefits of the method are demonstrated with synthetic and real data.     

高斯波包反射走时速度反演方法

扰动高斯波包理论指出,在Gabor域描述模型的扰动成分,且入射波场为短时宽带信号时,扰动波场可在时间域通过高斯波包算子描述.在此基础上通过拟合反射波的走时,提出一种速度反演方法.反射波走时残差利用地震道局部波形的互相关函数表示,以走时残差的二范数作为目标函数,优化目标函数实现对速度场的反演.基于一阶Born近似,利用扰动高斯波包理论推导出目标函数对速度场的梯度是本文理论部分的核心内容.梯度包括两部分:正传的背景波场与反传的扰动高斯波包之间的互相关,反传的背景波场和正传的扰动高斯波包之间的互相关.梯度表达式中背景波场和扰动波场均利用高斯波包算子模拟.计算梯度的具体算法中,如何模拟扰动波场,以及如何计算反射波的走时残差是两个要点,文中对此做了详细的讨论.数值实验进一步阐述了反演的实现策略,实验结果表明高斯波包反射走时速度反演方法和实现策略有效可行,并得到了理想的反演结果.     

Mie elastic scattering generated by cracks

Some numerical experiments are designed to elucidate geometrical details of fractures by studying scattering of elastic waves. The response in the time domain does not seem to provide much information. In the frequency domain, geometrical features of diffractors stamp a signature on reflected and diffracted wave fields. Results show that radiation patterns in the Mie regime are a promising device to infer some aspects such as shape and connectivity of the fractures. A combination of the direct and the indirect boundary element methods is used to compute numerical results. The numerical method is validated with analytic solutions for canonical problems.     

Review of ray-Born forward modeling for migration and diffraction analysis

The ray-Born approximation is a very useful tool for forward modeling of scattered waves. The fact that ray-Born modeling underlies most seismic migration techniques, and therefore shares their assumptions, is a justification in itself to consider it for forward modeling. The ray-Born approximation does not make an explicit distinction between specular reflections and nonspecular diffractions. It therefore allows the modeling of diffractions from structural discontinuities such as edges and tips, as well as caustic diffractions. In the simplest implementation ray-Born seismograms are multiple-free. Ray-Born modeling can be orders of magnitude faster than finite-difference modeling, both in two-and three dimensions.     

弹性各向同性介质一次散射波场高斯束Born正演

本文提出了一种弹性波一次散射波场的正演方法——弹性波高斯束Born正演.该方法以线性散射理论为基础,通过Born近似建立起地下散射点处不同波型的反射率同弹性波主分量波场之间的数据映射关系,利用高斯束所包含的走时、振幅和极性信息进行不同波型的局部平面波的合成,进而通过逆倾斜叠加将所合成的局部平面波转化为时空域的多分量地震记录.该方法不但保持了射线类方法高效的优点,还具备了处理多次走时波场的能力,从而保证了复杂构造的波场模拟的精度.文中两个数值模型的应用效果表明,本文所提出的弹性波高斯束Born正演算法具有近似于波动方程有限差分法的波场模拟精度以及高得多的计算效率.     

A METHOD FOR DETECTION OF DIFFRACTED WAVES ON COMMON-OFFSET SECTIONS*

A method of detection of diffracted waves on common-offset sections is proposed. The method utilizes the main kinematic and dynamic properties of the diffracted waves. The detection algorithm is defined by an automatic procedure including phase correlation of the diffracted waves and the application of certain statistical criteria. This procedure enables us to make decisions with regard to the presence of the diffracted waves and also to estimate parameters of the scattering objects. The method is applied to synthetic and field data and, even for a relatively low signal-to-noise ratio, it gives reliable results.     

