Comparison of P‐wave attenuation models of wave‐induced flow

Wave‐induced oscillatory fluid flow in the vicinity of inclusions embedded in porous rocks is one of the main causes for P‐wave dispersion and attenuation at seismic frequencies. Hence, the P‐wave velocity depends on wave frequency, porosity, saturation, and other rock parameters. Several analytical models quantify this wave‐induced flow attenuation and result in characteristic velocity–saturation relations. Here, we compare some of these models by analyzing their low‐ and high‐frequency asymptotic behaviours and by applying them to measured velocity–saturation relations. Specifically, the Biot–Rayleigh model considering spherical inclusions embedded in an isotropic rock matrix is compared with White's and Johnson's models of patchy saturation. The modeling of laboratory data for tight sandstone and limestone indicates that, by selecting appropriate inclusion size, the Biot‐Rayleigh predictions are close to the measured values, particularly for intermediate and high water saturations.     

Stochastic inversion of pressure and saturation changes from time-lapse multi component data

Knowledge about saturation and pressure distributions in a reservoir can help in determining an optimal drainage pattern, and in deciding on optimal well designs to reduce risks of blow‐outs and damage to production equipment. By analyzing time‐lapse PP AVO or time‐lapse multicomponent seismic data, it is possible to separate the effects of production related saturation and pressure changes on seismic data. To be able to utilize information about saturation and pressure distributions in reservoir model building and simulation, information about uncertainty in the estimates is useful. In this paper we present a method to estimate changes in saturation and pressure from time‐lapse multicomponent seismic data using a Bayesian estimation technique. Results of the estimations will be probability density functions (pdfs), giving immediate information about both parameter values and uncertainties. Linearized rock physical models are linked to the changes in saturation and pressure in the prior probability distribution. The relationship between the elastic parameters and the measured seismic data is described in the likelihood model. By assuming Gaussian distributed prior uncertainties the posterior distribution of the saturation and pressure changes can be calculated analytically. Results from tests on synthetic seismic data show that this method produces more precise estimates of changes in effective pressure than a similar methodology based on only PP AVO time‐lapse seismic data. This indicates that additional information about S‐waves obtained from converted‐wave seismic data is useful for obtaining reliable information about the pressure change distribution.     

Bayesian inversion of time‐lapse seismic data for the estimation of static reservoir properties and dynamic property changes

Seismic conditioning of static reservoir model properties such as porosity and lithology has traditionally been faced as a solution of an inverse problem. Dynamic reservoir model properties have been constrained by time‐lapse seismic data. Here, we propose a methodology to jointly estimate rock properties (such as porosity) and dynamic property changes (such as pressure and saturation changes) from time‐lapse seismic data. The methodology is based on a full Bayesian approach to seismic inversion and can be divided into two steps. First we estimate the conditional probability of elastic properties and their relative changes; then we estimate the posterior probability of rock properties and dynamic property changes. We apply the proposed methodology to a synthetic reservoir study where we have created a synthetic seismic survey for a real dynamic reservoir model including pre‐production and production scenarios. The final result is a set of point‐wise probability distributions that allow us to predict the most probable reservoir models at each time step and to evaluate the associated uncertainty. Finally we also show an application to real field data from the Norwegian Sea, where we estimate changes in gas saturation and pressure from time‐lapse seismic amplitude differences. The inverted results show the hydrocarbon displacement at the times of two repeated seismic surveys.     

用地震资料估算珊溪水库岩层孔隙度和饱和度

本文首先从室内岩石力学实验数据出发,利用Biot-Gassmann方程和Pride模型建立的岩石骨架与岩石基质体积模量函数关系式求出珊溪水库区岩石基质模量和固结系数,然后分别利用联合地震波走时方程组和多台和达曲线求得P波速度和波速比,最后以流纹斑岩为例,计算了岩石饱和度、孔隙度,并分析了地震中造成的饱和度和孔隙度的变化。结果表明:(1)地震过程中岩石饱和度均大于99%,且大多为100%,即地震中岩石处于水饱和或接近水饱和状态,波速和波速比的变化主要由岩石孔隙度的变化引起。(2)珊溪水库震中区流纹斑岩孔隙度的上限值为6.6%~15.5%,下限值为3.6%~4.2%。下限值与地震前由实验室测得的孔隙度相近。如果实验室测得的流纹斑岩孔隙度是其初始值,则地震中岩石孔隙度增大了3.2%~12.09%。(3)2008年1月地震以后震中区岩石孔隙度逐渐闭合,直到2014年8月孔隙度开始迅速增大,9月15日起原震区再次发生一组新的地震活动,震群活动前岩石出现了扩容现象。     

