**※ Download: ****Crack density attenuation**

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**Effect of pore structure on the dispersion and attenuation of fluid**

Effects of CO2 on P For penny shapes, the aspect ratio cannot be too large; otherwise, the predicted velocities will exceed the upper bound. Ross Lake Violet Grove Sask. Therefore, the crack density can be estimated from the values of the phase velocity for the cases of densely distributed cracks even if the effect of the multiple crack interactions is not considered. However, our modeling results show that thin, isolated regions with low Q also may be detected through changes in seismic waves scattered or reflected by them. Long-wavelength propagation in composite elastic media: J.

Wave attenuation and dispersion in randomly cracked solids—I. Slit cracks For simplicity, we show only the difference in the phase attribute that is caused by the finite Q values Figure 9c. This is because the cracked zone also behaves as a soft material to the incident long-wavelength wave due to the crack distribution. The crack density in a fault zone has been estimated on a basis of the static elastic properties of cracked media on the assumption of low wavenumber approximation e. The data are fitted by a power decay law function: Damage parameters as a function of normalized radial distance from impact point for three directions. From the results of the Kuster-Toksöz model, we find that the changes in rock properties depend largely on the inclusion shape.

Effects of CO2 on P Figure shows the aspect ratio distribution functions as a function of the effective pressure for sample T1 and T2, calculated by equation using the exponential curve fit relation of equation. Therefore the reduction of the measured compressional wave velocity in the x direction by the tensile cracks is expected to be higher than that in the other two directions, which agrees with our results and. Direct measurement of the crack damage using microscope will be carried out in the near future. Therefore, a fracture zone distributed parallel cracks is considered as an anisotropic layer rather than a low-velocity layer and the elastic constants, crack density and the thickness of the fracture zone can be estimated from the frequency dependence of the reflection coefficients for long incident wavelengths. There is a clear correlation between the increase in reflection amplitude and increased crack density. Nonlinear least squares fit of these data with the radial distance from the impact point follows a power decay law: Attenuation coefficients as a function of normalized radial distance from impact point for three directions.

Effects of shock‐induced cracks on the ultrasonic velocity and attenuation in granite The analysis is limited to small crack densities, and it has some direct relevance to the detection and characterization of damages in randomly cracked solids by ultrasonics. They still assumed the wavelength considerably longer than the crack length. In section , the new model is used to explain the measured velocities of these water-saturated samples, and the possible velocity dispersion of tight gas sandstone with very different pore structures is discussed. The new model is within 0. Several theoretical models of these effective properties developed in recent years predict that the fractured rock will be inelastic, with complex seismic velocities and elastic moduli. Tang proposed a squirt-flow model which included the effects of cracks, where the characteristic frequency and fluid transport parameters are represented in crack density and aspect ratio.

Scattering attenuation, dispersion and reflection of SH waves in two We consider an elastic medium with periodic distribution of cracks in a zone as illustrated in. The calculated velocity has an error of 2% as estimated by the accuracy of the traveltime and length measurements. Then, the possible velocity dispersion for our tight gas samples with very different pore structures is discussed with this new method. There was no attempt made to adjust parameters of the model to find lower values of Q since it was designed in part to use for other fluid flow studies, but it should be noted that by changing parameters related to porosity, permeability and fluid properties, it is possible to create realistic models with Q as low as 30. The green dash-dot lines are Hashin-Shtrikman bounds. It is also revealed from seismic observations, such as shear wave splitting and P-wave polarization anomalies , that a fault zone is characterized as a zone of densely distributed cracks aligned parallel to the fault plane. From the modeling results for tight sand from the Ross Lake area Figure 4b , we find that the P-velocity variations with crack density show an apparent dependence on rock properties of the uncracked rock, while the S-velocity displays a similar variation with crack density.

