2D cooperative inversion of direct current resistivity and gravity data: A case study of uranium bearing target rock

Interpretation of a single geophysical data set is not sufficient to get complete subsurface information. Cooperative or joint inversion of geophysical data sets is the preferred method for most case studies. In the present study, we present the results of the cooperative inversion approach of direct current resistivity and gravity data. The algorithm uses fuzzy c-means clustering to determine the petrophysical relationship between density and resistivity to obtain the similarity. Synthetic data set has demonstrated that the cooperative inversion approach can produce more reliable and better resistivity and density models of the subsurface as compared to those obtained through individual inversions. To utilize the presented cooperative inversion algorithm, the number of geologic units (number of clusters) in the study region must be known a priori. As a field study, the cooperative inversion approach was used to identify the extension of uranium-bearing target rock around the Beldih open cast mine. We noted the inconsistencies in both resistivity and density models obtained from the individual inversions. However, the presented cooperative inversion approach was able to produce similar resistivity and density models while maintaining the same error level of the respective individual inversions. We have considered four geologic units in the presented cooperative inversion as a field case study. We have also compared our cooperative results with drilled borehole and found to be a reliable tool to differentiate between the target rocks (kaolinite and quartz–magnetite–apatite rocks) and the ultramafic rock (host rock quartzite/alkaline granite). However, this study is subject to certain limitations such as the inability to differentiate between closely spaced kaolinite and quartz–magnetite–apatite rocks.     

Elastic full waveform inversion with probabilistic petrophysical clustering

Full waveform inversion aims to use all information provided by seismic data to deliver high-resolution models of subsurface parameters. However, multiparameter full waveform inversion suffers from an inherent trade-off between parameters and from ill-posedness due to the highly non-linear nature of full waveform inversion. Also, the models recovered using elastic full waveform inversion are subject to local minima if the initial models are far from the optimal solution. In addition, an objective function purely based on the misfit between recorded and modelled data may honour the seismic data, but disregard the geological context. Hence, the inverted models may be geologically inconsistent, and not represent feasible lithological units. We propose that all the aforementioned difficulties can be alleviated by explicitly incorporating petrophysical information into the inversion through a penalty function based on multiple probability density functions, where each probability density function represents a different lithology with distinct properties. We treat lithological units as clusters and use unsupervised K-means clustering to separate the petrophysical information into different units of distinct lithologies that are not easily distinguishable. Through several synthetic examples, we demonstrate that the proposed framework leads full waveform inversion to elastic models that are superior to models obtained either without incorporating petrophysical information, or with a probabilistic penalty function based on a single probability density function.     

基于交叉梯度耦合的大地电磁与地震走时资料三维联合反演

为了有效解决目前大地电磁和地震走时资料单方法反演结果一致性不好的问题,同时克服基于岩石不同物性参数间关系耦合约束联合反演的局限性,本文研究了基于交叉梯度耦合约束的大地电磁与地震走时资料的三维联合反演算法.以较为成熟的天然地震走时资料三维正反演和大地电磁三维正反演算法为基础,实现了具有共同的反演网格,以交叉梯度结构耦合约束,并能同时获得电阻率和速度模型的三维联合反演算法.分别利用单棱柱体模型和双棱柱体模型合成数据进行了联合反演试算.结果表明:无论是单棱柱体模型还是双棱柱体模型,联合反演结果比单独反演对异常体的空间形态都有更好的恢复,其中单棱柱体模型反演的异常体电阻率更接近于真实电阻率,双棱柱体模型的联合反演结果不仅消除了围岩的部分电阻率假异常,而且增强了对异常体深部速度结构特征的恢复程度.联合反演还能同时改善电阻率和速度反向变化异常体的单独反演结果,进一步证明交叉梯度耦合不依赖于岩石物性关系,而强调地下结构的相似性,具有更普遍的适用性.     