Diffraction separation by plane-wave prediction filtering

Seismic data processing typically deals with seismic wave reflections and neglects wave diffraction that affect the resolution. As a general rule, wave diffractions are treated as noise in seismic data processing. However, wave diffractions generally originate from geological structures, such as fractures, karst caves, and faults. The wave diffraction energy is much weaker than that of the reflections. Therefore, even if wave diffractions can be traced back to their origin, their energy is masked by that of the reflections. Separating and imaging diffractions and reflections can improve the imaging accuracy of diffractive targets. Based on the geometrical differences between reflections and diffractions on the plane-wave record; that is, reflections are quasi-linear and diffractions are quasi-hyperbolic, we use plane-wave prediction filtering to separate the wave diffractions. First, we estimate the local slope of the seismic event using planewave destruction filtering and, then, we predict and extract the wave reflections based on the local slope. Thus, we obtain the diffracted wavefield by directly subtracting the reflected wavefield from the entire wavefield. Finally, we image the diffracted wavefield and obtain high-resolution diffractive target results. 2D SEG salt model data suggest that the plane-wave prediction filtering eliminates the phase reversal in the plane-wave destruction filtering and maintains the original wavefield phase, improving the accuracy of imaging heterogeneous objects.     

Diffraction of seismic waves in an elastic, cracked halfplane using a boundary integral formulation

The presence of subsurface cracks in a halfspace excited by elastic waves may give rise to scattered body and surface waves. For many engineering applications, such as non-destructive testing or oil exploration, the scattered field may yield valuable information to detect cracks and other scatterers. We use the Indirect Boundary Element Method (IBEM) to study the diffraction of P, SV waves with various incidence angles and Rayleigh surface waves. This approximate boundary integral technique is based upon the integral representation for scattered elastic waves using single-layer boundary sources. Our approach is usually called indirect BEM as the sources' strengths should be obtained as an intermediate step. This indirect formulation can give to the analyst a deep physical insight on the generated diffracted waves because it is closer to the physical reality and can be regarded as a realization of Huygens' Principle. In any event, mathematically it is fully equivalent to the classical Somigliana's representation theorem. In order to gauge accuracy we test our method by comparing with previous results in the literature. Various crack configurations, including multiple cracks, are investigated. Results in frequency and time domains are displayed. Under certain conditions the amplitude spectra of those waves clearly show conspicuous resonance peaks.     

局域双曲线Radon变换压制散射波研究与应用

一般而言,由于地下非均质体的存在所产生的二次波源,由它再生成新的波场,叫散射波场。目前,将散射波作为有效波来成像,已开始在溶洞和裂缝等特殊地质体的识别中得到应用。但对于野外资料采集来说,地表复杂地区,如戈壁、砾石区和山前带,大量存在的散射波却是干扰波,它们的存在会严重影响资料的品质,而其研究与实际应用国内外还很少。因此,通过正演模拟,分析散射波的基本特征,在此基础上研究散射波的去噪方法显得十分必要。本文从地震波运动学时距关系出发,研究了反射波和散射波的几何特征;然后用有限差分正演,模拟了散射波场,用理论模型研究并测试了局域双曲线Radon变换散射波去噪新方法。对于实际炮集资料,分析了F-K滤波方法压制散射噪声的局限,采用局域双曲Radon变换有效地去除了炮集中存在的散射噪声,取得了较好的应用效果。     

基于高斯束与高斯波包的Gabor框架散射波模拟方法

在给出真实模型和相应光滑背景模型的情况下,如何计算扰动模型(散射体)产生的散射波场是一个有实际意义的正演问题.在Gabor变换域描述散射体,且入射波场为短时宽带信号时,散射波场可以在频率域用高斯束或时间域用高斯波包描述.相对于波动方程方法,高斯束和高斯波包的计算效率更高;背景模型光滑时,高斯束和高斯波包方法的精度也接近波动方程方法.文中导出了声波假设下应用高斯束和高斯波包计算散射波的方法.测试分析了高斯波包的计算精度.给出了一般散射体的散射波模拟策略.同时针对一个理论模型完成了本文方法计算散射波的实验,实验结果表明高斯波包散射波计算方法是有效可行的.     

