The Geostack technique is a method of analyzing seismic amplitude variation with offset (AVO) information. One of the outputs of the analysis is a set of direct hydrocarbon indicator traces called 'fluid factor' traces. The fluid factor trace is designed to be low amplitude for all reflectors in a clastic sedimentary sequence except for rocks that lie off the 'mudrock line.' The mudrock line is the line on a crossplot of P-wave velocity against S-wave velocity on which water-saturated sandstones, shales, and siltstones lie. Some of the rock types that lie off the mudrock line are gas-saturated sandstones, carbonates, and igneous rocks. In the absence of carbonates and igneous rocks, high amplitude reflections on fluid factor traces would be expected to represent gas-saturated sandstones. Of course, this relationship does not apply exactly in nature, and the extent to which the mudrock line model applies varies from area to area. However, it is a useful model in many basins of the world, including the one studied here.Geostack processing has been done on a 3-D seismic data set over the Mossel Bay gas field on the southern continental shelf of South Africa. We found that anomalously high amplitude fluid factor reflections occurred at the top and base of the gas-reservoir sandstone. Maps were made of the amplitude of these fluid factor reflections, and it was found that the high amplitude values were restricted mainly to the gas field area as determined by drilling. The highest amplitudes were found to be located roughly in the areas of best reservoir quality (i.e., highest porosity) in areas where the reservoir is relatively thick.

The compressional wave reflection coefficient R(theta ) given by the Zoeppritz equations is simplified to the following:EquationThe first term gives the amplitude at normal incidence (theta = 0), the second term characterizes R(theta ) at intermediate angles, and the third term describes the approach to critical angle. The coefficient of the second term is that combination of elastic properties which can be determined by analyzing the offset dependence of event amplitude in conventional multichannel reflection data. If the event amplitude is normalized to its value for normal incidence, then the quantity determined isEquationA 0 specifies the normal, gradual decrease of amplitude with offset; its value is constrained well enough that the main information conveyed is Delta sigma /R 0, where Delta sigma is the contrast in Poisson's ratio at the reflecting interface and R 0 is the amplitude at normal incidence. This simplified formula for R(theta ) accounts for all of the relations between R(theta ) and elastic properties first described by Koefoed in 1955.

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.

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.

To efficiently invert seismic amplitudes for elastic parameters, pseudoquartic approximations to the Zoeppritz equations are derived to calculate P-P-wave reflection and transmission coefficients as a function of the ray parameter p. These explicit expressions have a compact form in which the coefficients of the p 2 and p 4 terms are given in terms of the vertical slownesses. The amplitude coefficients are also represented as a quadratic function of the elastic contrasts at an interface and are compared to the linear approximation used in conventional amplitude variation with offset (AVO) analysis, which can invert for only two elastic parameters. Numerical analysis with the second-order approximation shows that the condition number of the Frechet matrix for three elastic parameters is improved significantly from using a linear approximation. Therefore, those quadratic approximations can be used directly with amplitude information to estimate not only two but three parameters: P-wave velocity contrast, S-wave velocity contrast, and the ratio of S-wave and P-wave velocities at an interface.

Pore-fluid identification is one of the key technologies in seismic exploration. Fluid indicators play important roles in pore-fluid identification. For sandstone reservoirs, the effective pore-fluid bulk modulus is more susceptible to pore-fluid than other fluid indicators. AVO (amplitude variation with offset) inversion is an effective way to obtain fluid indicators from seismic data directly. Nevertheless, current methods lack a high-order AVO equation for a direct, effective pore-fluid bulk modulus inversion. Therefore, based on the Zoeppritz equations and Biot–Gassmann theory, we derived a high-order P-wave AVO approximation for an effective pore-fluid bulk modulus. Series reversion and Bayesian theory were introduced to establish a direct non-linear P-wave AVO inversion method. By adopting this method, the effective pore-fluid bulk modulus, porosity, and density can be inverted directly from seismic data. Numerical simulation results demonstrate the precision of our proposed method. Model and field data evaluations show that our method is stable and feasible.