Seismic Models of Reflections from Attenuating Layers The thickness of the buffer plates was chosen to avoid overlapping of the reflected waves from different surfaces. Thus, sample T1 is dominated by at least two stiff pore systems and low-aspect ratio microcracks, and represents a typical dual porosity media, while the pores in sample T2 are more homogeneous, dominated mainly by stiff pores. We can also examine the instantaneous phase attribute, following the analysis applied to the homogeneous reservoir layer. The reflection coefficient calculated for the best-fit model of the single low-velocity layer is also plotted by the solid curve for the wavenumber range used in fitting in each of a and b. In general, a fault zone consists of several fault segments e.

Effects of CO2 on P The characteristic non-dimensional wavenumber of the wavelets, k ca, is assumed to be 0. This figure shows that both of the reflection coefficients agree well in the low wavenumber range but our result is not theoretically predicted in the high wavenumber range again. This means that a fracture zone distributed parallel cracks is considered as an anisotropic layer for long incident wavelengths. The porosity and permeability of T1 are 3. Squirt-flow is often considered important at well-logging and ultrasonic frequencies, and only plays a role in seismic exploration frequencies under the condition that the porous media is saturated with high viscosity fluid, or the rock has a very low permeability such as tight gas sandstone Pride et al, Batzle et al. Ravi Shekhar for assistance in creating some of the heterogeneous fractured reservoir models that were used to set up calculations of synthetic seismograms. We assume randomly distributed cracks in a rectangular-bounded region, which simulate a cracked zone.

Wave attenuation and dispersion in randomly cracked solids—I. Slit cracks Here the normalized amplitudes are larger than unity at the stations close to the ends of the crack distribution region. Ross Lake porous channel sand: the variation of effective velocities from the Kuster-Toksöz model with crack shape and aspect ratio. Because modeling wave propagation in 3-D inelastic media with exact finite difference techniques is slow and difficult to implement, we apply a technique using Born scattering theory, and our application is a unique and new implementation that allows us to examine the influence of localized regions of strongly attenuating materials embedded within the model. This limit is about 0. We show it is possible to estimate the crack density and thickness of a cracked zone by fitting the reflection coefficients to those of an anisotropic layer for incident long-wavelength waves. The velocity structure is not estimated correctly; it is obvious that the width is underestimated.

**Effect of pore structure on the dispersion and attenuation of fluid**

## Effects of CO2 on P

For penny shapes, the aspect ratio cannot be too large; otherwise, the predicted velocities will exceed the upper bound. Ross Lake Violet Grove Sask. Therefore, the crack density can be estimated from the values of the phase velocity for the cases of densely distributed cracks even if the effect of the multiple crack interactions is not considered. However, our modeling results show that thin, isolated regions with low Q also may be detected through changes in seismic waves scattered or reflected by them. Long-wavelength propagation in composite elastic media: J.

## Wave attenuation and dispersion in randomly cracked solids—I. Slit cracks

For simplicity, we show only the difference in the phase attribute that is caused by the finite Q values Figure 9c. This is because the cracked zone also behaves as a soft material to the incident long-wavelength wave due to the crack distribution. The crack density in a fault zone has been estimated on a basis of the static elastic properties of cracked media on the assumption of low wavenumber approximation e. The data are fitted by a power decay law function: Damage parameters as a function of normalized radial distance from impact point for three directions. From the results of the Kuster-Toksöz model, we find that the changes in rock properties depend largely on the inclusion shape.

## Effects of CO2 on P

Figure shows the aspect ratio distribution functions as a function of the effective pressure for sample T1 and T2, calculated by equation using the exponential curve fit relation of equation. Therefore the reduction of the measured compressional wave velocity in the x direction by the tensile cracks is expected to be higher than that in the other two directions, which agrees with our results and. Direct measurement of the crack damage using microscope will be carried out in the near future. Therefore, a fracture zone distributed parallel cracks is considered as an anisotropic layer rather than a low-velocity layer and the elastic constants, crack density and the thickness of the fracture zone can be estimated from the frequency dependence of the reflection coefficients for long incident wavelengths. There is a clear correlation between the increase in reflection amplitude and increased crack density. Nonlinear least squares fit of these data with the radial distance from the impact point follows a power decay law: Attenuation coefficients as a function of normalized radial distance from impact point for three directions.

