Based on a theory of porous solids previously developed by the author, the elasticity of a hexagonal close packing of equal spheres is treated. The packing is anisotropic and because of the weight of the spheres, also inhomogeneous. The velocities of propagation of elastic waves have been calculated for evacuated interspaces and for interspaces filled with a liquid or gas. In the case of evacuated or air‐filled interspaces, the wave rays and travel times have been computed. The packing which has been treated may be of use as a model for a dry or wet loose material such as gravel or sand. Though the model is very simplified, the results obtained show some typical effects such as anisotropy, in homogeneity, and a 90° angle of emergence.

This analysis draws together basic rock physics, amplitude variations with offset (AVO), and seismic amplitude inversion to discuss how fluid‐factor discrimination can be performed using prestack seismic data. From both Biot and Gassmann theories for porous, fluid‐saturated rocks, a general formula is first derived for fluid‐factor discrimination given that both the P and S impedances are available. In essence, the two impedances are transformed so that they better differentiate between the fluid and rock matrix of the porous medium. This formula provides a more sensitive discriminator of the pore‐fluid saturant than the acoustic impedance and is especially applicable in hard‐rock environments. The formulation can be expressed with either the Lamé constants and density, or the bulk and shear moduli and density. Numerical and well‐log examples illustrate the applicability of this approach. AVO inversion results are then incorporated to show how this method can be implemented using prestack seismic data. Finally, a shallow gas‐sand example from Alberta and a well‐log example from eastern Canada are shown to illustrate the technique.

The technique of amplitude variation with offset (AVO) allows geoscientists to extract fluid and lithology information from the analysis of prestack seismic amplitudes. Various AVO parameterizations exist, all of which involve the sum of three weighted elastic-constant terms. In present-day AVO approaches, the weighting terms involve either knowledge of the incidence angle only, or knowledge of both the incidence angle and the in situ VP/VS ratio. We have used the theory of poroelasticity to derive a generalized AVO approximation that provides the estimation of fluid, rigidity, and density parameters. We have combined two previously independent AVO formulations, thus reducing, instead of adding to, the total number of formulations. This new approach requires knowledge of a third parameter to compute the weights: the dry-rock VP/VS ratio. We have derived a new equation and applied it to model and real data sets. The new formulation has allowed us to estimate fluid properties of the reservoir in a more direct manner than previous formulations.

Fluid indicators estimated from seismic data play important roles in reservoir characterization and prospect identification. Traditionally, there are a variety of fluid indicators proposed, but they are very likely to provide ambiguous results for fluid identification due to the fact that their sensitivity is dependent upon the mixed effect of pore fluid and rock porosity. To raise the sensitivity of fluid indication, we used the effective pore-fluid bulk modulus as a fluid indicator. Starting with the poroelastic amplitude variation with offset (AVO) theory and the corresponding rock-physics model with the homogeneous sorting trend, we derived a new AVO approximation that allowed us to estimate the effective pore-fluid bulk modulus in a direct fashion. The inversion for the fluid indicator is formulated in Bayesian framework with the Cauchy distribution as a prior constraint. We tested the method on synthetic data and analyzed the feasibility and stability of the inversion. A field data example shows that the effective pore-fluid bulk modulus can reduce the ambiguity caused by the rock porosity and improve the quality of fluid discrimination in a clastic reservoir. Further research needs to be done on the reservoirs that do not fit the rock-physics model without a sorting trend.

裂缝储层岩石物理参数的准确获得对地下裂缝预测具有重要意义,而叠前地震反演是获得裂缝岩石物理参数的有效手段.本文从裂缝岩石物理等效模型的构建出发,从测井数据上估测了裂缝岩石物理参数,通过推导含裂缝岩石物理参数的方位各向异性弹性阻抗公式,探讨了基于方位各向异性弹性阻抗的裂缝岩石物理参数地震反演方法.实际工区地震数据应用表明,基于方位各向异性弹性阻抗的裂缝岩石物理参数反演方法合理、可靠,可以降低裂缝岩石物理参数估测的不确定性,为地下裂缝预测提供有力的依据.

裂缝型储层的描述包括预测裂缝分布特征和识别裂隙充填物.依据等效介质理论计算的纵波速度随裂缝密度的增大而减小.正演地震记录显示,裂缝介质含气时反射振幅最大,且变化程度比含油或含水时大.叠前方位AVO反演所得的各向异性梯度B^ani与裂缝密度成正比,可用于描述有效裂缝发育强度.对于不同的裂缝密度,各向异性梯度B^ani与各向同性梯度B^iso的比值I_fluid⁽¹⁾近似为常数,且对流体敏感.经裂缝纵横比和背景介质拉梅常数修正后,流体因子I_fluid既不随纵横比变化,又不受背景介质的影响,是裂缝型储层敏感的流体识别因子.在塔里木盆地塔北哈拉哈塘地区热瓦普区块碳酸盐岩储层裂缝发育区域,运用该参数在井点处的流体识别效果与钻井结果一致.

