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In this work, an experimental study was carried out with the aim of reconciling static and dynamic stiffness of Opalinus Clay. The static and dynamic stiffness of core plugs from a shaly and a sandy facies of Opalinus Clay were characterized at two different stress states. The measurements included undrained quasi-static loading–unloading cycles from which the static stiffness was derived, dynamic stiffness measurement at seismic frequencies (0.5–150 Hz) and ultrasonic velocity measurements (500 kHz) probing the dynamic stiffness at ultrasonic frequencies. The experiments were carried out in a special triaxial low-frequency cell. The obtained results demonstrate that the difference between static and dynamic stiffness is due to both dispersion and non-elastic effects: Both sandy and shaly facies of Opalinus Clay exhibit large dispersion, that is, a large frequency dependence of dynamic stiffness and acoustic velocities. Especially dynamic Young's moduli exhibit very high dispersion; between seismic and ultrasonic frequencies they may change by more than a factor 2. P-wave velocities perpendicular to bedding are by more than 200 m/s higher at ultrasonic frequencies than at seismic frequencies. The static undrained stiffness of both sandy and shaly facies is strongly influenced by non-elastic effects, resulting in significant softening during both loading and unloading with increasing stress amplitude. The zero-stress extrapolated static undrained stiffness, however, reflects the purely elastic response and agrees well with the dynamic stiffness at seismic frequency.  相似文献   

3.
We use residual moveouts measured along continuous full azimuth reflection angle gathers, in order to obtain effective horizontal transversely isotropic model parameters. The angle gathers are generated through a special angle domain imaging system, for a wide range of reflection angles and full range of phase velocity azimuths. The estimation of the effective model parameters is performed in two stages. First, the background horizontal transversely isotropic (HTI)/vertical transversely isotropic (VTI) layered model is used, along with the values of reflection angles, for converting the measured residual moveouts (or traveltime errors) into azimuthally dependent normal moveout (NMO) velocities. Then we apply a digital Fourier transform to convert the NMO velocities into azimuthal wavenumber domain, in order to obtain the effective HTI model parameters: vertical time, vertical compression velocity, Thomsen parameter delta and the azimuth of the medium axis of symmetry. The method also provides a reliability criterion of the HTI assumption. The criterion shows whether the medium possesses the HTI type of symmetry, or whether the azimuthal dependence of the residual traveltime indicates to a more complex azimuthal anisotropy. The effective model used in this approach is defined for a 1D structure with a set of HTI, VTI and isotropic layers (with at least one HTI layer). We describe and analyse the reduction of a multi‐layer structure into an equivalent effective HTI model. The equivalent model yields the same NMO velocity and the same offset azimuth on the Earth's surface as the original layered structure, for any azimuth of the phase velocity. The effective model approximates the kinematics of an HTI/VTI layered structure using only a few parameters. Under the hyperbolic approximation, the proposed effective model is exact.  相似文献   

4.
桂俊川  马天寿  陈平 《地球物理学报》2020,63(11):4188-4204

在龙马溪页岩微观物性特征分析的基础上,综合利用测井解释、微观测试分析资料,建立了一种适用于龙马溪页岩的横观各向同性岩石物理模型,该模型建模过程:将各向异性SCA和DEM模型联合模拟得到的黏土和干酪根混合物作为背景介质;采用SCA模型对脆性矿物混合物进行模拟,利用各向异性DEM将脆性矿物混合物添加到背景介质;进一步将空孔隙添加到页岩基质,并利用Brown-Korringa模型进行各向异性条件下的流体替换,从而得到横观各向同性页岩岩石物理模型.通过对四川盆地A井龙马溪页岩进行岩石物理建模分析,计算了孔隙纵横比、纵横波速、各向异性系数和弹性参数,检验了模型的准确性.研究结果表明:矿物颗粒和孔隙纵横比是影响模型精度的关键参数,黏土和干酪根颗粒纵横比为0.05,图像识别获得的脆性矿物颗粒纵横比主要分布于0.45~1.0(集中分布于0.5~0.85),横波波速反演获得的孔隙纵横比主要分布于0.1~0.3(平均值约为0.22);模型预测和实测纵波波速之间误差为-2.40%~2.21%(平均绝对误差仅1.20%),预测和实测横波波速之间误差为-1.93%~1.42%(平均绝对误差仅0.64%),证实了本文模型的准确性和精度.本文模型能够准确计算页岩5个独立的刚度系数,为页岩弹性参数、声波波速、各向异性和脆性分析提供了有效手段,也为后续地球物理和工程地质参数分析提供了重要依据.