Monte-Carlo Bayesian look-ahead inversion of walkaway vertical seismic profiles

We describe a method to invert a walkaway vertical seismic profile (VSP) and predict elastic properties (P‐wave velocity, S‐wave velocity and density) in a layered model looking ahead of the deepest receiver. Starting from Bayes's rule, we define a posterior distribution of layered models that combines prior information (on the overall variability of and correlations among the elastic properties observed in well logs) with information provided by the VSP data. This posterior distribution of layered models is sampled by a Monte‐Carlo method. The sampled layered models agree with prior information and fit the VSP data, and their overall variability defines the uncertainty in the predicted elastic properties. We apply this technique first to a zero‐offset VSP data set, and show that uncertainty in the long‐wavelength P‐wave velocity structure results in a sizable uncertainty in the predicted elastic properties. We then use walkaway VSP data, which contain information on the long‐wavelength P‐wave velocity (in the reflection moveout) and on S‐wave velocity and density contrasts (in the change of reflectivity with offset). The uncertainty of the look‐ahead prediction is considerably decreased compared with the zero‐offset VSP, and the predicted elastic properties are in good agreement with well‐log measurements.     

砂岩储层AVO特征影响因素的不确定性研究

传统的地震AVO正演研究多采用参数固定的岩石物理模型,而实际地层属性参数在勘探范围内具有不确定性.本研究以目标地层岩芯样品的实验室测试数据为基础,通过样品孔隙度和干燥状态下纵、横波阻抗的高度线性关系对岩石物理模型进行了简化,并结合实验测量和测井解释建立了主要模型参数的概率密度函数.采用Monte-Carlo随机正演和G...     

Bayesian inversion of joint SH seismic and seismoelectric data to infer glacier system properties

In glacial studies, properties such as glacier thickness and the basement permeability and porosity are key to understand the hydrological and mechanical behaviour of the system. The seismoelectric method could potentially be used to determine key properties of glacial environments. Here we analytically model the generation of seismic and seismoelectric signals by means of a shear horizontal seismic wave source on top of a glacier overlying a porous basement. Considering a one-dimensional setting, we compute the seismic waves and the electrokinetically induced electric field. We then analyse the sensitivity of the seismic and electromagnetic data to relevant model parameters, namely depth of the glacier bottom, porosity, permeability, shear modulus and saturating water salinity of the glacier basement. Moreover, we study the possibility of inferring these key parameters from a set of very low noise synthetic data, adopting a Bayesian framework to pay particular attention to the uncertainty of the model parameters mentioned above. We tackle the resolution of the probabilistic inverse problem with two strategies: (1) we compute the marginal posterior distributions of each model parameter solving multidimensional integrals numerically and (2) we use a Markov chain Monte Carlo algorithm to retrieve a collection of model parameters that follows the posterior probability density function of the model parameters, given the synthetic data set. Both methodologies are able to obtain the marginal distributions of the parameters and estimate their mean and standard deviation. The Markov chain Monte Carlo algorithm performs better in terms of numerical stability and number of iterations needed to characterize the distributions. The inversion of seismic data alone is not able to constrain the values of porosity and permeability further than the prior distribution. In turn, the inversion of the electric data alone, and the joint inversion of seismic and electric data are useful to constrain these parameters as well as other glacial system properties. Furthermore, the joint inversion reduces the uncertainty of the model parameters estimates and provides more accurate results.     

含流体砂岩地震波频散实验研究

为了研究孔隙流体对不同渗透率岩石地震波速度的影响,在实验室利用跨频带岩石弹性参数测试系统得到了应变幅值10-6的2~2000Hz频段下的地震波速度和1 MHz频率下的超声波速度,利用差分共振声谱法得到了频率600Hz岩石干燥和完全饱水情况下岩石声学参数.实验表明,在低饱和度下,致密砂岩在地震和超声频段下没有明显的频散;在高饱和度下纵波速度的频散变得明显.从干燥到完全水饱和条件,不同频率测量的致密砂岩的体积模量随岩石孔隙度增高而降低,且体积模量的变化量受岩石微观孔隙结构的影响较大.高孔、高渗砂岩无论在低含水度下还是在高含水饱和度下频散微弱,并且在地震频段下围压对于岩石纵横波速度的影响要大于频率的影响.高孔、高渗砂岩和致密砂岩不同含水饱和度下的频散差异可应用于储层预测,油气检测等方面,同时该研究可以更好地帮助理解岩石的黏弹性行为,促进岩石物理频散理论的发展,提高地震解释的精度.     

