Research Note: Experimental measurements of Q‐contrast reflections

While seismic reflection amplitudes are generally determined by real acoustical impedance contrasts, there has been recent interest in reflections due to contrasts in seismic‐Q. Herein we compare theoretical and modelled seismic reflection amplitudes for two different cases of material contrasts. In case A, we examine reflections from material interfaces that have a large contrast in real‐valued impedance () with virtually no contrast in seismic‐Q. In case B, we examine reflections from material interfaces that have virtually no contrast in but that have very large seismic‐Q contrasts. The complex‐valued reflection coefficient formula predicts non‐zero seismic reflection amplitudes for both cases. We choose physical materials that typify the physics of both case A and case B. Physical modelling experiments show significantly large reflections for both cases – with the reflections in the two cases being phase shifted with respect to each other, as predicted theoretically. While these modelling experiments show the existence of reflections that are predicted by theory, there are still intriguing questions regarding the size of the Q‐contrast reflections, the existence of large Q‐contrast reflections in reservoir rocks and the possible application of Q‐reflection analysis to viscosity estimation in heavy oilfields.     

Burial stress and elastic strain of carbonate rocks

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.     

Static and dynamic elastic moduli of organic-rich chalk

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.     

The influence of local fluid flow and the microstructure on elastic and anelastic rock properties

The frequency dependent mechanism of local fluid flow was found to be the decisive absorption and dispersion mechanism in fluid containing sandstones. In the ultrasonic frequency range local fluid flow and grain surface effects control the behaviour of highly porous and highly permeable rock if a pore fluid is present. Both mechanisms depend less on macroscopic rock parameters like porosity and permeability than essentially on microscopic parameters like crack size, crack density and grain contact properties. To demonstrate directly the important influence of the microstructure on the rock elastic and anelastic properties the microstructure of a sandstone was artificially changed by thermal cracking. The cracked rock exhibits a clearly changed behaviour at low uniaxial as well as at high hydrostatic pressure despite small changes of porosity and permeability. Fluid effects increase due to cracking. The experimental results are explained by means of a rock, model and local fluid flow. These results emphasize that it is the microstructure which controls the elastic and anelastic rock behaviour, even at high hydrostatic pressure.     

Forced oscillation measurements of seismic wave attenuation and stiffness moduli dispersion in glycerine-saturated Berea sandstone

Fluid pressure diffusion occurring on the microscopic scale is believed to be a significant source of intrinsic attenuation of mechanical waves propagating through fully saturated porous rocks. The so-called squirt flow arises from compressibility heterogeneities in the microstructure of the rocks. To study squirt flow experimentally at seismic frequencies the forced oscillation method is the most adequate, but such studies are still scarce. Here we present the results of forced hydrostatic and axial oscillation experiments on dry and glycerine-saturated Berea sandstone, from which we determine the dynamic stiffness moduli and attenuation at micro-seismic and seismic frequencies (0.004–30 Hz). We observe frequency-dependent attenuation and the associated moduli dispersion in response to the drained–undrained transition (∼0.1 Hz) and squirt flow (>3 Hz), which are in fairly good agreement with the results of the corresponding analytical solutions. The comparison with very similar experiments performed also on Berea sandstone in addition shows that squirt flow can potentially be a source of wave attenuation across a wide range of frequencies because of its sensitivity to small variations in the rock microstructure, especially in the aspect ratio of micro-cracks or grain contacts.     

Comparison of stress-dependent geophysical,hydraulic and mechanical properties of synthetic and natural sandstones for reservoir characterization and monitoring studies

Synthetic rock samples can offer advantages over natural rock samples when used for laboratory rock physical properties studies, provided their success as natural analogues is well understood. The ability of synthetic rocks to mimic the natural stress dependency of elastic wave, electrical and fluid transport properties is of primary interest. Hence, we compare a consistent set of laboratory multi-physics measurements obtained on four quartz sandstone samples (porosity range 20–25%) comprising two synthetic and two natural (Berea and Corvio) samples, the latter used extensively as standards in rock physics research. We measured simultaneously ultrasonic (P- and S-wave) velocity and attenuation, electrical resistivity, permeability and axial and radial strains over a wide range of differential pressure (confining stress 15–50 MPa; pore pressure 5–10 MPa) on the four brine saturated samples. Despite some obvious physical discrepancies caused by the synthetic manufacturing process, such as silica cementation and anisotropy, the results show only small differences in stress dependency between the synthetic and natural sandstones for all measured parameters. Stress dependency analysis of the dry samples using an isotropic effective medium model of spheroidal pores and penny-shaped cracks, together with a granular cohesion model, provide evidence of crack closure mechanisms in the natural sandstones, seen to a much lesser extent in the synthetic sandstones. The smaller grain size, greater cement content, and cementation under oedometric conditions particularly affect the fluid transport properties of the synthetic sandstones, resulting in lower permeability and higher electrical resistivity for a similar porosity. The effective stress coefficients, determined for each parameter, are in agreement with data reported in the literature. Our results for the particular synthetic materials that were tested suggest that synthetic sandstones can serve as good proxies for natural sandstones for studies of elastic and mechanical properties, but should be used with care for transport properties studies.     

