Seismic Wave Attenuation in Carbonates

The effect of pore fluids on seismic wave attenuation in carbonate rocks is important for interpreting remote sensing observations of carbonate reservoirs undergoing enhanced oil recovery. Here we measure the elastic moduli and attenuation in the laboratory for five carbonate samples with 20% to 30% porosity and permeability between 0.03 and 58.1 mdarcy. Contrary to most observations in sandstones, bulk compressibility losses dominate over shear wave losses for dry samples and samples fully saturated with either liquid butane or brine. This observation holds for four out of five samples at seismic (10–1000 Hz) and ultrasonic frequencies (0.8 MHz) and reservoir pressures. Attenuation modeled from the modulus data using Cole-Cole relations agrees in that the bulk losses are greater than the shear losses. On average, attenuation increases by 250% when brine substitutes a light hydrocarbon in these carbonate rocks. For some of our samples, attenuation is frequency-dependent, but in the typical exploration frequency range (10–100 Hz), attenuation is practically constant for the measured samples

Fracture of disordered solids in compression as a critical phenomenon: II. Model Hamiltonian for a population of interacting cracks

To obtain the probability distribution of 2D crack patterns in mesoscopic regions of a disordered solid, the formalism of Paper I requires that a functional form associating the crack patterns (or states) to their formation energy be developed. The crack states are here defined by an order parameter field representing both the presence and orientation of cracks at each site on a discrete square network. The associated Hamiltonian represents the total work required to lead an uncracked mesovolume into that state as averaged over the initial quenched disorder. The effect of cracks is to create mesovolumes having internal heterogeneity in their elastic moduli. To model the Hamiltonian, the effective elastic moduli corresponding to a given crack distribution are determined that includes crack-to-crack interactions. The interaction terms are entirely responsible for the localization transition analyzed in Paper III. The crack-opening energies are related to these effective moduli via Griffith's criterion as established in Paper I.Comment: 9 pages, 1 figur

Imaging and quantification of gas hydrate and free gas at the Storegga Slide offshore Norway

Wide–angle reflection seismic experiments were performed at the Storegga slide offshore Norway in 2002 with the goal to quantify the amount of gas hydrate and free gas in the sediment. Twenty‐two stations with Ocean Bottom Hydrophones (OBH) and Seismometers (OBS) were deployed for a 2D and a 3D experiment. Kirchhoff depth migration is used to transform the seismic wide–angle data into images of the sediment layers and to obtain P wave velocity–depth functions. The gas hydrate and free gas saturations are estimated from the elastic properties of the sediment on the basis of the Frenkel–Gassmann equations. There is 5–15% gas hydrate in the pore space of the sediment in the gas hydrate stability zone (GHSZ). The free gas saturation takes the value of 0.8% for a homogeneous distribution of gas in the pore water and 7% for the model of a patchy gas distribution

Seismic attenuation in fractured porous media: insights from a hybrid numerical and analytical model

Seismic attenuation in fluid-saturated porous rocks can occur by geometric spreading, wave scattering or the internal dissipation of energy, most likely due to the squirt-flow mechanism. In principle, the pattern of seismic attenuation recorded on an array of sensors contains information about the medium, in terms of material heterogeneity and anisotropy, as well as material properties such as porosity, crack density, and pore-fluid composition and mobility. In practice, this inverse problem is challenging. Here we provide some insights into the effects of internal dissipation by analysing synthetic data produced by a hybrid numerical and analytical model for seismic wave propagation in a fractured medium embedded within a layered geological structure. The model is made up of one anisotropic and three isotropic horizontal layers. The anisotropic layer consists of a porous, fluid-saturated material containing vertically aligned inclusions representing a set of fractures. This combination allows squirt-flow to occur between the pores in the matrix and the model fractures. Our results show that the fluid mobility and the associated relaxation time of the fluid-pressure gradient control the frequency range over which attenuation occurs. This induced attenuation increases with incidence angle and azimuth away from the fracture strike-direction. Azimuthal variations in the induced attenuation are elliptical allowing the fracture orientations to be obtained from the axes of the ellipse. These observations hold out the potential of using seismic attenuation as an additional diagnostic in the characterisation of rock formations for a variety of applications including hydrocarbon exploration and production, subsurface storage of CO2, and geothermal energy extraction