  相似文献   

5.
桂俊川  马天寿  陈平 《地球物理学报》1954,63(11):4188-4204
在龙马溪页岩微观物性特征分析的基础上,综合利用测井解释、微观测试分析资料,建立了一种适用于龙马溪页岩的横观各向同性岩石物理模型,该模型建模过程:将各向异性SCA和DEM模型联合模拟得到的黏土和干酪根混合物作为背景介质;采用SCA模型对脆性矿物混合物进行模拟,利用各向异性DEM将脆性矿物混合物添加到背景介质;进一步将空孔隙添加到页岩基质,并利用Brown-Korringa模型进行各向异性条件下的流体替换,从而得到横观各向同性页岩岩石物理模型.通过对四川盆地A井龙马溪页岩进行岩石物理建模分析,计算了孔隙纵横比、纵横波速、各向异性系数和弹性参数,检验了模型的准确性.研究结果表明:矿物颗粒和孔隙纵横比是影响模型精度的关键参数,黏土和干酪根颗粒纵横比为0.05,图像识别获得的脆性矿物颗粒纵横比主要分布于0.45~1.0(集中分布于0.5~0.85),横波波速反演获得的孔隙纵横比主要分布于0.1~0.3(平均值约为0.22);模型预测和实测纵波波速之间误差为-2.40%~2.21%(平均绝对误差仅1.20%),预测和实测横波波速之间误差为-1.93%~1.42%(平均绝对误差仅0.64%),证实了本文模型的准确性和精度.本文模型能够准确计算页岩5个独立的刚度系数,为页岩弹性参数、声波波速、各向异性和脆性分析提供了有效手段,也为后续地球物理和工程地质参数分析提供了重要依据.  相似文献   

6.
Anisotropy in subsurface geological models is primarily caused by two factors: sedimentation in shale/sand layers and fractures. The sedimentation factor is mainly modelled by vertical transverse isotropy (VTI), whereas the fractures are modelled by a horizontal transversely isotropic medium (HTI). In this paper we study hyperbolic and non‐hyperbolic normal reflection moveout for a package of HTI/VTI layers, considering arbitrary azimuthal orientation of the symmetry axis at each HTI layer. We consider a local 1D medium, whose properties change vertically, with flat interfaces between the layers. In this case, the horizontal slowness is preserved; thus, the azimuth of the phase velocity is the same for all layers of the package. In general, however, the azimuth of the ray velocity differs from the azimuth of the phase velocity. The ray azimuth depends on the layer properties and may be different for each layer. In this case, the use of the Dix equation requires projection of the moveout velocity of each layer on the phase plane. We derive an accurate equation for hyperbolic and high‐order terms of the normal moveout, relating the traveltime to the surface offset, or alternatively, to the subsurface reflection angle. We relate the azimuth of the surface offset to its magnitude (or to the reflection angle), considering short and long offsets. We compare the derived approximations with analytical ray tracing.  相似文献   

7.
Acoustic transversely isotropic models are widely used in seismic exploration for P‐wave processing and analysis. In isotropic acoustic media only P‐wave can propagate, while in an acoustic transversely isotropic medium both P and S waves propagate. In this paper, we focus on kinematic properties of S‐wave in acoustic transversely isotropic media. We define new parameters better suited for S‐wave kinematics analysis. We also establish the travel time and relative geometrical spreading equations and analyse their properties. To illustrate the behaviour of the S‐wave in multi‐layered acoustic transversely isotropic media, we define the Dix‐type equations that are different from the ones widely used for the P‐wave propagation.  相似文献   

