Catálogo de publicaciones - revistas

<jats:p> Separation filtering is incomplete even under the ideal synthetic condition of known power spectra of the regional and residual fields. I have designed some Wiener filters, which minimize the inevitable separation error, from previous statistical source models of Naidu, and Spector and Grant. This formulation includes the classic separation filters of Strakhov and of Elkins as Wiener filters. A proposed generalization of Wiener filters, denoted as uniformly suboptimum filters, quantitatively supports the statement that a wide span of separation problems may be solved adequately using some convenient, small standard filter family. A uniform random‐source model without assumed vertical correlations invokes upward continuation filters. In addition to this role as a Wiener filter, the upward continuation operator is given by elementary functions in both space and wavenumber domains, is numerically stable, and is also physically comprehensible when applied to real, nonrandom anomalies. In view of these distinguishing features, I propose to use the upward continuation operator to build a convenient, standard family of separation filters. </jats:p>

<jats:p>To decouple qP and qSV sheets of the slowness surface of a transversely isotropic (TI) medium, a sequence of rational approximations to the solution of the dispersion relation of a TI medium is introduced. Originally conceived to allow isotropic P-wave processing schemes to be generalized to encompass the case of qP-waves in transverse isotropy, the sequence of approximations was found to be applicable to qSV-wave processing as well, although a higher order of approximation is necessary for qSV-waves than for qP-waves to yield the same accuracy. The zeroth‐order approximation, about which all other approximations are taken, is that of elliptical TI, which contains the correct values of slowness and its derivative along and perpendicular to the medium’s axis of symmetry. Successive orders of approximation yield the correct values of successive orders of derivatives in these directions, thereby forcing the approximation into increasingly better fit at the intervening oblique angles. Practically, the first‐order approximation for qP-wave propagation and the second‐order approximation for qSV-wave propagation yield sufficiently accurate results for the typical transverse isotropy found in geological settings. After only slight modification to existing programs, the rational approximation allows for ray tracing, (f-k) domain migration, and split‐step Fourier migration in TI media—with little more difficulty than that encountered presently with such algorithms in isotropic media.</jats:p>

<jats:p> Fluid and solid substitution of bulk modulus are exact and unique for materials whose elastic bulk and/or shear moduli fall on the Hashin-Shtrikman bounds. For materials whose moduli lie between the bounds, solid and fluid substitution of bulk moduli can be computed exactly, but not uniquely. Every initial bulk modulus can be realized with an infinite number of microstructures and therefore transform to an infinite number of moduli upon substitution of the pore fill. This nonuniqueness arises when detailed information on the material pore geometry is not available. We evaluated four embedded-bound constructions for fluid and solid substitution that were based on realizable materials. In the limiting case of pore fluids, two of these constructions reduced to the bounds of Gibiansky and Torquato, which illustrated that those bounds were optimum. For solids, the first two constructions corresponded to a homogeneous pore stiffness and predicted the smallest change in modulus. The third construction prediction corresponded to a pore space with heterogeneous stiffness, and it predicted a much larger change in modulus. </jats:p>

<jats:p> Seismic reflections depend on the contrasts of the elastic properties of the subsurface and their 3D geometry. As a result, interpreting seismic data for petrophysical rock properties requires a theoretical rock-physics model that links the seismic response to a rock’s velocity and density. Such a model is based on controlled experiments in which the petrophysical and elastic rock properties are measured on the same samples, such as in the wellbore. Using data from three wells drilled through a clastic offshore gas reservoir, we establish a theoretical rock-physics model that quantitatively explains these data. The modeling is based on the assumption that only three minerals are present: quartz, clay, and feldspar. To have a single rock-physics transform to quantify the well data in the entire intervals under examination in all three wells, we introduced field-specific elastic moduli for the clay. We then used the model to correct the measured shear-wave velocity because it appeared to be unreasonably low. The resulting model-derived Poisson’s ratio is much smaller than the measured ratio, especially in the reservoir. The associated synthetic amplitude variation with offset response appears to be consistent with the recorded seismic angle stacks. We have shown how rock-physics modeling not only helps us to correct the well data, but also allows us to go beyond the settings represented in the wells and quantify the seismic signatures of rock properties and conditions varying in a wider range using forward seismic modeling. </jats:p>

<jats:p> In unconventional reservoirs with significant organic content, the Greenberg-Castagna (GC) S-wave velocity prediction method does not yield accurate S-wave velocity predictions, with observed mean errors varying from 6% to 16% in a variety of unconventional reservoirs rich in organic content. This is because kerogen content is not explicitly taken into account in the GC S-wave velocity prediction method. Two alternative approaches for bedding-normal S-wave velocity prediction from P-wave velocity and other well logs in relatively straight holes drilled in unconventional reservoirs are investigated. The first method is purely empirical, requiring minimal information such as P-wave velocity and total organic carbon content. This approach implicitly accounts for compositional and stress effects on mudrock elasticity. The second method can be classified as a hybrid technique, comprising the following three steps: (1) computing a nonkerogen phase P-wave velocity using the Vernik-Kachanov (VK) model, (2) determination of the nonkerogen S-wave velocity from the GC approach, and (3) using a simplified VK model to mix the nonkerogen matrix with nanoporous kerogen to predict the bedding-normal S-wave velocity of the organic mudrock. The second method explicitly takes into account all the variables that control elastic properties of organic mudrock reservoirs. Tests in nine wells from seven different oil and gas shale reservoirs indicate that both methods have prediction accuracy better than 3% error when input data are accurate. </jats:p>

