Stefano Picotti

P-wave seismic attenuation by slow-wave diffusion: Effects of inhomogeneous rock properties

Recent research has established that the dominant P-wave attenuation mechanism in reservoir rocks at seismic frequencies is because of 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, typically tens of centimeters) and generates fluid flow and slow (diffusion) Biot waves (continuity of pore pressure is achieved by energy conversion to slow P-waves, which diffuse away from the interfaces). In this context, we consider a periodically stratified medium and investigate the amount of attenuation (and velocity dispersion) caused by different types of heterogeneities in the rock properties, namely, porosity, grain and frame moduli, permeability, and fluid properties. The most effective loss mechanisms result from porosity variations and partial saturation, where one of the fluids is very stiff and the other is very compliant, such as, a highly permeable sandstone at shallow depths, saturated with small amounts of gas (around 10% saturation) and water. Grain- and frame-moduli variations are the next cause of attenuation. The relaxation peak moves towards low frequencies as the (background) permeability decreases and the viscosity and thickness of the layers increase. The analysis indicates in which cases the seismic band is in the relaxed regime, and therefore, when the Gassmann equation can yield a good approximation to the wave velocity.

Angular and Frequency-Dependent Wave Velocity and Attenuation in Fractured Porous Media

Wave-induced fluid flow generates a dominant attenuation mechanism in porous media. It consists of energy loss due to P-wave conversion to Biot (diffusive) modes at mesoscopic-scale inhomogeneities. Fractured poroelastic media show significant attenuation and velocity dispersion due to this mechanism. The theory has first been developed for the symmetry axis of the equivalent transversely isotropic (TI) medium corresponding to a poroelastic medium containing planar fractures. In this work, we consider the theory for all propagation angles by obtaining the five complex and frequency-dependent stiffnesses of the equivalent TI medium as a function of frequency. We assume that the flow direction is perpendicular to the layering plane and is independent of the loading direction. As a consequence, the behaviour of the medium can be described by a single relaxation function. We first consider the limiting case of an open (highly permeable) fracture of negligible thickness. We then compute the associated wave velocities and quality factors as a function of the propagation direction (phase and ray angles) and frequency. The location of the relaxation peak depends on the distance between fractures (the mesoscopic distance), viscosity, permeability and fractures compliances. The flow induced by wave propagation affects the quasi-shear (qS) wave with levels of attenuation similar to those of the quasi-compressional (qP) wave. On the other hand, a general fracture can be modeled as a sequence of poroelastic layers, where one of the layers is very thin. Modeling fractures of different thickness filled with CO2 embedded in a background medium saturated with a stiffer fluid also shows considerable attenuation and velocity dispersion. If the fracture and background frames are the same, the equivalent medium is isotropic, but strong wave anisotropy occurs in the case of a frameless and highly permeable fracture material, for instance a suspension of solid particles in the fluid.

P-wave seismic attenuation by slow-wave diffusion: Numerical experiments in partially saturated rocks

P-waveattenuationbyslow-wavediffusionisasignificant loss mechanism at seismic frequencies. This effect is known as mesoscopic loss, because it is a consequence of fluid flow at mesoscopic-scale inhomogeneities. These are larger than the pore size but smaller than the wavelength, typically tens of centimeters, and are due to local variations in lithological properties or to patches of immiscible fluids. Basically, a P-wave traveling in a porous medium induces a fluid-pressuregradientinregionsofdifferentproperties,suchaspatches saturated with different fluids, generating slow P-waves, which diffuse away from the interfaces separating the fluids. This mechanism can be explained by the combined effect of mesoscopic-scale inhomogeneities and mode conversion at interfaces. We consider a periodically stratified medium and perform numerical experiments to determine the P-wave quality factor in partially saturated rocks. The modeling method is an iterative domain-decomposition 2D finite-elementalgorithmforsolvingBiotequationsofmotioninaparallel computer, which is a requirement to run the numerical experiments at seismic frequencies. The simulated pulses show evidence of the mesoscopic-loss mechanism, and the quality factors estimated with the spectral-ratio and frequency-shift methods are in good agreement with the theoretical valuespredictedbytheWhitetheory.Errorsintheestimation of the quality factor are less than 5% spectral ratio and 3% frequencyshift.

