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ABSTRACT Relating seismic attributes to the characteristics of mesoscopic fractures is inherently challenging, yet these heterogeneities tend to dominate the mechanical and hydraulic properties of the medium. Analytical approaches linking the effects of material properties on seismic attributes, such as attenuation and velocity dispersion, tend to be limited to simple geometries, low fracture densities, and/or non-interacting fractures. Furthermore, the influence of fluid flow within interconnected fractures on P-wave and S-wave attenuation is difficult to accommodate in analytical models. One way to overcome these limitations is through numerical upscaling. In this paper, we apply a numerical upscaling approach based on the theory of quasi-static poroelasticity to fluid-saturated porous media containing randomly distributed horizontal and vertical fractures. The inferred frequency-dependent elastic moduli represent the effective behaviour of the underlying fractured medium if the considered sub-volume has at least the size of a representative elementary volume. We adapt a combined statistical and numerical approach originally proposed for elastic composites to explore wether the overall statistical properties of simple fracture networks can be captured by computationally feasible representative-elementary-volume sizes. Our results indicate that, for the considered scenarios, this is indeed possible and thus represent an important first step towards the estimation of frequency-dependent effective moduli of realistic fracture networks. [ABSTRACT FROM AUTHOR]

ABSTRACT The dependence of fluid-saturated rocks' elastic properties to the measuring frequency is related to fluid-flow phenomena at different scales. In the frequency range of [ABSTRACT FROM AUTHOR]

ABSTRACT Poroelastic modelling of micro-inhomogeneous rocks is of interest for applications in rock physics and geomechanics. Laboratory measurements from both communities indicate that the Biot poroelasticity framework is not adequate. For the case of a macroscopically homogeneous and isotropic rock, we present the most general poroelasticity framework within the scope of equilibrium thermodynamics that is able to capture the effects of micro-inhomogeneities in a natural way. Within this generalized poroelasticity framework, the concept of micro-inhomogeneity is generically related to partial localization of the deformational potential energy either in the solid phase, including the interfacial region or in the fluid phase. The former case can occur in the presence of surface roughness or multi-mineralic frame and the latter case can be related to suspended particles residing in the fluid phase. A measure for micro-inhomogeneity is the coefficient that governs the effective pressure dependence of porosity changes as described by the porosity perturbation equation of this framework. It can be therefore equivalently interpreted as porosity effective pressure coefficient or as micro-inhomogeneity parameter. We show how this parameter and the other poroelastic constants embedded in this framework can be expressed in terms of experimentally accessible poroelastic constants. [ABSTRACT FROM AUTHOR]

ABSTRACT Geological reservoirs can be structurally complex and can respond to CO2 injection both geochemically and geomechanically. Hence, predicting reservoir formation behaviour in response to CO2 injection and assessing the resulting hazards are important prerequisites for safe geological CO2 storage. This requires a detailed study of thermal-hydro-mechanical-chemical coupled phenomena that can be triggered in the reservoir formation, most readily achieved through laboratory simulations of CO2 injection into typical reservoir formations. Here, we present the first results from a new experimental apparatus of a steady-state drainage flooding test conducted through a synthetic sandstone sample, simulating real CO2 storage reservoir conditions in a shallow (∼1 km), low permeability ∼1mD, 26% porosity sandstone formation. The injected pore fluid comprised brine with CO2 saturation increasing in steps of 20% brine/CO2 partial flow rates up to 100% CO2 flow. At each pore fluid stage, an unload/loading cycle of effective pressure was imposed to study the response of the rock under different geomechanical scenarios. The monitoring included axial strains and relative permeability in a continuous mode (hydromechanical assessment), and related geophysical signatures (ultrasonic P-wave and S-wave velocities Vp and Vs, and attenuations Qp−1 and Qs−1, respectively, and electrical resistivity). On average, the results showed Vp and Vs dropped ∼7% and ∼4% respectively during the test, whereas Qp−1 increased ∼55% and Qs−1 decreased by ∼25%. From the electrical resistivity data, we estimated a maximum CO2 saturation of ∼0.5, whereas relative permeability curves were adjusted for both fluids. Comparing the experimental results to theoretical predictions, we found that Gassmann's equations explain Vp at high and very low CO2 saturations, whereas bulk modulus yields results consistent with White and Dutta-Odé model predictions. This is interpreted as a heterogeneous distribution of the two pore fluid phases, corroborated by electrical resistivity tomography images. The integration of laboratory geophysical and hydromechanical observations on representative shallow low-permeable sandstone reservoir allowed us to distinguish between pure geomechanical responses and those associated with the pore fluid distribution. This is a key aspect in understanding CO2 injection effects in deep geological reservoirs associated with carbon capture and storage practices. [ABSTRACT FROM AUTHOR]