<jats:p> The mechanical basis of the popular Cole-Cole rheological model in viscoelasticity is investigated by using Lagrangian mechanics with nonlinear energy dissipation. The Cole-Cole model is usually viewed as a convenient way to fit the observed frequency-dependent attenuation and velocity-dispersion spectra, but its time-domain and numerical formulations are complex and contradict standard physical principles. For example, time-domain modeling of Cole-Cole media requires special mathematical tools such as fractional derivatives, convolutional integrals, and/or memory variables. Nevertheless, we find that Cole-Cole spectra naturally arise from conventional mechanics with nonlinear internal friction (non-Newtonian viscosity). The Lagrangian mechanical formulation is applied to a finite body (a rock sample in a laboratory experiment) and a wave-propagating medium, in both cases providing rigorous differential equations of motion and revealing the time- and frequency-independent material properties. The model also leads to a generalized Cole-Cole (GCC) model with multiple internal variables (relaxation mechanisms), similar to the generalized standard linear solid (GSLS). As a practical application, the GSLS and GCC models are compared on interpretations of recent P-wave attenuation and dispersion measurements on bitumen-sand samples in the laboratory. The GSLS and GCC models can be used to predict the observed strain/stress ratios with adequate accuracy. However, each of these models offers certain advantages, which are the linearity (for GSLS) and potentially smaller number of dynamic variables and broader peaks in attenuation spectra (for GCC). Therefore, additional experiments focusing on linearity of internal friction are required to establish which of these models may be preferable for rock. The Lagrangian approach provides a simple and physically meaningful way for comparing all types of observations, formulating numerical modeling schemes, and predicting the propagation of waves and behavior of other deformations of earth media. </jats:p>

<jats:p> We have revisited the debate about whether flexural waves from dipole sonic tools and standard processing algorithms measure group or phase velocities in anisotropic formations. We observe that much of the confusion arises from a failure to understand the different meanings of group and phase velocities. Using a transversely isotropic medium with a vertical axis of symmetry that exhibits a triplication in its S-wave group slowness surface, we generate synthetic flexural sonic waveforms corresponding to boreholes at angles of 0°–90° with respect to the anisotropy symmetry axis in 1° increments. We processed these synthetic data using standard time- and frequency-domain semblance methods. The results conclusively demonstrate that dipole sonic logs measure the group slowness for the group angle corresponding to the angle between the borehole and the anisotropic symmetry axis. In addition, data that we have evaluated suggest that current tool geometries and semblance processing may not always be sensitive enough to resolve all branches of the group slowness triplication surface. </jats:p>

<jats:p> We have developed a viscoplastic model that reproduces creep behavior and inelastic deformation of rock during loading-unloading cycles. We use a Perzyna-type description of viscous deformation that derives from a maximization of dissipated energy during plastic flow, in combination with a modified Cam-clay model of plastic deformation. The plastic flow model is of the associative type, and the viscous deformation is proportional to the ratio of driving stress and a material viscosity. Our model does not rely on any explicit time parameters; therefore, it is well-suited for standard and cyclic loading of materials. We validate the model with recent triaxial experiments of time-dependent deformation in clay-rich (Haynesville Formation) and carbonate-rich (Eagle Ford Formation) shale samples, and we find that the deformation during complex, multiscale loading-unloading paths can be reproduced accurately. We elucidate the role and physical meaning of each model parameter, and we infer their value from a gradient-descent minimization of the error between simulation and experimental data. This inference points to the large, and often unrecognized, uncertainty in the preconsolidation stress, which is key to reproducing the observed hysteresis in material deformation. </jats:p>

<jats:p> To establish a consistent framework for seismic wave propagation that accommodates the effects of stress changes, it is critical to take into account the different definitions of stress and their corresponding effects on seismic quantities (e.g., wave speeds) as dictated by continuum mechanics. Revisiting this fundamental theoretical foundation, we first emphasize the role of stress within various forms of the wave equation resulting from different choices of stress definitions. Subsequently, using this basis, we investigate connections among existing theories that describe the variation of elastic moduli as a function of changes in stress. We find that there is a direct connection between predicting stress-induced elastic changes with the well-known third-order elasticity tensor and the recently proposed adiabatic pressure derivatives of elastic moduli. However, each of these approaches has different merits and drawbacks in terms of experimental validation as well as in their use. In addition, we investigate the connection with another general approach that relies on micromechanical structures (e.g., cracks and pores). Although this can be done algebraically, it remains unclear as to which definition of stress and which corresponding constitutive relationship should be considered in practical scenarios. We support our analysis with validations using previously published benchmark experimental data. </jats:p>

<jats:p> We have developed a workflow for computing the seismic-wave moduli dispersion and attenuation due to squirt flow in a numerical model derived from a micro X-ray computed tomography image of cracked (through thermal treatment) Carrara marble sample. To generate the numerical model, the image is processed, segmented, and meshed. The finite-element method is adopted to solve the linearized, quasistatic Navier-Stokes equations describing laminar flow of a compressible viscous fluid inside the cracks coupled with the quasistatic Lamé-Navier equations for the solid phase. We compute the effective P- and S-wave moduli in the three Cartesian directions for a model in dry conditions (saturated with air) and for a smaller model fully saturated with glycerin and having either drained or undrained boundary conditions. For the model saturated with glycerin, the results indicate significant and frequency-dependent P- and S-wave attenuation and the corresponding dispersion caused by squirt flow. Squirt flow occurs in response to fluid pressure gradients induced in the cracks by the imposed deformations. Our digital rock-physics workflow can be used to interpret laboratory measurements of attenuation using images of the rock sample. </jats:p>