Water Table Uncertainties due to Uncertainties in Structure and Properties of an Unconfined Aquifer

We consider two sources of geology‐related uncertainty in making predictions of the steady‐state water table elevation for an unconfined aquifer. That is the uncertainty in the depth to base of the aquifer and in the hydraulic conductivity distribution within the aquifer. Stochastic approaches to hydrological modeling commonly use geostatistical techniques to account for hydraulic conductivity uncertainty within the aquifer. In the absence of well data allowing derivation of a relationship between geophysical and hydrological parameters, the use of geophysical data is often limited to constraining the structural boundaries. If we recover the base of an unconfined aquifer from an analysis of geophysical data, then the associated uncertainties are a consequence of the geophysical inversion process. In this study, we illustrate this by quantifying water table uncertainties for the unconfined aquifer formed by the paleochannel network around the Kintyre Uranium deposit in Western Australia. The focus of the Bayesian parametric bootstrap approach employed for the inversion of the available airborne electromagnetic data is the recovery of the base of the paleochannel network and the associated uncertainties. This allows us to then quantify the associated influences on the water table in a conceptualized groundwater usage scenario and compare the resulting uncertainties with uncertainties due to an uncertain hydraulic conductivity distribution within the aquifer. Our modeling shows that neither uncertainties in the depth to the base of the aquifer nor hydraulic conductivity uncertainties alone can capture the patterns of uncertainty in the water table that emerge when the two are combined.     

Geoelectrical and seismic prospections in hydrogeology: Model and master curves for the evaluation of porosity and water saturation

The prevailing purpose of geoelectrical exploration is the location of acquifers, as resistivity is strongly sensitive to the presence of water. Through this method valuable information on the structure and volume of storage rocks may be acquired. However, the evaluation of saturation and porosity, which plays a strong role in the estimation of hydraulic parameters, is hitherto affected by a large uncertainty. Therefore, it is necessary to carry out expensive and often numerous drillings, in addition to the calibration ones. In this paper we argue how the uncertainty can be substantially reduced by carrying out a joint seismic and geoelectrical prospection.to profitably utilize the results of a joint seismic and geoelectrical survey, a model is proposed in which the geophysical characteristics of all the phases possibly present in underground rocks, i.e., matrix, clay, water and air (whose percentages give porosity and saturation degree of an acquifer) are taken into account. The four phases are considered contiguous, in parallel as regards the electrical conductivity and in series as regards the propagation of elastic waves. On the basis of the formulas related to the model, theoretical curves for porosity, degree of saturation and percentage of clay have been obtained, which enable us to calculate these parameters.As a test of the suggested methodology, porosity and saturation have been evaluated in an area of the Campi Flegrei Caldera (Napoli) of which porosity data were available after core drillings. The test was performed by practising a joint electrical and seismic prospection using the more customary and less expensive techniques of Vertical Electrical Sounding (VES) and Seismic Refraction. Our data permit us to produce porosity and saturation maps for two depths; the comparison between the porosity, derived from the maps in the points where core drillings have been made, and the porosity values found on the cores, shows a good agreement for the more superficial layer; for the greater depth, we derived lower values of porosity, probably due to difficulties of laboratory reproduction of thein situ condition of the cores. These results suggest that our model has value in water research.     