泥质砂岩中接触胶结泥质定量估算及对砂岩弹性的影响

在泥质砂岩的岩石物理建模中,明确泥质砂岩中泥质胶结物的接触类型及其含量对正确认识泥质的胶结作用对泥质砂岩声速的影响以及合理地建立岩石物理模型至关重要.现阶段,尚未有实验室定量估算胶结泥质的方法,导致应用胶结砂岩理论模型预测胶结砂岩地层的声速时往往由于胶结物含量被高估从而导致预测声速结果偏高.本文通过观察铸体薄片中泥质与颗粒之间的接触关系和相对分布提出了一种区分胶结泥质和分散泥质的方法：与两个或两个以上颗粒接触的连续分布的泥质为胶结泥质;与一个颗粒接触或者不与颗粒接触的泥质为分散泥质.基于这一准则,本文基于像素拾取法估算了人造泥质砂岩的胶结泥质含量,并将胶结泥质含量作为胶结砂岩模型的输入参数优化CCT模型.对比原始模型,本文方法声速误差下降了20%,预测准确度显著提高.本文方法适用于弱胶结地层的岩石物理建模,能够准确的预测声速以结合地震和测井资料识别有利储层,定量评价储层参数.

     

Static and dynamic stiffness measurements with Opalinus Clay

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.     

2D and 3D amplitude-preserving elastic reverse time migration based on the vector-decomposed P- and S-wave records

The elastic reverse time migration approach based on the vector-wavefield decomposition generally uses the scalar product imaging condition to image the multicomponent seismic data. However, the resulting images contain the crosstalk artefacts and the polarity reversal problems, which are caused by the nonphysical wave modes and the angle-dependent reduction of image amplitudes, respectively. To overcome these two problems, we develop an amplitude-preserving elastic reverse time migration approach based on the vector-decomposed P- and S-wave seismic records. This approach includes two key points. The first is that we employ the vector-decomposed P- and S-wave multicomponent records to independently reconstruct the PP and PS reflection images to mitigate the crosstalk artefacts. The second is that we propose two schemes in addressing the issue of polarity reversal problem in the conventional PP image. One solution is to adopt the angle-dependent equation. Another one is to reconstruct an amplitude-preserving PP image with a separated scalar P-wave particle velocity, which has a clear physical meaning. Numerical examples using two-dimensional and three-dimensional models demonstrate that the proposed elastic reverse time migration approach can provide the images with better amplitude-preserving performance and fewer crosstalk artefacts, compared with the conventional elastic reverse time migration approach based on the scalar product imaging condition.     

Effect of micro‐inhomogeneity on the effective stress coefficients and undrained bulk modulus of a poroelastic medium: a double spherical shell model

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.     

A semi-empirical approach to model pressure dependence of elastic moduli in granular media accounting for variations of coordination-number and Poisson-ratio

The effective medium theory based on the Hertz–Mindlin contact law is the most popular theory to relate dynamic elastic moduli (or elastic velocities) and confining pressure in dry granular media. However, many experimental results proved that the effective medium theory predicts pressure trends lower than experimental ones and over-predicts the shear modulus. To mitigate these mispredictions, several evolutions of the effective medium theory have been presented in the literature. Among these, the model named modified grain contact theory is an empirical approach in which three parametric curves are included in the effective medium theory model. Fitting the parameters of these curves permits to adjust the pressure trends of the Poisson ratio and the bulk modulus. In this paper, we present two variations of the modified grain contact theory model. First, we propose a minor modification in the fitting function for the porosity dependence of the calibration parameters that accounts for non-linearity in the vicinity of the critical porosity. Second, we propose a major modification that reduces the three-step modified grain contact theory model to a two-step model, by skipping the calibration parameter–porosity fit in the model and directly modelling the calibration parameter–pressure relation. In addition to an increased simplicity (the fitting parameters are reduced from 10 to 6), avoiding the porosity fit permits us to apply the model to laboratory data that are not provided with accurate porosity measurements. For this second model, we also estimate the uncertainty of the fitting parameters and the elastic velocities. We tested this model on dry core measurements from literature and we verified that it returns elastic velocity trends as good as the original modified grain contact theory model with a reduced number of fitting parameters. Possible developments of the new model to add predictive power are also discussed.     

