Estimating gas saturation in a thin layer by using frequency‐dependent amplitude versus offset modelling

Various models have been proposed to link partial gas saturation to seismic attenuation and dispersion, suggesting that the reflection coefficient should be frequency‐dependent in many cases of practical importance. Previous approaches to studying this phenomenon typically have been limited to single‐interface models. Here, we propose a modelling technique that allows us to incorporate frequency‐dependent reflectivity into convolutional modelling. With this modelling framework, seismic data can be synthesised from well logs of velocity, density, porosity, and water saturation. This forward modelling could act as a basis for inversion schemes aimed at recovering gas saturation variations with depth. We present a Bayesian inversion scheme for a simple thin‐layer case and a particular rock physics model and show that, although the method is very sensitive to prior information and constraints, both gas saturation and layer thickness theoretically can be estimated in the case of interfering reflections.     

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.     

频变AVO含气性识别技术研究与应用

在常规AVO理论的基础上,频变AVO属性计算方法利用多尺度裂缝介质模型中物性参数具有频变特征的优势,基于Zoeppritz方程建立反射系数与频率之间的数学关系,推导出截距、梯度、碳氢检测因子、流体检测因子、拟泊松比等AVO属性与频率之间的数学关系.应用地震反演方法,综合地质、地震、测井等数据,反演出高精度的频变AVO属性,在天然气敏感属性分析的基础上建立起频变AVO含气性识别技术.将该技术应用到川西新场陆相深层须家河组碎屑岩储层的含气性识别中,在孔隙度通常在1％～4％,渗透率普遍低于0.06×10-3 μm2的致密背景下,较准确地预测了孔隙度大于4％、渗透性偏高的富气优质储层分布带,为该区含气性识别难题的解决和钻井成功率的提高,提供了重要的技术支撑.     

Joint facies and rock properties Bayesian amplitude‐versus‐offset inversion using Markov random fields

Seismic reflection pre‐stack angle gathers can be simultaneously inverted within a joint facies and elastic inversion framework using a hierarchical Bayesian model of elastic properties and categorical classes of rock and fluid properties. The Bayesian prior implicitly supplies low frequency information via a set of multivariate compaction trends for each rock and fluid type, combined with a Markov random field model of lithotypes, which carries abundance and continuity preferences. For the likelihood, we use a simultaneous, multi‐angle, convolutional model, which quantifies the data misfit probability using wavelets and noise levels inferred from well ties. Under Gaussian likelihood and facies‐conditional prior models, the posterior has simple analytic form, and the maximum a‐posteriori inversion problem boils down to a joint categorical/continuous non‐convex optimisation problem. To solve this, a set of alternative, increasingly comprehensive optimisation strategies is described: (i) an expectation–maximisation algorithm using belief propagation, (ii) a globalisation of method (i) using homotopy, and (iii) a discrete space approach using simulated annealing. We find that good‐quality inversion results depend on both sensible, elastically separable facies definitions, modest resolution ambitions, reasonably firm abundance and continuity parameters in the Markov random field, and suitable choice of algorithm. We suggest usually two to three, perhaps four, unknown facies per sample, and usage of the more expensive methods (homotopy or annealing) when the rock types are not strongly distinguished in acoustic impedance. Demonstrations of the technique on pre‐stack depth‐migrated field data from the Exmouth basin show promising agreements with lithological well data, including prediction accuracy improvements of 24% in and twofold in density, in comparison to a standard simultaneous inversion. Much clearer and extensive recovery of the thin Pyxis gas field was evident using stronger coupling in the Markov random field model and use of the homotopy or annealing algorithms.     

Frequency‐ and angle‐dependent poroelastic seismic analysis for highly attenuating reservoirs

We extend the frequency‐ and angle‐dependent poroelastic reflectivity to systematically analyse the characteristic of seismic waveforms for highly attenuating reservoir rocks. It is found that the mesoscopic fluid pressure diffusion can significantly affect the root‐mean‐square amplitude, frequency content, and phase signatures of seismic waveforms. We loosely group the seismic amplitude‐versus‐angle and ‐frequency characteristics into three classes under different geological circumstances: (i) for Class‐I amplitude‐versus‐angle and ‐frequency, which corresponds to well‐compacted reservoirs having Class‐I amplitude‐versus‐offset characteristic, the root‐mean‐square amplitude at near offset is boosted at high frequency, whereas seismic energy at far offset is concentrated at low frequency; (ii) for Class‐II amplitude‐versus‐angle and ‐frequency, which corresponds to moderately compacted reservoirs having Class‐II amplitude‐versus‐offset characteristic, the weak seismic amplitude might exhibit a phase‐reversal trend, hence distorting both the seismic waveform and energy distribution; (iii) for Class‐III amplitude‐versus‐angle and ‐frequency, which corresponds to unconsolidated reservoir having Class‐III amplitude‐versus‐offset characteristic, the mesoscopic fluid flow does not exercise an appreciable effect on the seismic waveforms, but there exists a non‐negligible amplitude decay compared with the elastic seismic responses based on the Zoeppritz equation.     