Semiautomatic and Automatic Cooperative Inversion of Seismic and Magnetotelluric Data

Natural source electromagnetic methods have the potential to recover rock property distributions from the surface to great depths. Unfortunately, results in complex 3D geo-electrical settings can be disappointing, especially where significant near-surface conductivity variations exist. In such settings, unconstrained inversion of magnetotelluric data is inexorably non-unique. We believe that: (1) correctly introduced information from seismic reflection can substantially improve MT inversion, (2) a cooperative inversion approach can be automated, and (3) massively parallel computing can make such a process viable. Nine inversion strategies including baseline unconstrained inversion and new automated/semiautomated cooperative inversion approaches are applied to industry-scale co-located 3D seismic and magnetotelluric data sets. These data sets were acquired in one of the Carlin gold deposit districts in north-central Nevada, USA. In our approach, seismic information feeds directly into the creation of sets of prior conductivity model and covariance coefficient distributions. We demonstrate how statistical analysis of the distribution of selected seismic attributes can be used to automatically extract subvolumes that form the framework for prior model 3D conductivity distribution. Our cooperative inversion strategies result in detailed subsurface conductivity distributions that are consistent with seismic, electrical logs and geochemical analysis of cores. Such 3D conductivity distributions would be expected to provide clues to 3D velocity structures that could feed back into full seismic inversion for an iterative practical and truly cooperative inversion process. We anticipate that, with the aid of parallel computing, cooperative inversion of seismic and magnetotelluric data can be fully automated, and we hold confidence that significant and practical advances in this direction have been accomplished.     

基于改进差分进化算法的大地电磁测深和重力宽范围物性约束联合反演

宽范围物性约束技术容易实现、具有一定容错性,目前已在大地电磁测深（MT）和地震、MT和重力联合反演中实现,但该技术是结合模拟退火算法实现的.差分进化算法（DE）是一种全局优化算法,但该算法在地球物理联合反演领域应用较少.基于此,本文以双种群设置方案为框架改进了DE算法,并提出了基于改进DE算法的宽范围物性约束技术.MT和重力联合反演的模型试验表明：与传统的DE算法相比,改进的DE算法收敛速度更快,寻优能力更强;基于改进DE算法的宽范围物性约束技术可以促进不同岩石物性参数在一定"范围"内实现耦合,既可以利用岩石物性关联的导向作用,又可以发挥优化算法的寻优能力,进而降低地球物理联合反演对先验信息的要求;此外,该技术的实现也验证了宽范围物性约束思想在联合反演领域中的适用性,具有进一步推广至其他优化算法中的潜质.     

Seismic driven probabilistic classification of reservoir facies for static reservoir modelling: a case history in the Barents Sea

In this paper we present a case history of seismic reservoir characterization where we estimate the probability of facies from seismic data and simulate a set of reservoir models honouring seismically‐derived probabilistic information. In appraisal and development phases, seismic data have a key role in reservoir characterization and static reservoir modelling, as in most of the cases seismic data are the only information available far away from the wells. However seismic data do not provide any direct measurements of reservoir properties, which have then to be estimated as a solution of a joint inverse problem. For this reason, we show the application of a complete workflow for static reservoir modelling where seismic data are integrated to derive probability volumes of facies and reservoir properties to condition reservoir geostatistical simulations. The studied case is a clastic reservoir in the Barents Sea, where a complete data set of well logs from five wells and a set of partial‐stacked seismic data are available. The multi‐property workflow is based on seismic inversion, petrophysics and rock physics modelling. In particular, log‐facies are defined on the basis of sedimentological information, petrophysical properties and also their elastic response. The link between petrophysical and elastic attributes is preserved by introducing a rock‐physics model in the inversion methodology. Finally, the uncertainty in the reservoir model is represented by multiple geostatistical realizations. The main result of this workflow is a set of facies realizations and associated rock properties that honour, within a fixed tolerance, seismic and well log data and assess the uncertainty associated with reservoir modelling.     

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.     