## Effects of shock‐induced cracks on the ultrasonic velocity and attenuation in granite

The analysis is limited to small crack densities, and it has some direct relevance to the detection and characterization of damages in randomly cracked solids by ultrasonics. They still assumed the wavelength considerably longer than the crack length. In section , the new model is used to explain the measured velocities of these water-saturated samples, and the possible velocity dispersion of tight gas sandstone with very different pore structures is discussed. The new model is within 0. Several theoretical models of these effective properties developed in recent years predict that the fractured rock will be inelastic, with complex seismic velocities and elastic moduli. Tang proposed a squirt-flow model which included the effects of cracks, where the characteristic frequency and fluid transport parameters are represented in crack density and aspect ratio.

## Scattering attenuation, dispersion and reflection of SH waves in two

We consider an elastic medium with periodic distribution of cracks in a zone as illustrated in. The calculated velocity has an error of 2% as estimated by the accuracy of the traveltime and length measurements. Then, the possible velocity dispersion for our tight gas samples with very different pore structures is discussed with this new method. There was no attempt made to adjust parameters of the model to find lower values of Q since it was designed in part to use for other fluid flow studies, but it should be noted that by changing parameters related to porosity, permeability and fluid properties, it is possible to create realistic models with Q as low as 30. The green dash-dot lines are Hashin-Shtrikman bounds. It is also revealed from seismic observations, such as shear wave splitting and P-wave polarization anomalies , that a fault zone is characterized as a zone of densely distributed cracks aligned parallel to the fault plane. From the modeling results for tight sand from the Ross Lake area Figure 4b , we find that the P-velocity variations with crack density show an apparent dependence on rock properties of the uncracked rock, while the S-velocity displays a similar variation with crack density.

## Seismic Models of Reflections from Attenuating Layers

The thickness of the buffer plates was chosen to avoid overlapping of the reflected waves from different surfaces. Thus, sample T1 is dominated by at least two stiff pore systems and low-aspect ratio microcracks, and represents a typical dual porosity media, while the pores in sample T2 are more homogeneous, dominated mainly by stiff pores. We can also examine the instantaneous phase attribute, following the analysis applied to the homogeneous reservoir layer. The reflection coefficient calculated for the best-fit model of the single low-velocity layer is also plotted by the solid curve for the wavenumber range used in fitting in each of a and b. In general, a fault zone consists of several fault segments e.

## Effects of CO2 on P

The characteristic non-dimensional wavenumber of the wavelets, k ca, is assumed to be 0. This figure shows that both of the reflection coefficients agree well in the low wavenumber range but our result is not theoretically predicted in the high wavenumber range again. This means that a fracture zone distributed parallel cracks is considered as an anisotropic layer for long incident wavelengths. The porosity and permeability of T1 are 3. Squirt-flow is often considered important at well-logging and ultrasonic frequencies, and only plays a role in seismic exploration frequencies under the condition that the porous media is saturated with high viscosity fluid, or the rock has a very low permeability such as tight gas sandstone Pride et al, Batzle et al. Ravi Shekhar for assistance in creating some of the heterogeneous fractured reservoir models that were used to set up calculations of synthetic seismograms. We assume randomly distributed cracks in a rectangular-bounded region, which simulate a cracked zone.

## Wave attenuation and dispersion in randomly cracked solids—I. Slit cracks

Here the normalized amplitudes are larger than unity at the stations close to the ends of the crack distribution region. Ross Lake porous channel sand: the variation of effective velocities from the Kuster-Toksöz model with crack shape and aspect ratio. Because modeling wave propagation in 3-D inelastic media with exact finite difference techniques is slow and difficult to implement, we apply a technique using Born scattering theory, and our application is a unique and new implementation that allows us to examine the influence of localized regions of strongly attenuating materials embedded within the model. This limit is about 0. We show it is possible to estimate the crack density and thickness of a cracked zone by fitting the reflection coefficients to those of an anisotropic layer for incident long-wavelength waves. The velocity structure is not estimated correctly; it is obvious that the width is underestimated.