基于地震成像数据稀疏反演的不连续及非均质地质体检测方法

本文针对油气藏储层预测中的不连续及非均质地质信息识别问题,研究基于地震成像数据的稀疏反演方法.由于该类地质体的地震响应特征为弱信号,因此利用平面波破坏滤波器由地震成像数据中去除强反射同相轴.在此基础上,对剩余的地震数据进行非线性加强滤波,并构建L1稀疏反演模型.为有效求解L1模型,采用非光滑泛函L1范数逼近和拟牛顿求解算法.该方法考虑稀疏先验信息,能够提高反演结果信噪比.缝洞模型测试验证该方法在检测断点、微断裂、散射点等小尺度地质体上的有效性,塔北缝洞型碳酸盐岩储层预测的应用效果进一步证实该方法的实用性.     

Scattering ofP andS waves by a spherically symmetric inclusion

Scattering of an arbitrary elastic wave incident upon a spherically symmetric inclusion is considered and solutions are developed in terms of the spherical vector system of Petrashen, which produces results in terms of displacements rather than displacement potentials and in a form suitable for accurate numerical computations. Analytical expressions for canonical scattering coefficients are obtained for both the cases of incidentP waves and incidentS waves. Calculations of energy flux in the scattered waves lead to elastic optical theorems for bothP andS waves, which relate the scattering cross sections to the amplitude of the scattered fields in the forward direction. The properties of the solutions for a homogeneous elastic sphere, a sphere filled by fluid, and a spherical cavity are illustrated with scattering cross sections that demonstrate important differences between these types of obstacles. A general result is that the frequency dependence of the scattering is defined by the wavelength of the scattered wave rather than the wavelength of the incident wave. This is consistent with the finding that the intensity of thePS scattering is generally much stronger than theSP scattering. When averaged over all scattering angles, the mean intensity of thePS converted waves is2V _p ² /V _s ⁴ times the mean intensity of theSP converted waves, and this ratio is independent of frequency. The exact solutions reduce to simple and easily used expressions in the case of the low frequency (Rayleigh) approximation and the low contrast (Rayleigh-Born) approximation. The case of energy absorbing inclusions can also be obtained by assigning complex values to the elastic parameters, which leads to the result that an increase in attenuation within the inclusion causes an increased scattering cross section with a marked preference for scatteredS waves. The complete generality of the results is demonstrated by showing waves scattered by the earth's core in the time domain, an example of high-frequency scattering that reveals a very complex relationship between geometrical arrivals and diffracted waves.     

声波介质一次散射波场高斯束Born正演

Born正演是一种常用的地震波场正演模拟方法,也是线性化地震反演的理论基础.在实际应用时,Born正演通常结合常规的地震射线方法进行实现.为了克服常规地震射线方法的弊端,并且保证地震波场的模拟精度和计算效率,本文提出了一种基于高斯束的一阶散射波场Born正演方法.该方法分为两个环节:首先,我们利用高斯束的走时和振幅信息将地下散射点处的反射率映射为地表束中心位置处的局部平面波;然后,我们利用逆倾斜叠加将局部平面波转化为接收点处的时空域散射波场.在具体的实施过程中,我们提出一种以wavelet-bank方式实现的局部平面波合成方法,同现有的算法相比,可以在保持计算精度的同时,大大减少计算时间;此外,我们还利用最速下降法优化了高斯束的迭代循环过程,进一步提高了Born正演的计算效率.两个模型的应用效果证明,本文所提出的高斯束Born正演方法可以精确、高效的实现声波介质一次散射波场的正演模拟,为三维大规模地震波场的正演问题提供了一种切实可行的实现方案.     

Determining the microseismic event source parameters from the surface seismic array data with strong correlated noise and complex focal mechanisms of the source

The world experience shows that hydraulic fracturing (fracking) is an efficient tool for increasing oil and gas production of low-permeable reservoirs in hydrocarbon fields. The fracking-induced fractures in the rock, which are hydrodynamically connected with the wells, significantly enhance the volumes of extracted hydrocarbons. Controlling the processes of fracture formation and propagation is a vital question in the oil and gas reservoir management. A key means to implement this control is provided by microseismic monitoring of fracking, which makes it possible to promptly reconstruct the geometry of the fractures from the data on seismic waves from the microearthquakes induced by the formation and propagation of fractures.