ABSTRACT Seismic attenuation and velocity dispersion are potentially able to reveal the rock physical properties of the subsurface. Conventionally, a frequency-independent quality factor ( Q) is measured. This Q is equivalent to the total velocity dispersion in a seismic record and is inadequate for analysing the attenuation mechanism or rock physical properties. Here a new method is proposed to extract the velocity dispersion curves so that more attributes can be obtained from full-waveform multichannel sonic logging data, especially the critical frequency ( fc) if it is within the bandwidth of the data. This method first decomposes the seismic data into a series of frequency components, computes the semblance of each frequency component for different velocity values, cross-correlates the semblance matrices of adjacent frequency components to get the velocity gradients, and finally integrates to obtain a velocity dispersion curve. Results of this method are of satisfactory accuracy and robustness. This method is applied to the data acquired in Mallik 5L-38 gas hydrate research well in Mackenzie Delta, Northwest Territories, Canada. The observed P-wave velocity dispersion compares well with the geological setting. In the gas hydrate zone (about 900 m-1100 m), high concentration of gas hydrate causes very strong velocity dispersion and a distinct fc at about 15 kHz, likely due to strong scattering of centimetre-scale inclusions of gas hydrate; concurrently, water flow in connected cracks in some ranges of this zone adds a large part of velocity dispersion and a dimmer fc at about 9.5 kHz. Immediate underneath the gas hydrate zone, abundant free water in weakly laminated sediments causes quite strong velocity dispersion and an fc at about 6.5 kHz. Velocity dispersion is mild and without an obvious fc in sediments above the gas hydrate zone. [ABSTRACT FROM AUTHOR]

ABSTRACT A major cause of attenuation in fluid-saturated media is the local fluid flow (or squirt flow) induced by a passing wave between pores of different shapes and sizes. Several squirt flow models have been derived for isotropic media. For anisotropic media however, most of the existing squirt flow models only provide the low- and high-frequency limits of the saturated elastic properties. We develop a new squirt flow model to account for the frequency dependence of elastic properties and thus gain some insight into velocity dispersion and attenuation in anisotropic media. In this paper, we focus on media containing aligned compliant pores embedded in an isotropic background matrix. The low- and high-frequency limits of the predicted fluid-saturated elastic properties are respectively consistent with Gassmann theory and Mukerji-Mavko squirt flow model. Results are also expressed in terms of Thomsen anisotropy parameters. It turns out that the P-wave anisotropy parameter ε tends to zero in the high-frequency limit, whereas the δ parameter remains the only indicator of P-S⊥ anisotropy. The S-wave anisotropy parameter γ is not affected by the presence of fluid and remains the same for all frequency ranges. A new definition for attenuation anisotropy parameters is also proposed to quantify the attenuation anisotropy. In the most important case of liquid saturation, analytical expressions are derived for elastic properties, velocity anisotropy parameters, quality factors, and attenuation anisotropy parameters. A companion paper considers the case of cracks with an ellipsoidal distribution of orientations resulting from the application of anisotropic stress. [ABSTRACT FROM AUTHOR]

ABSTRACT A major cause of attenuation in fluid-saturated media is the local fluid flow (or squirt flow) induced by a passing wave between pores of different shapes and sizes. Several squirt flow models have been derived for isotropic media. For anisotropic media, however, most of the existing squirt flow models only provide the low- and high-frequency limits of the saturated elastic properties. We develop a new squirt flow model to account for the frequency dependence of elastic properties and thus gain some insight into velocity dispersion and attenuation in anisotropic media. In a companion paper, we focused on media containing aligned compliant pores embedded in an isotropic background matrix. In this paper, we investigate the case for which anisotropy results from the presence of cracks with an ellipsoidal distribution of orientations due to the application of anisotropic stress. The low- and high-frequency limits of the predicted fluid-saturated elastic properties are respectively consistent with Gassmann theory and Mukerji-Mavko squirt flow model. In the most important case of liquid saturation, analytical expressions are derived for elastic properties and Thomsen anisotropy parameters. The main observations drawn from this model are as follows. Crack closure perpendicular to the applied stress leads to an increase in seismic velocities as a function of stress in the direction of applied stress and a decrease in squirt-flow-induced dispersion and attenuation in this direction. The anisotropy of squirt flow dispersion engenders a decrease in the degree of anisotropy with frequency. The stress-induced anisotropy remains elliptical, even in saturated media, for all frequency ranges. [ABSTRACT FROM AUTHOR]