储层弹性与物性参数地震叠前同步反演的确定性优化方法

储层弹性与物性参数可直接应用于储层岩性预测和流体识别,是储层综合评价和油气藏精细描述的基本要素之一.现有的储层弹性与物性参数地震同步反演方法大都基于Gassmann方程,使用地震叠前数据,通过随机优化方法反演储层弹性与物性参数;或基于Wyllie方程,使用地震叠后数据,通过确定性优化方法反演储层弹性与物性参数.本文提出一种基于Gassmann方程、通过确定性优化方法开展储层弹性和物性参数地震叠前反演的方法,该方法利用Gassmann方程建立储层物性参数与叠前地震观测数据之间的联系,在贝叶斯反演框架下以储层弹性与物性参数的联合后验概率为目标函数,通过将目标函数的梯度用泰勒公式展开得到储层弹性与物性参数联合的方程组,其中储层弹性参数对物性参数的梯度用差分形式表示,最后通过共轭梯度算法迭代求解得到储层弹性与物性参数的最优解.理论试算与实际资料反演结果证明了方法的可行性.     

Estimation of petrophysical parameters by linearized inversion of angle domain pre-stack data

We describe a linear Bayesian inversion method to estimate the relevant petrophysical properties of the media forming a reflecting interface from the observations of amplitude variation with incidence angle. Three main steps characterize the proposed approach:
– information from borehole logs are statistically analysed to estimate the empirical models that describe the functional relationship between petrophysical (e.g. porosity, saturation, pressure or depth) and seismic variable(P and S velocities and density);
– the pure-mode (PP) reflection coefficient is parameterized in terms of the relevant petrophysical variables and is linearized in order to implement the linear inversion;
– the sought petrophysical parameters are estimated from the seismic reflected amplitudes by applying the linearized inversion where a priori information, data and model errors and solutions are described by probability density functions.
We test the method on synthetic and real data relative to reflections from a shale/gas-sand interface where the amplitude versus angle response, besides the lithological contrast, is mainly controlled by the saturation and porosity of the sand layer. The outcomes of the linearized inversion are almost identical to those obtained by a previously developed non-linear inversion method demonstrating the applicability of the linear inversion. It turns out that the gas-sand saturation in the range 0%–95% is a poorly resolved parameter while the porosity is the best resolved parameter. The issues of robustness and resolution of the inversion are discussed either through singular value decomposition analysis or the observation of the a posteriori probability density functions.
The linear inversion algorithm, compared with the previously developed non-linear method, reduces significantly the computation time allowing for more extensive applications.     

Petrophysical inversion of AVA data

We investigate the interactions between the elastic parameters, V_P, V_S and density, estimated by non-linear inversion of AVA data, and the petrophysical parameters, depth (pressure), porosity, clay content and fluid saturation, of an actual gas-bearing reservoir. In particular, we study how the ambiguous solutions derived from the non-uniqueness of the seismic inversion affect the estimates of relevant rock properties. It results that the physically admissible values of the rock properties greatly reduce the range of possible seismic solutions and this range contains the actual values given by the well. By means of a statistical inversion, we analyse how approximate a priori knowledge of the petrophysical properties and of their relationships with the seismic parameters can be of help in reducing the ambiguity of the inversion solutions and eventually in estimating the petrophysical properties of the specific target reservoir. This statistical inversion allows the determination of the most likely values of the sought rock properties along with their uncertainty ranges. The results show that the porosity is the best-resolved rock property, with its most likely value closely approaching the actual value found by the well, even when we insert somewhat erroneous a priori information. The hydrocarbon saturation is the second best-resolved parameter, but its most likely value does not match the well data. The depth of the target interface is the least-resolved parameter and its most likely value is strongly dependent on a priori information. Although no general conclusions can be drawn from the results of this exercise, we envisage that the proposed AVA–petrophysical inversion and its possible extensions may be of use in reservoir characterization.     

