This paper studies the effect on the overall properties of a cracked solid of the existence of connections between otherwise isolated cracks and of small-scale porosity within the 'solid' material. The intention is to provide effective medium models for the calculation of elastic wave propagation with wavelengths greater than the dimensions of the cracks. The method follows that of earlier papers in which the overall elastic properties are directly related to parameters governing the microstructure, such as crack number density and the mean radius and spacing distance of the cracks. Expressions derived by the method of smoothing are evaluated to second order in the number density of cracks, thereby incorporating crack-crack interactions through both the strain field in the solid and the flow field of fluids in the pores.Flow of interstitial liquids tends to weaken the material; the limit of zero flow is equivalent to isolating the cracks and the limit of free flow is equivalent to dry (gasfilled) cracks. It also introduces additional attenuation. The inclusion of small-scale porosity gives a model of 'equant porosity' which is more closely constrained by the details of crack dynamics than earlier models.

There is general agreement between different theories giving expressions for the overall properties of materials with dry, aligned cracks if the number density of cracks is small. There is also very fair agreement for fluid‐filled isolated cracks. However, there are considerable differences between two separate theories for fluid‐filled cracks with equant porosity. Comparison with recently published experimental data on synthetic sandstones gives a good fit with theory for dry samples. However, although the crack number density in the laboratory sample is such that first‐order theory is unlikely to apply, expressions correct to second order (in the number density) provide a worse fit. It also appears that the ratio of wavelength to crack size is not sufficiently great for any detailed comparison with effective‐medium theories, which are valid only when this ratio is large. The data show dispersion effects for dry cracks and scattering, neither of which will occur at sufficiently long wavelengths. Data from the water‐saturated samples indicate that the effect of equant porosity is significant, although the two theories differ strongly as to just how significant. Once again, and in spite of the reservations mentioned above, a reasonable fit between theory and observation can be shown.

S U M M A R YFluid flow in the Earth's crust plays an important role in a number of geological processes. In relatively tight rock formations such flow is usually controlled by open macrofractures, with significant implications for ground water flow and hydrocarbon reservoir management. The movement of fluids in the fractured media will result in changes in the pore pressure and consequently will cause changes to the effective stress, traction and elastic properties. The main purpose of this study is to numerically examine the effect of pore pressure changes on seismic wave propagation (i.e. the effects of pore pressures on amplitude, arrival time, frequency content). This is achieved by using dual simulations of fluid flow and seismic propagation in a common 2-D fracture network. Note that the dual simulations are performed separately as the coupled simulations of fluid flow and seismic wave propagations in such fracture network is not possible because the timescales of fluid flow and wave propagation are considerably different (typically, fluid flows in hours, whereas wave propagation in seconds). The flow simulation updates the pore pressure at consecutive time steps, and thus the elastic properties of the rock, for the seismic modelling. In other words, during each time step of the flow simulations, we compute the elastic response corresponding to the pore pressure distribution. The relationship between pore pressure and fractures is linked via an empirical relationship given by Schoenberg and the elastic response of fractures is computed using the equivalent medium theory described by Hudson and Liu. Therefore, we can evaluate the possibility of inferring the changes of fluid properties directly from seismic data. Our results indicate that P waves are not as sensitive to pore pressure changes as S and coda (or scattered) waves. The increase in pore pressure causes a shift of the energy towards lower frequencies, as shown from the spectrum (as a result of scattering attenuation). Another important observation is that the fluid effects on the wavefield vary significantly with the source-receiver direction, that is, the azimuth relative to the fracture orientation. These results have significant implications for the characterization of naturally fractured reservoirs using seismic methods, and may impact on experimental design to infer such attributes in a real reservoir situation, particularly in acquiring time-lapse seismic data.

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Fluid flow in the Earth's crust plays an important role in a number of geological processes, and such flow is usually believed to be controlled by open macro-fractures in at least carbonate reservoirs. The movement of fluids in the fractured media will result in changes on the pore pressure and consequently will cause changes to the effective stress, traction and elastic properties. The main purpose of this study is to examine the effect of pore pressure changes on seismic wave propagation (i.e. amplitude, frequency range). This is achieved by using a dual simulation of fluid flow and seismic propagation in a common fracture network. The flow simulation updates the pore pressure at consecutive time steps, and thus the elastic properties of the rock, for the seismic modelling. Therefore we can evaluate the possibility of inferring the changes of fluid properties directly from seismic data. Our results indicate that Pwaves are not as sensitive to pore pressure changes as Sand coda or scattered waves. The increase in pore pressure causes a shift of the energy towards lower frequencies, as shown from the spectrum (as a result of attenuation). Another important observation is that the fluid effects on the wavefield vary significantly with the source-receiver direction, i.e. the azimuth relative to the fracture orientation.