为了解决各向异性下的流体识别问题,将纵波各向异性裂缝预测以及Russell的流体因子融合到直角坐标系中,提出了一种能够同时检测裂缝发育情况以及流体性质的新的裂缝流体因子(Factor of Fluid-filled Fracture,FFF),并通过一组岩性参数检验了裂缝流体因子在裂缝预测及流体识别中的有效性.在理论研究的基础上,选取松辽盆地某地区的火成岩裂缝及流体识别研究为应用实例.通过与测井流体及裂缝信息的对比验证,裂缝流体因子能够较为准确地预测研究区裂缝和流体的分布情况,且裂缝流体因子在单井上的计算结果与单井含气饱和度吻合度较高.此外,根据实际应用效果,指出裂缝流体因子在应用中的局限性:裂缝流体因子在平面成图时受地层厚度影响较大,且无法预测裂缝方向.

A new linearized AVO inversion technique is developed in a Bayesian framework. The objective is to obtain posterior distributions for P‐wave velocity, S‐wave velocity, and density. Distributions for other elastic parameters can also be assessed—for example, acoustic impedance, shear impedance, and P‐wave to S‐wave velocity ratio. The inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the Zoeppritz equation. The solution is represented by a Gaussian posterior distribution with explicit expressions for the posterior expectation and covariance; hence, exact prediction intervals for the inverted parameters can be computed under the specified model. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero. With realistic noise levels, acoustic impedance was the best determined parameter, while the inversion provided practically no information about the density. The inversion algorithm has also been tested on a real 3‐D data set from the Sleipner field. The results show good agreement with well logs, but the uncertainty is high.

针对确定性叠前三参数反演存在的精度低、稳定性差、抗噪性差以及过度依赖初始模型的问题,虽然利用随机反演方法实现叠前三参数同步反演有助于解决这些问题,但此类方法反演效率较低。为此,提出了利用自适应粒子群优化马尔科夫链蒙特卡洛(APSO-MCMC)算法以提高叠前三参数反演的计算效率。结合纵波速度、横波速度以及密度的变化统计扰动关系,建立模型扰动的高斯分布,根据三参数扰动先验分布抽样获取初始粒子群。在每一步迭代过程中,利用跃迁矩阵改变粒子的演化,根据粒子之间的距离计算演化因子,判定粒子群的收敛状态。此外,利用精英策略,帮助粒子实现跳出局部极小值的困境。由于传统叠前近似公式在宽角度区域与非近似公式误差较大,故利用Zoeppritz公式来保证叠前三参数反演在各个角度的精度。NS地区二维海洋实际数据应用表明,该方法估算纵波速度、横波速度和密度有效,稳定收敛,计算效率高于传统的随机方法,具有较好的精度和抗噪性。

Deterministic inversion of prestack data has problems concerning inaccuracy,instability,poor noise resistance,and excessive dependence on the initial model.Therefore,a stochastic inversion method was previously proposed to determine the prestack three-parameter simultaneous inversion;however,the efficiency of conventional stochastic inversion is low.In this study,the APSO-MCMC method was developed to improve the computational efficiency of the prestack simultaneous inversion.According to the statistical perturbation relationship of the P-wave velocity,S-wave velocity,and density,the Gaussian distribution of the model perturbation is constructed.Based on the acceptance-rejection method,an initial swarm is generated as an input for the inversion process.During the iteration,a transition matrix is employed to change the evolution of the particles.Additionally,the evolution factor was calculated based on the distance between the particles to determine the convergence state of the particle swarm.In each iteration,an elite learning strategy was employed to determine the jump-out of the local minimum.Because the conventional forward modeling algorithm is not accurate in wide-angle regions,this study employed the Zoeppritz equations to ensure the accuracy of the prestack three-parameter inversion.The field data test of the NS area shows that the method correctly estimates the P-wave velocity,S-wave velocity,and density,and has a stability of convergence,high resistance to noise,and better efficiency than conventional stochastic approaches.

常规随机稀疏反射系数反演方法采用单道反演策略,实现过程中需要依据经验预设非零反射系数个数,不恰当的预设参数会引起诸多问题,另外,方法的收敛准则从本质上放大了以振幅较大为特征的异常值的影响。为此,引入相邻地震道数据作为约束条件,提出了一种多道的随机稀疏反射系数反演方法。通过对目标地震道数据的非零反射系数的位置和倾角进行同时非线性搜索,有效提升了反演预设参数的选择稳定性,同时减轻了异常值对反演结果的影响。作为单道随机稀疏反射系数反演方法的拓展,该方法保留了可以对反演结果进行不确定性分析的优势,可以提高地震数据高分辨率处理结果的可信性。利用该方法获得的高分辨率反射系数和地震剖面能够得到更多的构造和界面信息,有利于后续的解释工作。

A simple method for including the effects of geologically realistic fractures on the seismic propagation through fractured rocks can be obtained by writing the effective compliance tensor of the fractured rock as the sum of the compliance tensor of the unfractured background rock and the compliance tensors for each set of parallel fractures or aligned fractures. The compliance tensor of each fracture set is derivable from a second rank fracture compliance tensor. For a rotationally symmetric set of fractures, the fracture compliance tensor depends on only two fracture compliances, one controlling fracture compliance normal, the other, tangential, to the plane of the fractures. The stiffness tensor, which is more useful in the consideration of elastic wave propagation through rocks, can then be obtained by inversion. The components of the excess fracture compliance tensor represent the maximum amount of information that can be obtained from seismic data. If the background rock is isotropic and the normal and shear compliance of each fracture are equal, although different from those of other fractures, the effective elastic behavior of the fractured rock is orthorhombic for any orientation distribution of fractures. A comparison of the theory with recent ultrasonic experiments on a simulated fractured medium shows near equality of the normal and shear compliance for the case of air‐filled fractures.