Imaging the Kristineberg mining area with two perpendicular magnetotelluric profiles in the Skellefte Ore District,northern Sweden

New magnetotelluric (MT) data from two perpendicular profiles in the Kristineberg area, northern Sweden, were analysed and modelled. In the Skellefte Ore District, the Kristineberg volcanic hosted massive sulphide (VHMS) deposit mine is one of the largest and deepest (1250 m). Seventeen broadband magnetotelluric stations were installed along two existing seismic reflection lines. The profiles were 6 and 12 km long with 500 m and 1 km site spacing, respectively. The obtained MT transfer functions in the period range of 0.0015–200 s are of fairly good quality. Detailed strike and dimensionality analysis reveal consistent but period dependent, strike directions, indicating a change in the geoelectrical strike with depth. From the two‐dimensional inversion of the determinant of the impedance tensor, two stable conductivity models with good data fit were obtained. The addition of seismic reflection information from the co‐located survey, improved the data fit of one of them. Extensive sensitivity analyses helped to delineate the well resolved regions of the models and to determine the position of pronounced boundaries. The results are in good agreement with previous studies, especially regarding the presence of a deep conductor interpreted as a structural basement to the district. They also reveal with more detail the configuration of the main geological units of the Skellefte Ore District, especially of the ore bearing volcanic rocks and the embedded alteration zones.     

电阻率和速度随机分布的MT与地震联合反演

在已有研究成果的基础上,为了适应物性参数剧烈变化的复杂模型并满足联合反演的要求,开发了速度和电阻率随机分布共网格单元模型的建模技术.基于这种统一的物性随机分布的网格介质模型,利用有限元方法和改进的射线追踪法分别正演计算大地电磁场和地震走时,结合改进的模拟退火算法,研究实现了电阻率和速度随机分布条件下的大地电磁与地震资料的同步联合反演.对物性界面不完全一致和物性变化剧烈的带地形复杂模型的试验,表明了该方法在精细反演复杂电阻率和速度结构方面的效果,克服了以往研究局限于简单模型的不足.对地震资料品质差的地区开展的实际资料联合反演,表明了方法的适用性,先验信息约束下的联合反演提高了反演精度.     

基于弹性阻抗的储层物性参数预测方法

储层物性参数是储层描述的重要参数,常规的基于贝叶斯理论的储层物性参数反演方法大多是通过反演获得的弹性参数进一步转换而获得物性参数,本文提出一种基于弹性阻抗数据预测储层物性参数的反演方法.该方法主要通过建立可以表征弹性阻抗与储层物性参数之间关系的统计岩石物理模型,联合蒙特卡罗仿真模拟技术,在贝叶斯理论框架的指导下,应用期望最大化算法估计物性参数的后验概率分布,最终实现储层物性参数反演.经过模型测试和实际资料的处理,其结果表明本文提出的方法具有预测精度高,稳定性强,横向连续性好等优点.     

高分辨率非线性储层物性参数反演方法和应用

对于陆相沉积环境下的复杂隐蔽岩性储层,由于观测信息不准确,如信息重叠、信息缺失和噪音污染,以及岩石物理关系模糊等原因,储层横向预测存在不惟一性、不稳定性和不确定性.基于线性假定的常规储层横向预测技术已不适用于复杂隐蔽岩性储层的勘探.本文采用一种非线性储层岩性物性褶积模型,建立波阻抗与孔隙度/泥质含量的函数关系;通过多级结构分解和双向边沿子波检测来刻画复杂岩石物理关系;通过Caianiello褶积神经网络实现确定性反演、统计反演和非线性理论三者有机结合;最后联合应用基于逆算子的反演方法和基于正算子的重建算法实现了综合地质、测井和地震波阻抗信息进行高分辨率储层物性参数反演.非线性储层物性参数反演采用多井约束机制和分频反演方式,在陆相和近海油气勘探资料的实际应用中,取得了明显应用效果.     