Prestack seismic inversion is widely used in fluid indication and reservoir prediction. Compared with linear inversion, nonlinear inversion is more precise and can be applied to high-contrast situations. The inversion results can be affected by the parameters’ sensitivity, so the parameterization of nonlinear equations is very significant. Considering the poor nonlinear amplitude-variation-with-offset (AVO) inversion results of impedance and velocity parameters, we adjust the parameters of the nonlinear equation, avoid the inaccuracy caused by parameters sensitivity and get the ideal nonlinear AVO inversion results of the Lamé parameters. The feasibility and stability of the nonlinear equation based on the Lamé parameters and method are verified by the model and the real data examples. The resolution and the lateral continuity of nonlinear inversion results are better compared with the linear inversion results.

At an interface separating two viscoelastic media, the variation of the reflection coefficient with the incident angle is associated with the quality factors (Q-factors) of both media; this sets up a theoretical foundation for Q-factor inversion by amplitude variation with incident angle (AVA). The AVA inversion for Q-factors was applied to a field example of a gas reservoir to detect gas. Considering that the AVA inversion is commonly performed to obtain P- and S-wave velocities in the previous interpretation of the field seismic data, a new AVA inversion process for Q-factors was designed. The existing P- and S-wave velocities were used as the reference phase velocities at the dominant frequency of seismic signals in viscoelastic media, and then the Q-factors for P- and S-waves were inverted from the isofrequency components of the partial angle stack gathers with known reference phase velocities. The application in the field example found that this process obtained stable inverted Q-factor results, providing more powerful evidence for reservoir characterization.

研究表明流体引起衰减与频散往往表现为频变AVO现象.一些频散地震属性,例如纵波频散,已经证实为可靠的碳氢指示因子.为了更有效地识别流体,基于f-μ-ρ近似构建了新的流体因子D_f,即频变流体项.该属性的反演首先需要连续小波变换(CWT)谱分解得到不同频带地震数据,通过去相关与先验约束来保证反演结果可靠性.模型试算证实了频变反射系数近似公式的精度可靠性,D_f可以识别出强衰减介质所引起的频散现象.实际数据试算中,D_f可以较好地识别储层孔隙流体,尤其对于气层,具有较好的指示效果.该流体因子将Gassmann流体项的高孔隙流体敏感性与叠前数据丰富的振幅频率信息相结合,反演效果与岩石物理认识相符.此研究有助于利用衰减频散现象借助AVO反演实现流体识别.

Inversion of seismic data and quantification of reservoir properties, such as porosity, lithology, or fluid saturation, are commonly executed in two consecutive steps: a geophysical inversion to estimate the elastic parameters and a petrophysical inversion to estimate the reservoir properties. We combine within an integrated formulation the geophysical and petrophysical components of the problem to estimate the elastic and reservoir properties jointly. We solve the inverse problem following a Monte Carlo sampling approach, which allows us to quantify the uncertainties of the reservoir estimates accounting for the combination of geophysical data uncertainties, the deviations of the elastic properties from the calibrated petrophysical transform, and the nonlinearity of the geophysical and petrophysical relations. We implement this method for the inference of the total porosity and the acoustic impedance in a reservoir area, combining petrophysical and seismic information. In our formulation, the porosity and impedance are related with a statistical model based on the Wyllie transform calibrated to well-log data. We simulate the seismic data using a convolutional model and evaluate the geophysical likelihood of the joint porosity-impedance models. Applying the Monte Carlo sampling method, we generate a large number of realizations that jointly explain the seismic observations and honor the petrophysical information. This approach allows the calculation of marginal probabilities of the model parameters, including medium porosity, impedance, and seismic source wavelet. We show a synthetic validation of the technique and apply the method to data from an eastern Venezuelan hydrocarbon reservoir, satisfactorily predicting the medium stratification and adequate correlation between the seismic inversion and well-log estimates for total porosity and acoustic impedance.