Forced imbibition into a limestone: measuring P‐wave velocity and water saturation dependence on injection rate

Quantitative interpretation of time‐lapse seismic data requires knowledge of the relationship between elastic wave velocities and fluid saturation. This relationship is not unique but depends on the spatial distribution of the fluid in the pore‐space of the rock. In turn, the fluid distribution depends on the injection rate. To study this dependency, forced imbibition experiments with variable injection rates have been performed on an air‐dry limestone sample. Water was injected into a cylindrical sample and was monitored by X‐Ray Computed Tomography and ultrasonic time‐of‐flight measurements across the sample. The measurements show that the P‐wave velocity decreases well before the saturation front approaches the ultrasonic raypath. This decrease is followed by an increase as the saturation front crosses the raypath. The observed patterns of the acoustic response and water saturation as functions of the injection rate are consistent with previous observations on sandstone. The results confirm that the injection rate has significant influence on fluid distribution and the corresponding acoustic response. The complexity of the acoustic response —‐ that is not monotonic with changes in saturation, and which at the same saturation varies between hydrostatic conditions and states of dynamic fluid flow – may have implications for the interpretation of time‐lapse seismic responses.     

Quantitative estimation of water storage and residence time in the epikarst with time‐lapse refraction seismic

The hydrodynamic characterization of the epikarst, the shallow part of the unsaturated zone in karstic systems, has always been challenging for geophysical methods. This work investigates the feasibility of coupling time‐lapse refraction seismic data with petrophysical and hydrologic models for the quantitative determination of water storage and residence time at shallow depth in carbonate rocks. The Biot–Gassmann fluid substitution model describing the seismic velocity variations with water saturation at low frequencies needs to be modified for this lithology. I propose to include a saturation‐dependent rock‐frame weakening to take into account water–rock interactions. A Bayesian inversion workflow is presented to estimate the water content from seismic velocities measured at variable saturations. The procedure is tested first with already published laboratory measurements on core samples, and the results show that it is possible to estimate the water content and its uncertainty. The validated procedure is then applied to a time‐lapse seismic study to locate and quantify seasonal water storage at shallow depth along a seismic profile. The residence time of the water in the shallow layers is estimated by coupling the time‐lapse seismic measurements with rainfall chronicles, simple flow equations, and the petrophysical model. The daily water input computed from the chronicles is used to constraint the inversion of seismic velocities for the daily saturation state and the hydrodynamic parameters of the flow model. The workflow is applied to a real monitoring case, and the results show that the average residence time of the water in the epikarst is generally around three months, but it is only 18 days near an infiltration pathway. During the winter season, the residence times are three times shorter in response to the increase in the effective rainfall.     

基于自适应杂交遗传算法的CO_2地质封存的储层参数反演研究

二氧化碳地质封存是减少温室气体排放和减缓温室效应的重要手段.二氧化碳封存的一个重要组成部分是地震监测,即用地震的方法监测封存后的二氧化碳的分布变化.为了实现这个目标,需要建立储层参数与地震性质之间的关系(岩石物理模型)和从地震监测数据中反演获得储层流体的饱和度等参数.首先,本文以Biot理论为基础,结合多相流模型研究了多个物理参数(孔隙度、二氧化碳饱和度、温度和压力等)对同时含有二氧化碳和水的孔隙介质的波速和衰减等属性的影响.结果表明:孔隙度和二氧化碳饱和度对岩石的频散和衰减属性影响强烈,而温度和压力通过孔隙流体性质对岩石的波速产生影响.然后,本文基于含多相流的Biot理论,应用抗干扰能力强、且具有更好的局部搜索能力和抗早熟能力的自适应杂交遗传算法对实际数据进行了反演研究.对岩心实验数据的反演研究表明了算法的有效性,而且表明含多相流的Biot理论能够很好地解释水和二氧化碳饱和岩石的波速特征.最后,我们将自适应杂交遗传算法应用于实际封存项目的地震监测数据,获得了封存后不同时期的二氧化碳饱和度,达到了用地震方法监测二氧化碳分布的目的.     

基于微增模型的海洋可控源电磁法三维非结构化矢量有限元数值模拟

为了分析海洋中含金属矿的储油气砂层的成分、结构对于海洋可控源电磁场的影响特征,引入多相微增等效介质模型,结合非结构化网格实现了海洋可控源电磁三维矢量有限元正演.首先对多相微增模型进行了介绍,并分析不同参数影响下的等效电导率变化特征.而后,详细推导了频率域可控源电磁法非结构化矢量有限元方程.接着,利用预处理的IDR （s）迭代算法求解线性方程组.最后设计典型的海洋地电模型,通过正演计算,验证了本文算法的正确性和有效性,同时研究了海洋储油砂层中的金属矿的含量、孔隙度、含水饱和度等参数对于可控源电磁场响应特征的影响.     