Monitoring CO2 saturation using time‐lapse amplitude versus offset analysis of 3D seismic data from the Ketzin CO2 storage pilot site,Germany

The injection of CO₂ at the Ketzin pilot site commenced in June 2008 and was terminated in August 2013 after 67 kT had been injected into a saline formation at a depth of 630–650 m. As part of the site monitoring program, four 3D surface seismic surveys have been acquired to date, one baseline and three repeats, of which two were conducted during the injection period, and one during the post‐injection phase. The surveys have provided the most comprehensive images of the spreading CO₂ plume within the reservoir layer. Both petrophysical experiments on core samples from the Ketzin reservoir and spectral decomposition of the 3D time‐lapse seismic data show that the reservoir pore pressure change due to CO₂ injection has a rather minor impact on the seismic amplitudes. Therefore, the observed amplitude anomaly is interpreted to be mainly due to CO₂ saturation. In this study, amplitude versus offset analysis has been applied to investigate the amplitude versus offset response from the top of the sandstone reservoir during the injection and post‐injection phases, and utilize it to obtain a more quantitative assessment of the CO₂ gaseous saturation changes. Based on the amplitude versus offset modelling, a prominent decrease in the intercept values imaged at the top of the reservoir around the injection well is indeed associated solely with the CO₂ saturation increase. Any change in the gradient values, which would, in case it was positive, be the only signature induced by the reservoir pressure variations, has not been observed. The amplitude versus offset intercept change is, therefore, entirely ascribed to CO₂ saturation and used for its quantitative assessment. The estimated CO₂ saturation values around the injection area in the range of 40%–60% are similar to those obtained earlier from pulsed neutron‐gamma logging. The highest values of 80% are found in the second seismic repeat in close vicinity to the injection and observation wells.     

基于贝叶斯理论的叠前多波联合反演弹性模量方法

AVO反演可以获得地层岩性和流体信息,而叠前反演问题都是高维的和非适定的,因此获得可靠稳定的解对叠前反演至关重要. 本文给出了一种基于贝叶斯理论的纵波和转换波联合反演密度比和模量比的方法. 鉴于剪切模量比、体积模量比可以更好地指示油气,基于岩石物理中速度比与模量比之间的关系,将此关系式代入Zoeppritz方程的近似形式Aki-Richards公式中,得到与模量比有关的反射系数近似公式. 联合纵波和转换波,利用最小二乘准则构建目标函数,最终反演出密度比、剪切模量比、体积模量比三个参数. 在反演过程中引入贝叶斯理论,假定先验信息服从高斯分布,待求参数服从改进的Cauchy分布,并去除待求参数之间的相关性. 利用模型数据和实际数据对本文方法进行测试,并与常规的单独利用纵波数据来反演方法进行比较,结果表明联合反演稳定性更好、精度更高、抗噪音能力更强,验证了本文方法的可行性和有效性.     

Joint PP‐ and PSV‐wave amplitudes versus offset and azimuth inversion for fracture compliances in horizontal transversely isotropic media

We propose a robust approach for the joint inversion of PP‐ and PSV‐wave angle gathers along different azimuths for the elastic properties of the homogeneous isotropic host rock and excess compliances due to the presence of fractures. Motivated by the expression of fluid content indicator in fractured reservoirs and the sensitivity of Lamé impedances to fluid type, we derive PP‐ and PSV‐wave reflection coefficients in terms of Lamé impedances, density, and fracture compliances for an interface separating two horizontal transversely isotropic media. Following a Bayesian framework, we construct an objective function that includes initial models. We employ the iteratively reweighted least‐squares algorithm to solve the inversion problem to estimate unknown parameters (i.e., Lamé impedances, density, and fracture compliances) from PP‐ and PSV‐wave angle gathers along different azimuths. Synthetic tests reveal that the unknown parameters estimated using the joint inversion approach match true values better than those estimated using a PP‐wave amplitude inversion only. A real data test indicates that reasonable results for subsurface fracture detection are obtained from the joint inversion approach.