ABSTRACT Quantitative interpretation of time-lapse seismic signatures aims at assisting reservoir engineering and management operations. Time-lapse signatures are thought to be primarily induced by saturation and pressure changes. Core-flooding and reservoir flow simulations indicate that a change of the driving forces during dynamic fluid injection gives rise to a varying saturation scale. This saturation scale is yet another variable controlling the time-lapse seismic signal. In this work, we investigate the saturation scale effect on time-lapse seismic signatures by analysing simple modelling scenarios. We consider three characteristic saturation scales, ranging from few millimetres to metres, which may form during gas injection in an unconsolidated water-saturated reservoir. Using the random patchy saturation model, we compare the corresponding acoustic signatures, i.e., attenuation, reflectivity, and seismic gather associated with each saturation scale. The results show that the millimetre saturation scale produces minimum attenuation and the same seismic signatures with those obtained from the elastic modelling. The centimetre saturation scale produces maximum attenuation, whereas the metre saturation scale causes highest velocity dispersion. The analyses of the time shift and amplitude change indicate that ignoring a time-dependent saturation scale can result in biased estimation/discrimination of the saturation and the fluid pressure. In particular, the 4D signal can be strongly affected by the saturation-scale change when the reservoir gas saturation is low and the effective pressure is high. In the presence of an increasing (decreasing) saturation scale during injection, interpreting an observed time shift and amplitude change using the Gassmann model will lead to underestimation (overestimation) of the change in gas saturation and fluid pressure. We show that including the effects of capillarity and residual saturation into the rock physics modelling can potentially reduce the interpretation uncertainty due to the saturation-scale change. [ABSTRACT FROM AUTHOR]

ABSTRACT We present a generalized effective poroelastic model for periodically layered media in the mesoscopic scale range, which accounts for both Biot's global and interlayer wave-induced fluid flow, as well as for the anisotropy associated with the layering. Correspondingly, it correctly predicts the existence of the fast and slow P-waves as well as quasi and pure S-waves. The proposed analytical model is validated through comparisons of the P-wave and S-wave phase velocity dispersion and attenuation characteristics with those inferred from a one-dimensional numerical solution of Biot's poroelastic equations of motion. We also compare our model with the classical mesoscopic model of White for a range of scenarios. The results demonstrate that accounting for both wave-induced fluid flow mechanisms is essential when Biot's global flow prevails at frequencies that are comparable or smaller with respect to those governing interlayer flow. This is likely to be the case in media of high permeability, such as, for example, unconsolidated sediments, clean sandstones, karstic carbonates, or fractured rocks. Conversely, when interlayer flow occurs at smaller frequencies with respect to Biot's global flow, the predictions of this model are in agreement with White's model, which is based on quasi-static poroelasticity. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper introduces an efficiency improvement to the sparse-grid geometric sampling methodology for assessing uncertainty in non-linear geophysical inverse problems. Traditional sparse-grid geometric sampling works by sampling in a reduced-dimension parameter space bounded by a feasible polytope, e.g., a generalization of a polygon to dimension above two. The feasible polytope is approximated by a hypercube. When the polytope is very irregular, the hypercube can be a poor approximation leading to computational inefficiency in sampling. We show how the polytope can be regularized using a rotation and scaling based on principal component analysis. This simple regularization helps to increase the efficiency of the sampling and by extension the computational complexity of the uncertainty solution. We demonstrate this on two synthetic 1D examples related to controlled-source electromagnetic and amplitude versus offset inversion. The results show an improvement of about 50% in the performance of the proposed methodology when compared with the traditional one. However, as the amplitude versus offset example shows, the differences in the efficiency of the proposed methodology are very likely to be dependent on the shape and complexity of the original polytope. However, it is necessary to pursue further investigations on the regularization of the original polytope in order to fully understand when a simple regularization step based on rotation and scaling is enough. [ABSTRACT FROM AUTHOR]

ABSTRACT Wavefield decomposition forms an important ingredient of various geophysical methods. An example of wavefield decomposition is the decomposition into upgoing and downgoing wavefields and simultaneous decomposition into different wave/field types. The multi-component field decomposition scheme makes use of the recordings of different field quantities (such as particle velocity and pressure). In practice, different recordings can be obscured by different sensor characteristics, requiring calibration with an unknown calibration factor. Not all field quantities required for multi-component field decomposition might be available, or they can suffer from different noise levels. The multi-depth-level decomposition approach makes use of field quantities recorded at multiple depth levels, e.g., two horizontal boreholes closely separated from each other, a combination of a single receiver array combined with free-surface boundary conditions, or acquisition geometries with a high-density of vertical boreholes. We theoretically describe the multi-depth-level decomposition approach in a unified form, showing that it can be applied to different kinds of fields in dissipative, inhomogeneous, anisotropic media, e.g., acoustic, electromagnetic, elastodynamic, poroelastic, and seismoelectric fields. We express the one-way fields at one depth level in terms of the observed fields at multiple depth levels, using extrapolation operators that are dependent on the medium parameters between the two depth levels. Lateral invariance at the depth level of decomposition allows us to carry out the multi-depth-level decomposition in the horizontal wavenumber-frequency domain. We illustrate the multi-depth-level decomposition scheme using two synthetic elastodynamic examples. The first example uses particle velocity recordings at two depth levels, whereas the second example combines recordings at one depth level with the Dirichlet free-surface boundary condition of zero traction. Comparison with multi-component decomposed fields shows a perfect match in both amplitude and phase for both cases. The multi-depth-level decomposition scheme is fully customizable to the desired acquisition geometry. The decomposition problem is in principle an inverse problem. Notches may occur at certain frequencies, causing the multi-depth-level composition matrix to become uninvertible, requiring additional notch filters. We can add multi-depth-level free-surface boundary conditions as extra equations to the multi-component composition matrix, thereby overdetermining this inverse problem. The combined multi-component-multi-depth-level decomposition on a land data set clearly shows improvements in the decomposition results, compared with the performance of the multi-component decomposition scheme. [ABSTRACT FROM AUTHOR]