8.
The elastic moduli and anisotropy of organic-rich rocks are of great importance to geoengineering and geoprospecting of oil and gas reservoirs. In this paper, we probe into the static and dynamic moduli of the Ghareb–Mishash chalk through laboratory measurements and new analytical approaches. We define a new anisotropy parameter, ‘hydrostatic strain ratio’ (Ω), which describes the differential contraction of anisotropic rocks consequent to hydrostatic compression. Ω depends on the C11, C12, C13 and C33 stiffness constants of a transversely isotropic material, and therefore enables a unique insight into the anisotropic behaviour of TI rocks. Ω proves more sensitive to anisotropy within the weak anisotropy range, when compared with Thomsen's ε and γ parameters. We use Ω to derive static moduli from triaxial compression tests performed on a single specimen. This is done by novel employment of a hydrostatic-deviatoric combination for transversely isotropic elastic stiffnesses. Dynamic moduli are obtained from acoustic velocities measurements. We find that the bedding-normal velocities are described well by defining kerogen as the load-supporting matrix in a Hashin–Shtrikman model (‘Hashin–Shtrikman (HS) kerogen’). The dynamic moduli of the Ghareb–Mishash chalk in dry conditions are significantly higher than the static moduli. The dynamic/static moduli ratio decreases from ∼4 to ∼2 with increasing kerogen content. Both the static and dynamic moduli decrease significantly with increasing porosity and kerogen content. The effect of porosity on them is two times stronger than the effect of kerogen.  相似文献   

9.
Although most rocks are complex multi‐mineralic aggregates, quantitative interpretation workflows usually ignore this complexity and employ Gassmann equation and effective stress laws that assume a micro‐homogeneous (mono‐mineralic) rock. Even though the Gassmann theory and effective stress concepts have been generalized to micro‐inhomogeneous rocks, they are seldom if at all used in practice because they require a greater number of parameters, which are difficult to measure or infer from data. Furthermore, the magnitude of the effect of micro‐heterogeneity on fluid substitution and on effective stress coefficients is poorly understood. In particular, it is an open question whether deviations of the experimentally measurements of the effective stress coefficients for drained and undrained elastic moduli from theoretical predictions can be explained by the effect of micro‐heterogeneity. In an attempt to bridge this gap, we consider an idealized model of a micro‐inhomogeneous medium: a Hashin assemblage of double spherical shells. Each shell consists of a spherical pore surrounded by two concentric spherical layers of two different isotropic minerals. By analyzing the exact solution of this problem, we show that the results are exactly consistent with the equations of Brown and Korringa (which represent an extension of Gassmann's equation to micro‐inhomogeneous media). We also show that the effective stress coefficients for bulk volume α, for porosity n? and for drained and undrained moduli are quite sensitive to the degree of heterogeneity (contrast between the moduli of the two mineral components). For instance, while for micro‐homogeneous rocks the theory gives n? = 1, for strongly micro‐inhomogenous rocks, n? may span a range of values from –∞ to ∞ (depending on the contrast between moduli of inner and outer shells). Furthermore, the effective stress coefficient for pore volume (Biot–Willis coefficient) α can be smaller than the porosity ?. Further studies are required to understand the applicability of the results to realistic rock geometries.  相似文献   

10.
Pore-pressure depletion causes changes in the triaxial stress state. Pore-pressure depletion in a flat reservoir, for example, can be reasonably approximated as uniaxial compaction, in which the horizontal effective stress change is smaller than the vertical effective stress. Furthermore, the stress sensitivity of velocities can be angle-dependent. Therefore, time-lapse changes in reservoir elastic anisotropy are expected as a consequence of production, which can complicate the interpretation of the 4D seismic response. The anisotropic 4D seismic response caused by pore-pressure depletion was investigated using existing core velocity measurements. To make a direct comparison between the anisotropic 4D seismic response and the isotropic response based only on vertical velocities, pseudoisotropic elastic properties were utilized, and the two responses were compared in terms of a dynamic rock physics template. A comparison of the dynamic rock physics templates indicates that time-lapse changes in reservoir elastic anisotropy have a noticeable impact on the interpretation of 4D seismic data. Changes in anisotropy as a result of pore-pressure depletion cause a time-lapse amplitude variation with offset response as if there is a reduction in VP/VS (i.e., pseudoisotropic VP/VS decreases), although the vertical VP/VS increases. The impact of time-lapse changes in anisotropy on the amplitude variation with offset gradient was also investigated, and the time-lapse anisotropy was found to enhance changes in the amplitude variation with offset gradient for a given case.  相似文献   

