The exploding-reflector concept for ground-penetrating-radar modeling

The simulation of a stacked radargram requires the calculation of a set of common-source experiments and application of the standard processing sequence. To reduce computing time, a zero-offset stacked section can be obtained with a single simulation, by using the exploding-reflector concept and the so-called non-reflecting wave equation. This non-physical modification of the wave equation implies a constant impedance model to avoid multiple reflections, which are, in principle, absent from stacked sections and constitute unwanted artifacts in migration processes. Magnetic permeability is used as a free parameter to obtain a constant impedance model and avoid multiple reflections. The reflection strength is then implicit in the source strength. Moreover, the method generates normal-incidence reflections, i.e. those having identical downgoing and upgoing wave paths.Exploding reflector experiments provide correct travel times of diffraction and reflection events, in contrast to the plane-wave method

Numerical experiments of fracture-induced velocity and attenuation anisotropy

Fractures are common in the Earth's crust due to different factors, for instance, tectonic stresses and natural or artificial hydraulic fracturing caused by a pressurized fluid. A dense set of fractures behaves as an effective long-wavelength anisotropic medium, leading to azimuthally varying velocity and attenuation of seismic waves. Effective in this case means that the predominant wavelength is much longer than the fracture spacing. Here, fractures are represented by surface discontinuities in the displacement u and particle velocity v as [κ · u + η · v], where the brackets denote the discontinuity across the surface, κ is a fracture stiffness and η is a fracture viscosity. We consider an isotropic background medium, where a set of fractures are embedded. There exists an analytical solution-with five stiffness components-for equispaced plane fractures and an homogeneous background medium. The theory predicts that the equivalent medium is transversely isotropic and viscoelastic. We then perform harmonic numerical experiments to compute the stiffness components as a function of frequency, by using a Galerkin finite-element procedure, and obtain 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 algorithm is tested with the analytical solution and then used to obtain the stiffness components for general heterogeneous cases, where fractal variations of the fracture compliances and background stiffnesses are considered.Este documento tiene una corrección (ver documento relacionado).Facultad de Ciencias Astronómicas y Geofísica

Anisotropic poroelasticity and wave-induced fluid flow: Harmonic finite-element simulations

A dominant P-wave attenuation mechanism in reservoir rocks at seismic frequencies is due to wave-induced fluid flow (mesoscopic loss). The P-wave induces a fluid-pressure difference at mesoscopic-scale inhomogeneities (larger than the pore size but smaller than the wavelength), generating fluid flow and slow (diffusion) Biot waves. The theory has been developed in the 1970s for the symmetry axis of the equivalent transversely isotropic (TI) medium corresponding to a finely layered medium, and has recently been generalized to all propagation angles. The new theory states that the fluid-flow direction is perpendicular to the layering plane and it is independent of the loading direction. As a consequence, the relaxation behaviour can be described by a single relaxation function, since the medium consists of plane homogeneous layers. Besides P-wave losses, the coupling between the qP and qSV waves generates shear-wave anisotropic velocity dispersion and attenuation. In this work, we introduce a set of quasi-static numerical experiments to determine the equivalent viscoelastic TI medium to a finely layered poroelastic medium, which is validated using a recently developed analytical solution. The modelling technique is the finite-element (FE) method, where the equations of motion are solved in the space-frequency domain. Numerical rock physics may, in many circumstances, offer an alternative to laboratory measurements. Numerical experiments are inexpensive and informative since the physical process of wave propagation can be inspected during the experiment. Moreover, they are repeatable, essentially free from experimental errors, and may easily be run using alternative models of the rock and fluid properties. We apply the methodology to the Utsira aquifer of the North Sea, where carbon dioxide (CO2) has been injected during the last 15 years. The tests consider alternating layers of the same rock saturated with gas and brine and a sequence of gas-saturated sandstone and mudstone layers, which represent possible models of the reservoir and cap rock of the aquifer system. The numerical examples confirm the new theory and illustrate the implementation of the harmonic tests to determine the complex and frequency-dependent effective stiffnesses and the associated wave velocities and quality factors.Facultad de Ciencias Astronómicas y Geofísica

Numerical experiments of fracture-induced velocity and attenuation anisotropy

Fractures are common in the Earth's crust due to different factors, for instance, tectonic stresses and natural or artificial hydraulic fracturing caused by a pressurized fluid. A dense set of fractures behaves as an effective long-wavelength anisotropic medium, leading to azimuthally varying velocity and attenuation of seismic waves. Effective in this case means that the predominant wavelength is much longer than the fracture spacing. Here, fractures are represented by surface discontinuities in the displacement u and particle velocity v as [κ · u + η · v], where the brackets denote the discontinuity across the surface, κ is a fracture stiffness and η is a fracture viscosity. We consider an isotropic background medium, where a set of fractures are embedded. There exists an analytical solution-with five stiffness components-for equispaced plane fractures and an homogeneous background medium. The theory predicts that the equivalent medium is transversely isotropic and viscoelastic. We then perform harmonic numerical experiments to compute the stiffness components as a function of frequency, by using a Galerkin finite-element procedure, and obtain 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 algorithm is tested with the analytical solution and then used to obtain the stiffness components for general heterogeneous cases, where fractal variations of the fracture compliances and background stiffnesses are considered.Este documento tiene una corrección (ver documento relacionado).Facultad 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.Facultad de Ciencias Astronómicas y Geofísica

Anisotropic poroelasticity and wave-induced fluid flow: Harmonic finite-element simulations

