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

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

Discrimination of fizz water and gas reservoir by AVO analysis: a modified approach

Amplitude versus offset response is analogous to variation in P-wave velocity re- sulting from different pore fluid saturations. However, the input parameters of fluid mixtures such as fluid modulus and density are often estimated using volume average method, and the resulting estimates of fluid effects can be overestimated. In seismic frequency band, the vol- ume average method ignores the heat and mass transfers between the liquid and gas phases, which are caused by pore pressure perturbations. These effects need to be accounted for the interpretation of the seismic events and forward modeling of fizz water reservoirs. The con- ventional model is corrected in present study by considering the thermodynamic properties of the fluid phases. This corrected model is then successfully applied on a gas producing field in the North Sea. AVO response, based on the corrected model is highly affected by pressure related variations in bulk modulus of multi-phase formation fluid. Velocity push down effect appears, as the free gas saturation generates stronger AVO response than ob- tained by a conventional AVO model. The, present research reveals that such response is helpful to discriminate fizz water from commercial gas, to detect primary leakage of gas (CO 2 or CH 4 ) from geological structures and to model free gas effects on seismic attributes

Multiple scattering of surface waves

Multiple scattering of elastic waves in disordered media offers a complexity of the wave field that is challenging to unravel. The subsurface is an example of a medium with disordered inhomogeneity at all scales. However, because waves that bounce around for a long time and/or distance sample the Earth well, they potentially offer great insight into the structure of the subsurface. A surface wave scattering model is presented to aid the understanding of multiple scattering. Advantages of this model include accessibility of the wave field within the scattering medium, tunable scattering strength, availability of phase and amplitude information, and the relative longevity of surface waves. Accompanied by a state-ofthe-art non-contacting data acquisition scheme, this system proved ideal for unveiling the effects of multiple scattering. When a pulse is launched in a strongly scattering medium, it travels ballistically at first, but turns diffusive as multiply scattered waves interfere with the incident pulse. Radiative transfer has proven to describe both the transmission of the coheren