A viscoelastic representation of wave attenuation in porous media

The theories developed by White and co-workers describe the complex moduli of a medium partially saturated with spherical gas pockets and those of stratified layers composed of two heterogeneous porous media. A generalization to gas patches of arbitrary shape has been given by Johnson. These models represent the mesoscopic-loss mechanism, which is one of the most significant causes of attenuation of seismic waves in reservoir rocks. Comparison of Whites and Johnsons models show that, as the patch shape complexity increases, the patch geometry affects much more the relaxation frequency than it affects the maximum loss. The simulation of synthetic seismograms requires solving Biots differential equations with very small grid spacings, because the loss mechanism involves the conversion of fast P-wave energy to diffusion energy in the form of the Biot slow wave. Because the wavelength of this wave can be very small, the poroelastic solution requires a very large amount of storage and computer time. An efficient approach is to approximate Whites moduli by the Zener model and then solve the single-phase viscoelastic differential equations.

Seismic modeling to monitor CO2 geological storage: The Atzbach- Schwanenstadt gas field

[1] We develop a petro-elastical numerical methodology to compute realistic synthetic seismograms and analyze the sensitivity of the seismic response when injecting carbon dioxide (CO2) in a depleted gas reservoir. The petro-elastical model describes the seismic properties of the reservoir rock saturated with CO2, methane and brine, and allows us to estimate the distribution and saturation of CO2 during the injection process. The gas properties, as a function of the in-situ pressure and temperature conditions, are computed with the Peng-Robinson equation of state, taking into account the absorption of gas by brine. Wave attenuation and velocity dispersion are based on the mesoscopic loss mechanism, which is simulated by an upscaling procedure to obtain an equivalent viscoelastic medium corresponding to partial saturation at the mesoscopic scale. Having the equivalent complex and frequency-dependent bulk (dilatational) modulus, we include shear attenuation and perform numerical simulations of wave propagation at the macroscale by solving the viscoelastic differential equations using the memory-variable approach. The pseudo-spectral modeling method allows general material variability and provides a complete and accurate characterization of the reservoir. The methodology is used to assess the sensitivity of the seismic method for monitoring the CO2 geological storage at the Atzbach-Schwanestadt depleted gas-field in Austria. The objective of monitoring is the detection of the CO2 plume in the reservoir and possible leakages of CO2. The leakages are located at different depths, where the CO2 is present as gaseous, liquid and supercritical phases. Even though the differences can be very subtle, this work shows that seismic monitoring of CO2 from the surface is possible. While the identification of shallow leakages is feasible, the detection of the plume and deep leakages, located in the caprock just above the injection formation, is more difficult, but possible by using repeatability metrics, such as the normalized RMS (NRMS) images. Considering real-data conditions, affected by random noise, a reference detection threshold for deep leakages and the CO2 plume in the reservoir corresponds to a signal-to-noise ratio of about 10 dB.

Anisotropy and crystalline fabric of Whillans Ice Stream (West Antarctica) inferred from multicomponent seismic data

Crystal orientation fabric (COF) describes the intrinsic anisotropic nature of ice and is an important parameter for modeling glacier flow. We present the results of three-component active-source seismic observations from the Whillans Ice Stream (WIS), a fast-flowing ice stream in West Antarctica. Surface-wave dispersion analysis, ray tracing, and traveltime inversion of compressional (P) and shear (S) waves reveal the presence of transversely isotropic ice with a vertical axis of symmetry (VTI) beneath approximately 65 m of isotropic firn. The ice stream is characterized by weak anisotropy, involving an average ice thickness of approximately 780 m. The analysis indicates that about 95% of the ice mass is anisotropic, and the crystalline c axes span within an average broad cone angle of 73 ± 10° with respect to the vertical axis. Moreover, the mean temperature T (below the firn) estimated from seismic data is −15 ± 5°C. These data do not show evidence of englacial seismic reflectivity, which indicates the lack of abrupt changes in the COF. The presence of azimuthal anisotropy due to transversely compressive flow or fractures aligned along a preferential direction is also excluded. We suggest that the observed VTI ice structure is typical of large ice streams in regions where basal sliding and bed deformation dominate over internal glacial deformation.

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

Oscillatory numerical experiments in finely layered anisotropic viscoelastic media

[{\varvec{ \kappa}}\cdot {\bf u} + {\varvec{\eta}} \cdot {\bf v} ],