A dominant P-wave attenuation mechanism in reservoir rocks at seismic frequencies is due to wave-induced fluid flow (mesoscopic loss). The P-wave induces a fluid-pressure difference at mesoscopic-scale inhomogeneities (larger than the pore size but smaller than the wavelength), generating fluid flow and slow (diffusion) Biot waves. The theory has been developed in the 1970s for the symmetry axis of the equivalent transversely isotropic (TI) medium corresponding to a finely layered medium, and has recently been generalized to all propagation angles. The new theory states that the fluid-flow direction is perpendicular to the layering plane and it is independent of the loading direction. As a consequence, the relaxation behaviour can be described by a single relaxation function, since the medium consists of plane homogeneous layers. Besides P-wave losses, the coupling between the qP and qSV waves generates shear-wave anisotropic velocity dispersion and attenuation. In this work, we introduce a set of quasi-static numerical experiments to determine the equivalent viscoelastic TI medium to a finely layered poroelastic medium, which is validated using a recently developed analytical solution. The modelling technique is the finite-element (FE) method, where the equations of motion are solved in the space-frequency domain. Numerical rock physics may, in many circumstances, offer an alternative to laboratory measurements. Numerical experiments are inexpensive and informative since the physical process of wave propagation can be inspected during the experiment. Moreover, they are repeatable, essentially free from experimental errors, and may easily be run using alternative models of the rock and fluid properties. We apply the methodology to the Utsira aquifer of the North Sea, where carbon dioxide (CO2) has been injected during the last 15 years. The tests consider alternating layers of the same rock saturated with gas and brine and a sequence of gas-saturated sandstone and mudstone layers, which represent possible models of the reservoir and cap rock of the aquifer system. The numerical examples confirm the new theory and illustrate the implementation of the harmonic tests to determine the complex and frequency-dependent effective stiffnesses and the associated wave velocities and quality factors.Facultad de Ciencias Astronómicas y Geofísica

Acoustic and mechanical response of reservoir rocks under variable saturation and effective pressure

We investigate the acoustic and mechanical properties of a reservoir sandstone saturated by two immiscible hydrocarbon fluids, under different saturations and pressure conditions. The modeling of static and dynamic deformation processes in porous rocks saturated by immiscible fluids depends on many parameters such as, for instance, porosity, permeability, pore fluid, fluid saturation, fluid pressures, capillary pressure, and effective stress. We use a formulation based on an extension of Biot's theory, which allows us to compute the coefficients of the stress-strain relations and the equations of motion in terms of the properties of the single phases at the in situ conditions. The dry-rock moduli are obtained from laboratory measurements for variable confining pressures. We obtain the bulk compressibilities, the effective pressure, and the ultrasonic phase velocities and quality factors for different saturations and pore-fluid pressures ranging from normal to abnormally high values. The objective is to relate the seismic and ultrasonic velocity and attenuation to the microstructural properties and pressure conditions of the reservoir. The problem has an application in the field of seismic exploration for predicting pore-fluid pressures and saturation regimes

Erratum: "Numerical experiments of fracture-induced velocity and attenuation anisotropy"

Este documento es una errata de "Numerical experiments of fracture-induced velocity and attenuation anisotropy" (ver documento relacionado).Facultad de Ciencias Astronómicas y Geofísica

Numerical experiments of fracture-induced velocity and attenuation anisotropy

Fractures are common in the Earth's crust due to different factors, for instance, tectonic stresses and natural or artificial hydraulic fracturing caused by a pressurized fluid. A dense set of fractures behaves as an effective long-wavelength anisotropic medium, leading to azimuthally varying velocity and attenuation of seismic waves. Effective in this case means that the predominant wavelength is much longer than the fracture spacing. Here, fractures are represented by surface discontinuities in the displacement u and particle velocity v as [κ · u + η · v], where the brackets denote the discontinuity across the surface, κ is a fracture stiffness and η is a fracture viscosity. We consider an isotropic background medium, where a set of fractures are embedded. There exists an analytical solution-with five stiffness components-for equispaced plane fractures and an homogeneous background medium. The theory predicts that the equivalent medium is transversely isotropic and viscoelastic. We then perform harmonic numerical experiments to compute the stiffness components as a function of frequency, by using a Galerkin finite-element procedure, and obtain 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 algorithm is tested with the analytical solution and then used to obtain the stiffness components for general heterogeneous cases, where fractal variations of the fracture compliances and background stiffnesses are considered.Este documento tiene una corrección (ver documento relacionado).Facultad de Ciencias Astronómicas y Geofísica

Geophysical signature of a World War i tunnel-like anomaly in the Forni Glacier (Punta Linke, Italian Alps)

Global warming and the associated glacier retreat recently revealed the entrance to an ice\u2013rock tunnel, at an altitude of 3c3600 m a.s.l., in the uppermost portion of the Forni Glacier in the Central Italian Alps. The tunnel served as an entrance to an Austro-Hungarian cableway station excavated in the rocks during the Great War just behind the frontline. A comprehensive geophysical survey, based on seismic and ground-penetrating radar profiling, was then undertaken to map other possibleWorldWar I (WWI) remains still embedded in the ice. The ice\u2013rock interface was reconstructed over the entire saddle and in the uppermost portion of the glacier. A prominent linear reflector was surprisingly similar to the common response of buried pipes. The reflector orientation, almost longitudinal to the slope, does not seem to be compatible with a glacial conduit or with other natural features. Numerical simulations of a series of possible targets constrained interpretation to a partly water-filled rounded shape cavity. The presence of a preserved WWI tunnel connecting Mount Vioz and Punta Linke could be considered a realistic hypothesis. The Forni glacier could be still considered polythermal and comprised of cold ice without basal sliding in its top portion