Seismic and electromagnetic controlled-source interferometry in dissipative media

Seismic interferometry deals with the generation of new seismic responses by crosscorrelating existing ones. One of the main assumptions underlying most interferometry methods is that the medium is lossless. We develop an ‘interferometry‐by‐deconvolution’ approach which circumvents this assumption. The proposed method applies not only to seismic waves, but to any type of diffusion and/or wave field in a dissipative medium. This opens the way to applying interferometry to controlled‐source electromagnetic (CSEM) data. Interferometry‐by‐deconvolution replaces the overburden by a homogeneous half space, thereby solving the shallow sea problem for CSEM applications. We demonstrate this at the hand of numerically modeled CSEM data.     

转换波叠前横波速度反演

摘要 地震波速度对地震资料偏移成像、岩性和岩相解释以及储层预测,均起着非常重要的作用. 在储层预测中,需要获得横波层速度信息,以减少仅用纵波速度在区分岩性和孔隙中流体类型以及含气饱和度方面的不确定性. 基于Zoeppritz方程组,提出了数值求解和速度扫描方法,对叠前转换波资料求取横波层速度. 理论模型和实际转换波资料的反演结果, 均表明该方法的效果较好.      

Modelling elastic properties of impure chalk from South Arne Field, North Sea

In impure chalk, the elastic moduli are not only controlled by porosity but also by contact‐cementation, resulting in relatively large moduli for a given porosity, and by admixtures of clay and fine silica, which results in relatively small moduli for a given porosity. Based on a concept of solids suspended in pore fluids as well as composing the rock frame, we model P‐wave and S‐wave moduli of dry and wet plug samples by an effective‐medium Hashin–Shtrikman model, using chemical, mineralogical and textural input. For a given porosity, the elastic moduli correspond to a part of the solid (the iso‐frame value) forming the frame of an Upper Hashin–Shtrikman bound, whereas the remaining solid is modelled as suspended in the pore fluid. The iso‐frame model is thus a measure of the pore‐stiffness or degree of cementation of the chalk. The textural and mineralogical data may be assessed from logging data on spectral gamma radiation, density, sonic velocity and water saturation in a hydrocarbon zone, whereas the iso‐frame value of a chalk may be assessed from the density and acoustic P‐wave logs alone. The iso‐frame concept may thus be directly used in conventional log‐analysis and is a way of incorporating sonic‐logging data. The Rigs‐1 and Rigs‐2 wells in the South Arne field penetrate the chalk at the same depth but differ in porosity and in water saturation although almost the entire chalk interval has irreducible water saturation. Our model, combined with petrographic data, indicates that the difference in porosity is caused by a higher degree of pore‐filling cementation in Rigs‐1. Petrographic data indicate that the difference in water saturation is caused by a higher content of smectite in the pores of Rigs‐1. In both wells, we find submicron‐size diagenetic quartz.     

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.     

Inversion of shear wave interval velocity on prestack converted wave data

Seismic velocity is important to migration of seismic data,interpretation of lithology and lithofacies as well asprediction of reservoir.The information of shear wave velocity is required to reduce the uncertainty for discrimi-nating lithology,identifying fluid type in porous material and calculating gas saturation in reservoir prediction.Based on Zoeppritz equations,a numeral and scanning method was proposed in this paper.Shear wave velocitycan be calculated with prestack converted wave data.The effects were demonstrated by inversion of theoreticaland real seismic data.     

Joint AVO inversion, wavelet estimation and noise-level estimation using a spatially coupled hierarchical Bayesian model

The main objective of the AVO inversion is to obtain posterior distributions for P-wave velocity, S-wave velocity and density from specified prior distributions, seismic data and well-log data. The inversion problem also involves estimation of a seismic wavelet and the seismic-noise level. The noise model is represented by a zero mean Gaussian distribution specified by a covariance matrix. A method for joint AVO inversion, wavelet estimation and estimation of the noise level is developed in a Bayesian framework. The stochastic model includes uncertainty of both the elastic parameters, the wavelet, and the seismic and well-log data. The posterior distribution is explored by Markov-chain Monte-Carlo simulation using the Gibbs' sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The use of a coloured seismic-noise model resulted in about 10% lower uncertainties for the P-wave velocity, S-wave velocity and density compared with a white-noise model. The uncertainty of the estimated wavelet is low. In the Heidrun example, the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results.