11.
Burial stress on a sediment or sedimentary rock is relevant for predicting compaction or failure caused by changes in, e.g., pore pressure in the subsurface. For this purpose, the stress is conventionally expressed in terms of its effect: “the effective stress” defined as the consequent elastic strain multiplied by the rock frame modulus. We cannot measure the strain directly in the subsurface, but from the data on bulk density and P‐wave velocity, we can estimate the rock frame modulus and Biot's coefficient and then calculate the “effective vertical stress” as the total vertical stress minus the product of pore pressure and Biot's coefficient. We can now calculate the elastic strain by dividing “effective stress” with the rock frame modulus. By this procedure, the degree of elastic deformation at a given time and depth can be directly expressed. This facilitates the discussion of the deformation mechanisms. The principle is illustrated by comparing carbonate sediments and sedimentary rocks from the North Sea Basin and three oceanic settings: a relatively shallow water setting dominated by coarse carbonate packstones and grainstones and two deep water settings dominated by fine‐grained carbonate mudstones and wackestones.  相似文献   

12.
Understanding how physical properties and seismic signatures of present day rocks are related to ancient geological processes is important for enhanced reservoir characterization. In this paper, we have studied this relationship for the Kobbe Formation sandstone in the Barents Sea. These rocks show anomalous low shear velocities and high VP/VS ratios, which does not agree well with conventional rock physics models for moderately to well consolidated sandstones. These sandstones have been buried relatively deeply and subsequently uplifted 1–2 km. We compared well log data of the Kobbe sandstone with velocity–depth trends modelled by integrating basin modelling principles and rock physics. We found that more accurate velocity predictions were obtained when first honouring mechanical and chemical compaction during burial, followed by generation of micro-cracks during uplift. We suspect that these micro-cracks are formed as overburden is eroded, leading to changes in the subsurface stress-field. Moreover, the Kobbe Formation is typically heterogeneous and characterized by structural clays and mica that can reduce the rigidity of grain contacts. By accounting for depositional and burial history, our velocity predictions become more consistent with geophysical observables. Our approach yields more robust velocity predictions, which are important in prospect risking and net erosion estimates.  相似文献   

13.
李磊  郝重涛 《地球物理学报》2011,54(11):2819-2830
Thomsen提出的横向各向同性(TI)介质各向异性参数(α0、β0、ε、δ、γ)是各向异性理论研究和实际资料处理中的常用参数,Thomsen参数的取值必须符合物理学定律和实际地学情况,随意的取值可能导致无意义乃至错误的结果.本文根据热力学定律和弹性常数的物理意义,结合大量的实测数据,提出常见TI介质的Thomsen参数需要满足以下约束条件:1/4f=1-β02/α02ε>-f/2; 1/2f-1δf-1); -1/2γε)/4(1-f)-1/2.Thomsen参数ε、δ、γ的取值区间主要受P、S波参考速度比β0/α0的约束,其值可正可负,实测参数中ε和γ正多负少;δ、γ、β0/α0的取值范围都有上下界,而ε没有上限;γ与ε正相关且取值上限受到ε的限制;ε、γ与δ之间不存在明显的约束.鉴于椭圆各向异性介质和薄互层等效TI介质在实际应用中的普遍性,专门给出了这两种介质各向异性参数的附加约束条件.一些在实际资料中可观测到的P波特殊偏振方向和SV波三叉现象也能为各向异性参数提供额外的约束.之后,我们将TI介质弹性常数和各向异性参数的约束条件扩展到对正交各向异性介质弹性常数和各向异性参数的约束.本文提出的各向异性参数约束条件简单实用,为各向异性理论研究和数值模拟中参数的选择提供依据,为实际资料的各向异性参数反演提供约束,既能避免出现无物理意义的研究结果,又能加速反演的搜索过程,提高生产效率,具有理论指导意义和实际应用价值.  相似文献   