Velocity model building from seismic reflection data by full‐waveform inversion

Full‐waveform inversion is re‐emerging as a powerful data‐fitting procedure for quantitative seismic imaging of the subsurface from wide‐azimuth seismic data. This method is suitable to build high‐resolution velocity models provided that the targeted area is sampled by both diving waves and reflected waves. However, the conventional formulation of full‐waveform inversion prevents the reconstruction of the small wavenumber components of the velocity model when the subsurface is sampled by reflected waves only. This typically occurs as the depth becomes significant with respect to the length of the receiver array. This study first aims to highlight the limits of the conventional form of full‐waveform inversion when applied to seismic reflection data, through a simple canonical example of seismic imaging and to propose a new inversion workflow that overcomes these limitations. The governing idea is to decompose the subsurface model as a background part, which we seek to update and a singular part that corresponds to some prior knowledge of the reflectivity. Forcing this scale uncoupling in the full‐waveform inversion formalism brings out the transmitted wavepaths that connect the sources and receivers to the reflectors in the sensitivity kernel of the full‐waveform inversion, which is otherwise dominated by the migration impulse responses formed by the correlation of the downgoing direct wavefields coming from the shot and receiver positions. This transmission regime makes full‐waveform inversion amenable to the update of the long‐to‐intermediate wavelengths of the background model from the wide scattering‐angle information. However, we show that this prior knowledge of the reflectivity does not prevent the use of a suitable misfit measurement based on cross‐correlation, to avoid cycle‐skipping issues as well as a suitable inversion domain as the pseudo‐depth domain that allows us to preserve the invariant property of the zero‐offset time. This latter feature is useful to avoid updating the reflectivity information at each non‐linear iteration of the full‐waveform inversion, hence considerably reducing the computational cost of the entire workflow. Prior information of the reflectivity in the full‐waveform inversion formalism, a robust misfit function that prevents cycle‐skipping issues and a suitable inversion domain that preserves the seismic invariant are the three key ingredients that should ensure well‐posedness and computational efficiency of full‐waveform inversion algorithms for seismic reflection data.     

基于宽范围岩石物性约束的大地电磁和地震联合反演

岩石物性约束是地球物理联合反演重要的实现方式.在以往联合反演研究中,这种约束通常以点对点的映射方式出现,要求经验性的岩石物性关联是相对精确的,无形中提高了岩石物性约束应用于联合反演的条件.基于此,本文结合全局寻优的模拟退火算法,提出了宽范围岩石物性约束技术.该技术将岩石物性约束与模拟退火模型扰动、模型接受准则相结合,实现了空间对空间的映射,将电阻率和速度耦合在一起.文章以MT和地震正则化同步联合反演为例,检验了不同的先验信息条件下的宽范围岩石物性约束技术的适用性.模型试验表明:新技术容易实现,容错性高,可降低"不精确"岩石物性关联信息引入带来的风险,提高岩石物性约束应用的灵活性.     

基于统计岩石物理模型的各向异性页岩储层参数反演

提出了各向异性页岩储层统计岩石物理反演方法.通过统计岩石物理模型建立储层物性参数与弹性参数的定量关系,使用测井数据及井中岩石物理反演结果作为先验信息,将地震阻抗数据定量解释为储层物性参数、各向异性参数的空间分布.反演过程在贝叶斯框架下求得储层参数的后验概率密度函数,并从中得到参数的最优估计值及其不确定性的定量描述.在此过程中综合考虑了岩石物理模型对复杂地下介质的描述偏差和地震数据中噪声对反演不确定性的影响.在求取最大后验概率过程中使用模拟退火优化粒子群算法以提高收敛速度和计算准确性.将统计岩石物理技术应用于龙马溪组页岩气储层,得到储层泥质含量、压实指数、孔隙度、裂缝密度等物性,以及各向异性参数的空间分布及相应的不确定性估计,为页岩气储层的定量描述提供依据.     

Constraining the anisotropy structure of the crust by joint inversion of seismic reflection travel times and wave polarizations