Modelling the wave phenomena in acoustic and elastic media with sharp variations of physical properties using the grid‐characteristic method

This paper introduces a novel method of modelling acoustic and elastic wave propagation in inhomogeneous media with sharp variations of physical properties based on the recently developed grid‐characteristic method which considers different types of waves generated in inhomogeneous linear‐elastic media (e.g., longitudinal, transverse, Stoneley, Rayleigh, scattered PP‐, SS‐waves, and converted PS‐ and SP‐waves). In the framework of this method, the problem of solving acoustic or elastic wave equations is reduced to the interpolation of the solutions, determined at earlier time, thus avoiding a direct solution of the large systems of linear equations required by the FD or FE methods. We apply the grid‐characteristic method to compare wave phenomena computed using the acoustic and elastic wave equations in geological medium containing a hydrocarbon reservoir or a fracture zone. The results of this study demonstrate that the developed algorithm can be used as an effective technique for modelling wave phenomena in the models containing hydrocarbon reservoir and/or the fracture zones, which are important targets of seismic exploration.     

Rock elasticity as a function of the uniaxial stress: laboratory measurements and theoretical modelling of vertical transversely isotropic and orthorhombic shales

We apply a rock-physics model that describes the relationship between the effective stress and rock elasticity. We experimentally obtain and analyse a data set containing one vertical transversely isotropic and one orthorhombic shale sample. The vertical transversely isotropic symmetry of the first sample is caused by the layered structure of the rock. The seismic orthorhombicity of the second sample could be explained after microscopic analysis of thin section, which demonstrates an imperfect disorder of inhomogeneities. Both samples were loaded uniaxially in a quasi-static regime. During the loading, we measured stress-dependent seismic velocities and sample deformations. For the analysis of the stress-dependent velocities and stiffnesses, we modelled the measured data set using a recent generalization of the porosity deformation approach. Comparison of the experimentally determined and numerically modelled data supports the applicability of the theory and helps in the interpretation of experimentally obtained data. In agreement with the theory, uniaxial stress increases the elliptic component of the seismic anisotropy and does not impact the anellipticity parameter. We demonstrate the distinct influence of the stiff and compliant porosities on the stress sensitivity of the elastic properties.     

孔隙-裂隙性质和黏土含量对页岩油层系致密岩石弹性波耗散规律的影响研究

作为一种非常规油气资源,页岩油储量丰富、分布范围广,具有巨大的勘探开发潜力,是近年来油气产业关注的重点与热点.然而,页岩油储层具有岩石矿物组分多样、低孔低渗、孔隙结构复杂、非均质性强等特征,与常规油气资源存在明显差异.本研究选取鄂尔多斯盆地中生界延长组长7油层组的10块致密砂岩样本,基于X射线衍射分析得到各样本的矿物组分,开展不同围压和流体条件下的超声波实验观测,进而获得样本的纵、横波速度和纵波衰减逆品质因子.基于实验测量获得变压力条件下的孔隙度,结合线性外推的方法,估算各样本的裂隙孔隙度,代入EIAS（Equivalent Inclusion-Average Stress,等效嵌入体应力平均）模型,求取对应的裂隙纵横比和裂隙密度,分析页岩油储层孔隙-裂隙性质对纵波衰减的影响.结果显示相对于衰减,致密砂岩总孔隙度、裂隙纵横比、裂隙密度和衰减变化量（不同围压下的衰减观测值与最大围压下的衰减观测值的差）之间的相关性更加明显.基于薄片分析,结果显示致密样本存在孔内黏土包体、微裂隙包体和粒间孔的三重孔隙结构,因此本文引入三重孔隙结构模型,定量估算各样本的孔内黏土含量,进而分析孔内黏土含量及总黏土含量和纵波衰减之间的关系.结果显示孔内黏土含量是主导页岩油储层纵波衰减大小的主要因素之一,而非总黏土含量.本研究可为页岩油储层衰减特征分析、岩石物理模型构建及地震勘探方法研究提供理论支撑.

     

Comparison of acoustic and elastic full-waveform inversion of 2D towed-streamer data in the presence of salt

Over the last years, full-waveform inversion has become an important tool in the list of processing and imaging technologies available to the industry. For marine towed-streamer data, full-waveform inversion is typically applied using an acoustic approximation because S-waves do not propagate in water and elastic effects in recorded data are generally assumed to be small. We compare acoustic and elastic modelling and full-waveform inversion for a field data set acquired offshore Angola over sediments containing a salt body with significant topology. Forward modelling tests reveal that such geological structures lead to significant mode conversions at interfaces and, consequently, to significant relative amplitude differences when elastically and acoustically modelled traces are compared. Using an acoustic approach for modelling in full-waveform inversion therefore leads to problems matching the synthetic data with the field data, even for recorded pressure data and with trace normalization applied. Full-waveform inversion is unable to find consistent model updates. Applying elastic full-waveform inversion leads to more consistent and reliable model updates with less artefacts, at the expense of additional computation cost. Although two-dimensional marine towed-streamer data are least favourable for the application of full-waveform inversion compared to three-dimensional data or ocean-bottom data, it is recommended to check on the existence of elastic effects before deciding on the final processing and imaging approach.     