14.
In this paper we propose a method for the characterization of naturally fractured reservoirs by quantitative integration of seismic and production data. The method is based on a consistent theoretical frame work to model both effective hydraulic and elastic properties of fractured porous media and a (non‐linear) Bayesian method of inversion that provides information about uncertainties as well as mean (or maximum likelihood) values. We model a fractured reservoir as a porous medium containing a single set of vertical fractures characterized by an unknown fracture density, azimuthal orientation and aperture. We then look at the problem of fracture parameter estimation as a non‐linear inverse problem and try to estimate the unknown fracture parameters by joint inversion of seismic amplitude versus angle and azimuth data and dynamic production data. Once the fracture parameters have been estimated the corresponding effective stiffness and permeability tensors can be estimated using consistent models. A synthetic example is provided to clearly explain and test the workflow. It shows that seismic and production data complement each other, in the sense that the seismic data resolve a non‐uniqueness in the fracture orientation and the production data help to recover the true fracture aperture and permeability, because production data are more sensitive to the fracture aperture than the seismic data.  相似文献   

15.
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.  相似文献   

16.
Differential effective medium theory has been applied to determine the elastic properties of porous media. The ordinary differential equations for bulk and shear moduli are coupled and it is more difficult to obtain accurate analytical formulae about the moduli of dry porous rock. In this paper, in order to decouple these equations we first substitute an analytical approximation for the dry‐rock modulus ratio into the differential equation and derive analytical solutions of the bulk and shear moduli for dry rock with three specific pore shapes: spherical pores, needle‐shaped pores and penny‐shaped cracks. Then, the validity of the analytical approximations is tested by integrating the full differential effective medium equation numerically. The analytical formulae give good estimates of the numerical results over the whole porosity range for the cases of the three given pore shapes. These analytical formulae can be further simplified under the assumption of small porosity. The simplified formulae for spherical pores are the same as Mackenzie's equations. The analytical formulae are relatively easy to analyse the relationship between the elastic moduli and porosity or pore shapes and can be used to invert some rock parameters such as porosity or pore aspect ratio. The predictions of the analytical formulae for experimental data show that the formulae for penny‐shaped cracks are suitable to estimate the elastic properties of micro‐crack rock such as granite, they can be used to estimate the crack aspect ratio while the crack porosity is known and also to estimate the crack porosity evolution with pressure if the crack aspect ratio is given.  相似文献   

17.
We investigate the dependence of quasi P-wave phase velocity propagating in orthotropic media on particular elasticity parameters. Specifically, due to mathematical facilitation, we consider the squared-velocity difference, , resulted from propagation in two mutually perpendicular symmetry planes. In the context of the effective medium theory, may be viewed as a parameter evaluating the influence of cracks – embedded in the background medium – parallel to one or both aforementioned planes. Our investigation is both theoretical and numerical. Based on Christoffel's equations, we propose two accurate approximations of . Due to them, we interpret the aforementioned squared-velocity difference as being twice more dependent on , than on . To describe the magnitude of the dependence, we consider the proportions between the partial derivatives of . Further, it occurs that is influenced by the ratio of vertically propagating quasi P-wave to vertically propagating quasi S-wave. Anomalously high might be caused by the low P/S ratio, which in turn can be an indicator of the presence of gas in natural fractures or aligned porosity. Also, we carry out numerical sensitivity study, according to which is approximately twice more dependent on than on , twice more sensitive to than to , and equally dependent on as on . The dependence on and can be neglected, especially for small phase angles. We verify the approximations and perform the sensitivity study, using eight examples of the elasticity tensors.  相似文献   