ABSTRACT According to the classical approach to physical interpretation of multiple roots of the Christoffel equation in the theory of elastic wave propagation in anisotropic media, a sum of isonormal plane waves propagating in the direction of acoustic axes can have either arbitrary or circular polarization. The main question posed in this paper is as follows: can one apply conclusions drawn for plane waves to other phenomena, in particular, to waves generated by a point source? The paper proposes a new principle of physical interpretation of degeneracies stating that any assessment of the polarizations (and the group velocities) of waves propagating in anisotropic media is reasonable if there exists an experiment with a point source in which the assessment agrees with the general symmetry of the experiment. From the viewpoint of this interpretation, all degeneracies are considered on the wavefront. The inferences drawn from the performed analysis might appear surprising: in all considered cases of degeneracies (such as conic axes, tangent degeneracy on the symmetry axis of infinite order in transversely isotropic media, intersections of the slowness surfaces), ambiguity in determination of the polarization vectors either does not exist for any experiment or can be removed based on the symmetry of an experiment. A condition for convexity of the slowness surface of the fastest wave is formulated in this context. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper discusses reducing computation costs for traveltime calculations in multi-layered anisotropic models. Fomel and Stovas () suggested a two-ray five-parameter approximation that they named 'generalized' because it reduces to several known three-parameter forms. Model tests, demonstrated by the authors, showed that this generalized approximation provided very high accuracy, implying it can be used in place of the exact moveout function in modelling, migration and traveltime inversion. However, detailed model studies show that for some models, with a high-velocity layer, this approximation leads to significant errors. I develop a new three-ray eight-parameter approximation that provides higher accuracy and can replace the exact traveltime function that requires numerical ray calculations for each receiver. I call it a 'two-interval approximation' because it uses two different equations for two offset intervals. Model tests show that this two-interval approximation can bring much higher accuracy compared to the generalized approximation due to the use of an additional reference ray. The two-interval new approximation can be used instead of exact traveltimes for many practical purposes. [ABSTRACT FROM AUTHOR]

2.5D modelling approximates 3D wave propagation in the dip-direction of a 2D geological model. Attention is restricted to raypaths for waves propagating in a plane. In this way, fast inversion or migration can be performed. For velocity analysis, this reduction of the problem is particularly useful. We review 2.5D modelling for Born volume scattering and Born–Helmholtz surface scattering. The amplitudes are corrected for 3D wave propagation, taking into account both in-plane and out-of-plane geometrical spreading. We also derive some new inversion/migration results. An AVA-compensated migration routine is presented that is simplified compared with earlier results. This formula can be used to create common-image gathers for use in velocity analysis by studying the residual moveout. We also give a migration formula for the energy-flux-normalized plane-wave reflection coefficient that models large contrast in the medium parameters not treated by the Born and the Born–Helmholtz equation results. All results are derived using the generalized Radon transform (GRT) directly in the natural coordinate system characterized by scattering angle and migration dip. Consequently, no Jacobians are needed in their calculation. Inversion and migration in an orthorhombic medium or a transversely isotropic (TI) medium with tilted symmetry axis are the lowest symmetries for practical purposes (symmetry axis is in the plane). We give an analysis, using derived methods, of the parameters for these two types of media used in velocity analysis, inversion and migration. The kinematics of the two media involve the same parameters, hence there is no distinction when carrying out velocity analysis. The in-plane scattering coefficient, used in the inversion and migration, also depends on the same parameters for both media. The out-of-plane geometrical spreading, necessary for amplitude-preserving computations, for the TI medium is dependent on the same parameters that govern in-plane kinematics. For orthorhombic media, information on additional parameters is required that is not needed for in-plane kinematics and the scattering coefficients. Resolution analysis of the scattering coefficient suggests that direct inversion by GRT yields unreliable parameter estimates. A more practical approach to inversion is amplitude-preserving migration followed by AVA analysis. SYMBOLS AND NOTATION A list of symbols and notation is given in . [ABSTRACT FROM AUTHOR]