Analytical approximations of bulk and shear moduli for dry rock based on the differential effective medium theory

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.     

Seismic dispersion and attenuation in layered porous rocks with fractures of varying orientations

Wave‐induced fluid flow plays an important role in affecting the seismic dispersion and attenuation of fractured porous rocks. While numerous theoretical models have been proposed for the seismic dispersion and attenuation in fractured porous rocks, most of them neglect the wave‐induced fluid flow resulting from the background anisotropy (e.g. the interlayer fluid flow between different layers) that can be normal in real reservoirs. Here, according to the theories of poroelasticity, we present an approach to study the frequency‐dependent seismic properties of more realistic and complicated rocks, i.e. horizontally and periodically layered porous rock with horizontal and randomly orienting fractures, respectively, distributed in one of the two periodical layers. The approach accounts for the dual effects of the wave‐induced fluid flow between the fractures and the background pores and between different layers (the interlayer fluid flow). Because C₃₃ (i.e., the modulus of the normally incident P‐wave) is directly related to the P‐wave velocity widely measured in the seismic exploration, and its comprehensive dispersion and attenuation are found to be most significant, we study mainly the effects of fracture properties and the stiffness contrast between the different layers on the seismic dispersion and attenuation of C₃₃. The results show that the increasing stiffness contrast enhances the interlayer fluid flow of the layered porous rocks with both horizontal and randomly orienting fractures and weakens the wave‐induced fluid flow between the fractures and the background pores, especially for the layered porous rock with horizontal fractures. The modelling results also demonstrate that for the considered rock construction, the increasing fracture density reduces the interlayer fluid flow while improves the dispersion and attenuation in the fracture‐relevant frequency band. Increasing fracture aspect ratio is found to reduce the dispersion and attenuation in the fracture‐relevant frequency band only, especially for the layered porous rock with horizontal fractures.     

Laboratory measurements of seismic attenuation and Young's modulus dispersion in a partially and fully water‐saturated porous sample made of sintered borosilicate glass

We measured the extensional‐mode attenuation and Young's modulus in a porous sample made of sintered borosilicate glass at microseismic to seismic frequencies (0.05–50 Hz) using the forced oscillation method. Partial saturation was achieved by water imbibition, varying the water saturation from an initial dry state up to ～99%, and by gas exsolution from an initially fully water‐saturated state down to ～99%. During forced oscillations of the sample effective stresses up to 10 MPa were applied. We observe frequency‐dependent attenuation, with a peak at 1–5 Hz, for ～99% water saturation achieved both by imbibition and by gas exsolution. The magnitude of this attenuation peak is consistently reduced with increasing fluid pressure and is largely insensitive to changes in effective stress. Similar observations have recently been attributed to wave‐induced gas exsolution–dissolution. At full water saturation, the left‐hand side of an attenuation curve, with a peak beyond the highest measured frequency, is observed at 3 MPa effective stress, while at 10 MPa effective stress the measured attenuation is negligible. This observation is consistent with wave‐induced fluid flow associated with mesoscopic compressibility contrasts in the sample's frame. These variations in compressibility could be due to fractures and/or compaction bands that formed between separate sets of forced‐oscillation experiments in response to the applied stresses. The agreement of the measured frequency‐dependent attenuation and Young's modulus with the Kramers–Kronig relations and additional data analyses indicate the good quality of the measurements. Our observations point to the complex interplay between structural and fluid heterogeneities on the measured seismic attenuation and they illustrate how these heterogeneities can facilitate the dominance of one attenuation mechanism over another.     

Monitoring and volumetric estimation of injected CO2 using 4D seismic,petrophysical data,core measurements and well logging: a case study at Ketzin,Germany

More than 50 000 tons of CO₂ have been injected at Ketzin into the Stuttgart Formation, a saline aquifer, at approximately 620 m depth, as of summer 2011. We present here results from the 1^st repeat 3D seismic survey that was performed at the site in autumn 2009, after about 22 000 tons of CO₂ had been injected. We show here that rather complex time‐lapse signatures of this CO₂ can be clearly observed within a radius of about 300 m from the injection well. The highly irregular amplitude response within this radius is attributed to the heterogeneity of the injection reservoir. Time delays to a reflection below the injection level are also observed. Petrophysical measurements on core samples and geophysical logging of CO₂ saturation levels allow an estimate of the total amount of CO₂ visible in the seismic data to be made. These estimates are somewhat lower than the actual amount of CO₂ injected at the time of the survey and they are dependent upon the choice of a number of parameters. In spite of some uncertainty, the close agreement between the amount injected and the amount observed is encouraging for quantitative monitoring of a CO₂ storage site using seismic methods.