Retrieving shallow shear-wave velocity profiles from 2D seismic-reflection data with severely aliased surface waves

The inversion of surface-wave phase-velocity dispersion curves provides a reliable method to derive near-surface shear-wave velocity profiles. In this work, we invert phase-velocity dispersion curves estimated from 2D seismic-reflection data. These data cannot be used to image the first 50 m with seismic-reflection processing techniques due to the presence of indistinct first breaks and significant NMO-stretching of the shallow reflections. A surface-wave analysis was proposed to derive information about the near surface in order to complement the seismic-reflection stacked sections, which are satisfactory for depths between 50 and 700 m. In order to perform the analysis, we had to overcome some problems, such as the short acquisition time and the large receiver spacing, which resulted in severe spatial aliasing. The analysis consists of spatial partitioning of each line in segments, picking of the phase-velocity dispersion curves for each segment in the f-k domain, and inversion of the picked curves using the neighborhood algorithm. The spatial aliasing is successfully circumvented by continuously tracking the surface-wave modal curves in the f-k domain. This enables us to sample the curves up to a frequency of 40 Hz, even though most components beyond 10 Hz are spatially aliased. The inverted 2D VS sections feature smooth horizontal layers, and a sensitivity analysis yields a penetration depth of 20–25 m. The results suggest that long profiles may be more efficiently surveyed by using a large receiver separation and dealing with the spatial aliasing in the described way, rather than ensuring that no spatially aliased surface waves are acquired.Fil: Onnis, Luciano Emanuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Osella, Ana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Carcione, Jose M.. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; Itali

Fracture-induced anisotropic attenuation

The triaxial nature of the tectonic stress in the earth's crust favors the appearance of vertical fractures. The resulting rheology is usually effective anisotropy with orthorhombic and monoclinic symmetries. In addition, the presence of fluids leads to azimuthally varying attenuation of seismic waves. A dense set of fractures embedded in a background medium enhances anisotropy and rock compliance. Fractures are modeled as boundary discontinuities in the displacement u and particle velocity v as [ κ · u + ν · v] where the brackets denote discontinuities across the fracture surface, j is a fracture stiffness, and g is a viscosity related to the energy loss. We consider a transversely isotropic background medium (e.g., thin horizontal plane layers), with sets of long vertical fractures. Schoenberg and Muir's theory combines the background medium and sets of vertical fractures to provide the 13 complex stiffnesses of the long-wavelength equivalent monoclinic and viscoelastic medium. Long-wavelength equivalent means that the dominant wavelength of the signal is much longer than the fracture spacing. The symmetry plane is the horizontal plane. The equations for orthorhombic and transversely isotropic media follow as particular cases. We compute the complex velocities of the medium as a function of frequency and propagation direction, which provide the phase velocities, energy velocities (wavefronts), and quality factors. The effective medium ranges from monoclinic symmetry to hexagonal (transversely isotropic) symmetry from the low-to the high-frequency limits in the case of a particle-velocity discontinuity (lossy case) and the attenuation shows typical Zener relaxation peaks as a function of frequency. The attenuation of the coupled waves may show important differences when computed versus the ray or phase angles, with triplication appearing in the Q factor of the qS wave. We have performed a full-wave simulation to compute the field corresponding to the coupled qP-qS waves in the symmetry plane of an effective monoclinic medium. The simulations agree with the predictions of the plane-wave analysis.Fil: Carcione, Jose M.. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; ItaliaFil: Santos, Juan Enrique. Universidad de Buenos Aires. Facultad de Ingeniería. Instituto del Gas y del Petróleo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata; ArgentinaFil: Picotti, Stefano. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; Itali

Reflection and transmission coefficients of a single layer in poroelastic media

Wave propagation in poroelastic media is a subject that finds applications in many fields of research, from geophysics of the solid Earth to material science. In geophysics, seismic methods are based on the reflection and transmission of waves at interfaces or layers. It is a relevant canonical problem, which has not been solved in explicit form, i.e., the wave response of a single layer, involving three dissimilar media, where the properties of the media are described by Biot's theory. The displacement fields are recast in terms of potentials and the boundary conditions at the two interfaces impose continuity of the solid and fluid displacements, normal and shear stresses, and fluid pressure. The existence of critical angles is discussed. The results are verified by taking proper limits—zero and 100% porosity—by comparison to the canonical solutions corresponding to single-phase solid (elastic) media and fluid media, respectively, and the case where the layer thickness is zero, representing an interface separating two poroelastic half-spaces. As examples, it was calculated the reflection and transmission coefficients for plane wave incident at a highly permeable and compliant fluid-saturated porous layer, and the case where the media are saturated with the same fluid.Facultad de IngenieríaFacultad de Ciencias Astronómicas y Geofísica