In the context of wide-angle seismic profiling, the determination of the physical properties of the Earth crust, such as the elastic layer depth and seismic velocity, is often performed by inversion of P- and/or S-phases propagation data supplying the geometry of the medium (reflector depths) or any other structural parameter (P- or S-wave velocity, density...). Moreover, the inversion for velocity structure and interfaces is commonly performed using only seismic reflection travel times and/or crustal phase amplitudes in isotropic media. But it is very important to utilize more available information to constrain the non-uniqueness of the solution. In this paper, we present a simultaneous inversion method of seismic reflection travel times and polarizations data of transient elastic waves in stratified media to reconstruct not only layer depth and vertical P-wave velocity but also the anisotropy feature of the crust based on the estimation of the Thomsen’s parameters. We carry out a checking with synthetic data, comparing the inversion results obtained by anisotropic travel-time inversion to the results derived by joint inversion of seismic reflection travel times and polarizations data. The comparison proves that the first procedure leads to biased anisotropic models, while the second one fits nearly the real model. This makes the joint inversion method feasible. Finally, we investigate the geometry, P-wave velocity structure and anisotropy of the crust beneath Southeastern China by applying the proposed inversion method to previously acquired wide-angle seismic data. In this case, the anisotropy signature provides clear evidence that the Jiangshan-Shaoxing fault is the natural boundary between the Yangtze and Cathaysia blocks.     

数据域特征波反射走时反演

地震波的运动学信息(走时、斜率等)通常用于宏观速度建模.针对走时反演方法,一个基本问题是走时拾取或反射时差的估计.对于成像域反演方法,可以通过成像道集的剩余深度差近似计算反射波时差.在数据域中,反射地震观测数据是有限频带信号,如果不能准确地确定子波的起跳时间,难以精确地确定反射波的到达时间.另一方面,如果缺乏关于模型的先验信息,则很难精确测量自地下同一个反射界面的观测数据同相轴和模拟数据同相轴之间的时差.针对走时定义及时差测量问题,首先从叠前地震数据的稀疏表达出发,利用特征波场分解方法,提取反射子波并估计局部平面波的入射和出射射线参数.进一步,为了实现自动和稳定的走时拾取,用震相的包络极值对应的时间定义反射波的到达时,实现了立体数据中间的自动生成.理论上讲,利用包络极值定义的走时大于真实的反射波走时,除非观测信号具有无限带宽(即delta脉冲).然而,走时反演的目的是估计中-大尺度的背景速度结构,因此走时误差导致的速度误差仍然在可以接受的误差范围内.利用局部化传播算子及特征波聚焦成像条件将特征波数据直接投影到地下虚拟反射点,提出了一种新的反射时差估计方法.既避免了周期跳跃现象以及串层等可能性,又消除了振幅因素对时差测量的影响.最后,在上述工作基础之上,提出了一种基于特征波场分解的新型全自动反射走时反演方法(CWRTI).通过对泛函梯度的线性化近似,并用全变差正则化方法提取梯度的低波数部分,实现了背景速度迭代反演.在理论上,无需长偏移距观测数据或低频信息、对初始模型依赖性低且计算效率高,可以为后续的全波形反演提供可靠的初始速度模型.理论和实际资料的测试结果证明了本文方法的有效性.     

Rock skeleton models and seismic porosity inversion

By substituting rock skeleton modulus expressions into Gassmann approximate fluid equation, we obtain a seismic porosity inversion equation. However, conventional rock skeleton models and their expressions are quite different from each other, resuling in different seismic porosity inversion equations, potentially leading to difficulties in correctly applying them and evaluating their results. In response to this, a uniform relation with two adjusting parameters suitable for all rock skeleton models is established from an analysis and comparison of various conventional rock skeleton models and their expressions including the Eshelby-Walsh, Pride, Geertsma, Nur, Keys-Xu, and Krief models. By giving the two adjusting parameters specific values, different rock skeleton models with specific physical characteristics can be generated. This allows us to select the most appropriate rock skeleton model based on geological and geophysical conditions, and to develop more wise seismic porosity inversion. As an example of using this method for hydrocarbon prediction and fluid identification, we apply this improved porosity inversion, associated with rock physical data and well log data, to the ZJ basin. Research shows that the existence of an abundant hydrocarbon reservoir is dependent on a moderate porosity range, which means we can use the results of seismic porosity inversion to identify oil reservoirs and dry or water-saturated reservoirs. The seismic inversion results are closely correspond to well log porosity curves in the ZJ area, indicating that the uniform relations and inversion methods proposed in this paper are reliable and effective.