Microstructural attributes of cracks and fractures, such as crack density, aspect ratio, and fluid infill, determine the elastic properties of a medium containing a set of parallel, vertical fractures. Although the tangential weakness [Formula: see text] of the fractures does not vary with the fluid content, the normal weakness [Formula: see text] exhibits significant dependence on fluid infill. Based on linear-slip theory, we used the ratio [Formula: see text] — termed the fluid indicator — as a quantitative measure of the fluid content in the fractures, with g representing the square of the ratio of S- and P-wave velocity in the unfractured medium. We used a Born formalism to derive the sensitivity to fracture weakness of PP- and PS-reflection coefficients for an interface separating an unfractured medium from a vertically fractured medium. Our formulae reveal that the PP-reflection coefficient does not depend on the 2D microcorrugation/surface roughness with ridges and valleys parallel to the fracture strike, whereas the PS-reflection coefficient is sensitive to this microstructural property of the fractures. Based on this formulation, we developed a method to compute the fluid indicator from wide-azimuth PP-AVOA data. Inversion of synthetic data corrupted with 10% random noise reliably estimates the normal and tangential fracture weaknesses and hence the fluid indicator can be determined accurately when the fractures are liquid-filled or partially saturated. As the gas saturation in the fractures increases, the quality of inversion becomes poorer. Errors of 15%–20% in g do not affect the estimation of fluid indicator significantly in case of liquid infill or partial saturation. However, for gas-saturated fractures, incorrect values of g may have a significant effect on fluid-indicator estimates.

It is unclear whether one can (or should) write a tutorial about Bayes. It is a little like writing a tutorial about the sense of humor. However, this tutorial is about the Bayesian approach to the solution of the ubiquitous inverse problem. Inasmuch as it is a tutorial, it has its own special ingredients. The first is that it is an overview; details are omitted for the sake of the grand picture. In fractal language, it is the progenitor of the complex pattern. As such, it is a vision of the whole. The second is that it does, of necessity, assume some ill‐defined knowledge on the part of the reader. Finally, this tutorial presents our view. It may not appeal to, let alone be agreed to, by all.

Three-term AVO inversion can be used to estimate P-wave velocity, S-wave velocity, and density perturbations from reflection seismic data. The density term, however, exhibits little sensitivity to amplitudes and, therefore, its inversion is unstable. One way to stabilize the density term is by including a scale matrix that provides correlation information between the three unknown AVO parameters. We investigate a Bayesian procedure to include sparsity and a scale matrix in the three-term AVO inversion problem. To this end, we model the prior distribution of the AVO parameters via a Trivariate Cauchy distribution. We found an iterative algorithm to solve the Bayesian inversion and, in addition, comparisons are provided with the classical inversion approach that uses a Multivariate Gaussian prior. It is important to point out that the Multivariate Gaussian prior allows us to include the correlation of the AVO parameters in the solution of the inverse problem. The Trivariate Cauchy prior not only permits us to incorporate correlation but also leads to high-resolution (broadband) P-wave velocity, S-wave velocity, and density perturbations.

Young’s modulus and Poisson’s ratio are related to quantitative reservoir properties such as porosity, rock strength, mineral and total organic carbon content, and they can be used to infer preferential drilling locations or sweet spots. Conventionally, they are computed and estimated with a rock physics law in terms of P-wave, S-wave impedances/velocities, and density which may be directly inverted with prestack seismic data. However, the density term imbedded in Young’s modulus is difficult to estimate because it is less sensitive to seismic-amplitude variations, and the indirect way can create more uncertainty for the estimation of Young’s modulus and Poisson’s ratio. This study combines the elastic impedance equation in terms of Young’s modulus and Poisson’s ratio and elastic impedance variation with incident angle inversion to produce a stable and direct way to estimate the Young’s modulus and Poisson’s ratio, with no need for density information from prestack seismic data. We initially derive a novel elastic impedance equation in terms of Young’s modulus and Poisson’s ratio. And then, to enhance the estimation stability, we develop the elastic impedance varying with incident angle inversion with damping singular value decomposition (EVA-DSVD) method to estimate the Young’s modulus and Poisson’s ratio. This method is implemented in a two-step inversion: Elastic impedance inversion and parameter estimation. The introduction of a model constraint and DSVD algorithm in parameter estimation renders the EVA-DSVD inversion more stable. Tests on synthetic data show that the Young’s modulus and Poisson’s ratio are still estimated reasonable with moderate noise. A test on a real data set shows that the estimated results are in good agreement with the results of well interpretation.