18.
Compressional and shear-wave velocities have been measured and a novel approach using digital processing employed to study wave attenuation for brine- and gas- saturated sandstones, over a range of effective stresses from 5 to 60 MPa. Also measured were the complex conductivity in the brine-saturated state and permeability in the gas-saturated state over the same range of stresses as for the velocity measurements. Broadband ultrasonic pulses of P- and orthogonally polarized S-waves in the frequency range 0.3–0.8 MHz are transmitted through the specimen to be characterized for comparison with a reference (aluminium) having low attenuation. The attenuation is calculated in terms of the quality factor Q from the Fourier spectral ratios, using the frequency spectral ratios technique. The corrections necessary for the effects of diffraction due to the finite size of the ultrasonic transducers have been carried out for the case of measurements under lower confining stress. To interpret the laboratory measured velocity and attenuation data under the physical conditions of this study and to estimate the effects of pore structure, numerical modelling of velocities and attenuation as functions of the confining stress have been performed, based on the MIT model. Theoretical models based on several hypothesized attenuation mechanisms are considered in relation to laboratory data of the effects of confining pressure, fluid saturation and pore structure on attenuation. Numerical calculations using these models with the experimental data indicate that friction on thin cracks and grain boundaries is the dominant attenuation mechanism for dry and brine-saturated sandstones at low effective stresses for the frequencies tested. However, for brine-saturated sandstones at moderately high effective stresses, fluid flow could play a more important role in ultrasonic S-wave attenuation, depending on the pore structure of the sample.  相似文献   

19.
This paper tests the ability of various rock physics models to predict seismic velocities in shallow unconsolidated sands by comparing the estimates to P and S sonic logs collected in a shallow sand layer and ultrasonic laboratory data of an unconsolidated sand sample. The model fits are also evaluated with respect to the conventional model for unconsolidated sand. Our main approach is to use Hertz‐Mindlin and Walton contact theories, assuming different weight fractions of smooth and rough contact behaviours, to predict the elastic properties of the high porosity point. Using either the Hertz‐Mindlin or Walton theories with rough contact behaviour to define the high porosity endpoint gives an over‐prediction of the velocities. The P‐velocity is overpredicted by a factor of ~1.5 and the S‐velocity by a factor of ~1.8 for highly porous gas‐sand. The degree of misprediction decreases with increasing water saturation and porosity.Using the Hertz‐Mindlin theory with smooth contact behaviour or weighted Walton models gives a better fit to the data, although the data are best described using the Walton smooth model. To predict the properties at the lower porosities, the choice of bounding model attached to the Walton Smooth model controls the degree of fit to the data, where the Reuss bound best captures the porosity variations of dry and wet sands in this case since they are caused by depositional differences. The empirical models based on lab experiments on unconsolidated sand also fit the velocity data measured by sonic logs in situ, which gives improved confidence in using lab‐derived results.  相似文献   

20.
Seismic monitoring of reservoir and overburden performance during subsurface CO2 storage plays a key role in ensuring efficiency and safety. Proper interpretation of monitoring data requires knowledge about the rock physical phenomena occurring in the subsurface formations. This work focuses on rock stiffness and elastic velocity changes of a shale overburden formation caused by both reservoir inflation induced stress changes and leakage of CO2 into the overburden. In laboratory experiments, Pierre shale I core plugs were loaded along the stress path representative for the in situ stress changes experienced by caprock during reservoir inflation. Tests were carried out in a triaxial compaction cell combining three measurement techniques and permitting for determination of (i) ultrasonic velocities, (ii) quasistatic rock deformations, and (iii) dynamic elastic stiffness at seismic frequencies within a single test, which allowed to quantify effects of seismic dispersion. In addition, fluid substitution effects connected with possible CO2 leakage into the caprock formation were modelled by the modified anisotropic Gassmann model. Results of this work indicate that (i) stress sensitivity of Pierre shale I is frequency dependent; (ii) reservoir inflation leads to the increase of the overburden Young's modulus and Poisson's ratio; (iii) in situ stress changes mostly affect the P‐wave velocities; (iv) small leakage of the CO2 into the overburden may lead to the velocity changes, which are comparable with one associated with geomechanical influence; (v) non‐elastic effects increase stress sensitivity of an acoustic waves; (iv) and both geomechanical and fluid substitution effects would create significant time shifts, which should be detectable by time‐lapse seismic.  相似文献   

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