Reflection and transmission coefficients of a single layer in poroelastic media

Wave propagation in poroelastic media is a subject that finds applications in many fields of research, from geophysics of the solid Earth to material science. In geophysics, seismic methods are based on the reflection and transmission of waves at interfaces or layers. It is a relevant canonical problem, which has not been solved in explicit form, i.e., the wave response of a single layer, involving three dissimilar media, where the properties of the media are described by Biot's theory. The displacement fields are recast in terms of potentials and the boundary conditions at the two interfaces impose continuity of the solid and fluid displacements, normal and shear stresses, and fluid pressure. The existence of critical angles is discussed. The results are verified by taking proper limits—zero and 100% porosity—by comparison to the canonical solutions corresponding to single-phase solid (elastic) media and fluid media, respectively, and the case where the layer thickness is zero, representing an interface separating two poroelastic half-spaces. As examples, it was calculated the reflection and transmission coefficients for plane wave incident at a highly permeable and compliant fluid-saturated porous layer, and the case where the media are saturated with the same fluid.Facultad de IngenieríaFacultad de Ciencias Astronómicas y Geofísica

Numerical simulation of two-phase fluid flow

We simulate two-phase fluid flow using a stress–strain relation based on Biot’s theory of poroelasticity for partial saturation combined with the mass conservation equations. To uncouple flow and elastic strain, we use a correction to the stiffness of the medium under conditions of uniaxial strain. The pressure and saturation differential equations are then solved with an explicit time stepping scheme and the Fourier pseudospectral method to compute the spatial derivatives. We assume an initial pressure state and at each time step compute the wetting- and non wetting-fluid pressures at a given saturation. Then, we solve Richards’s equation for the non wetting-fluid saturation and proceed to the next time step with the updated saturations values. The pressure and saturation equations are first solved separately and the results compared to known analytical solutions showing the accuracy of the algorithm. Then, the coupled system is solved. In all the cases, the non-wetting fluid is injected at a given point in space as a boundary condition and capillarity effects are taken into account. The examples consider oil injection in a water-saturated porous medium.Fil: Carcione, Jose M.. Instituto Nazionale di Oceanografia e di Geofisica Sperimentale; ItaliaFil: Picotti, Stefano. Instituto Nazionale di Oceanografia e di Geofisica Sperimentale; ItaliaFil: Santos, Juan Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Instituto del Gas y del Petróleo; Argentina. Universidad Nacional de La Plata; Argentina. Purdue University; Estados UnidosFil: Qadrouh, Ayman. King Abdulaziz City For Science And Technology; Arabia SauditaFil: Almalki, Hashim S.. King Abdulaziz City For Science And Technology; Arabia Saudit

A nodal discontinuous Galerkin finite element method for the poroelastic wave equation

We use the nodal discontinuous Galerkin method with a Lax-Friedrich flux to model the wave propagation in transversely isotropic and poroelastic media. The effect of dissipation due to global fluid flow causes a stiff relaxation term, which is incorporated in the numerical scheme through an operator splitting approach. The well-posedness of the poroelastic system is proved by adopting an approach based on characteristic variables. An error analysis for a plane wave propagating in poroelastic media shows a convergence rate of O(hn+1). Computational experiments are shown for various combinations of homogeneous and heterogeneous poroelastic media

Finite-element harmonic experiments to model fractured induced anisotropy in poroelastic media

Fractures in a fluid-saturated poroelastic-Biot-medium can be modeled as very thin highly permeable and compliant layers within a porous background. A Biot medium containing a dense set of aligned fractures behaves as an effective transversely isotropic and viscoelastic (TIV) medium at the macroscale when the predominant wavelength is much larger than the average distance between fractures. One important mechanism in Biot media at seismic frequencies is wave-induced fluid flow generated by fast compressional waves at mesoscopic-scale heterogeneities, generating slow diffusion-type Biot waves. In this work, we present and analyze a collection of time-harmonic finite element experiments that take into account the effects of the presence of aligned fractures and interlayer fluid flow occurring at the mesoscale, allowing us to determine the complex and frequency dependent stiffnesses of the effective TIV medium at the macroscale.These numerical upscaling experiments are defined as boundary value problems on representative samples of the fractured material, with boundary conditions associated with compressibility and shear tests, which are solved using the finite element (FE) method. The FE space chosen to discretize each component of the solid displacement vector is that of globally continuous piecewise bilinear functions, while for the fluid phase the vector part of the Raviart-Thomas-Nedelec space of zero order is employed. We present results on the uniqueness of the solution of the continuous and discrete problems, and derive optimal a priori energy error estimates. First, the numerical results are validated with those of a theory valid for fluid flow perpendicular to the fracture layering and independent of the loading direction, so that the attenuation mechanism can be represented by a single relaxation function. Then, the methodology is applied to cases for which no analytical solutions are available, such as a fractured Biot medium saturated with brine and patches of CO2 and a brine saturated sample of uniform background and fractures with fractal variations in their petrophysical properties.Fil: Santos, Juan Enrique. Universidad de Buenos Aires. Facultad de Ingeniería. Instituto del Gas y del Petróleo; Argentina. Purdue University; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Carcione, Jose M.. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; Itali