Wave attenuation in partially saturated rocks

Geophysics ◽  
1979 ◽  
Vol 44 (2) ◽  
pp. 161-178 ◽  
Author(s):  
Gerald M. Mavko ◽  
Amos Nur
Keyword(s):  
Crack Width ◽  
Seismic Waves ◽  
Liquid Drop ◽  
Wave Attenuation ◽  
Pore Shape ◽  
Liquid Droplets ◽  
Wave Excitation ◽  
Partially Saturated ◽  
Aspect Ratios ◽  
Complete Saturation

A model is presented to describe the attenuation of seismic waves in rocks with partially liquid‐saturated flat cracks or pores. The presence of at least a small fraction of a free gaseous phase permits the fluid to flow freely when the pore is compressed under wave excitation. The resulting attenuation is much higher than with complete saturation as treated by Biot. In general, the attenuation increases with increasing liquid concentration, but is much more sensitive to the aspect ratios of the pores and the liquid droplets occupying the pores, with flatter pores resulting in higher attenuation. Details of pore shape other than aspect ratio appear to have little effect on the general behavior provided the crack width is slowly varying over the length of the liquid drop.

Effects of fluid viscosity on shear‐wave attenuation in saturated sandstones

Geophysics ◽  
1990 ◽  
Vol 55 (6) ◽  
pp. 712-722 ◽  
Author(s):  
D. Vo‐Thanh
Keyword(s):  
Shear Wave ◽  
Wave Attenuation ◽  
Crack Density ◽  
Viscoelastic Model ◽  
Fluid Viscosity ◽  
Partially Saturated ◽  
Aspect Ratios ◽  
Viscous Shear ◽  
Shear Relaxation ◽  
Water Saturated

Measurements of shear wave velocity and attenuation as a function of temperature were made in the kilohertz frequency range in sandstones saturated with various liquids. For sandstones partially saturated with glycerol, two attenuation peaks are observed between −80°C and 100°C; they are attributed to viscous shear relaxation and squirt flow. For fully water‐saturated Berea sandstone, the attenuation decreases as the crack density increases. The displacement of the squirt peak, caused by the increase of the central aspect ratio of cracks, is at the origin of this decrease. A simple viscoelastic model, based on the model of O’Connell and Budiansky using a Cole‐Cole distribution of cracks, is proposed for calculation of the shear modulus of fluid‐saturated rocks. This model interprets the experimental data satisfactorily. The data suggest that the shear attenuation and velocity are controlled by the distribution of crack aspect ratios.

An improved method to estimate Q based on the logarithmic spectrum of moving peak points

2019 ◽  
Vol 7 (2) ◽  
pp. T255-T263 ◽  
Author(s):  
Yanli Liu ◽  
Zhenchun Li ◽  
Guoquan Yang ◽  
Qiang Liu
Keyword(s):  
Seismic Waves ◽  
Wave Attenuation ◽  
Real Data ◽  
Peak Frequency ◽  
Seismic Reflection Data ◽  
The Real ◽  
Time Frequency ◽  
Reflection Data ◽  
Text Filtering ◽  
The Impact

The quality factor ([Formula: see text]) is an important parameter for measuring the attenuation of seismic waves. Reliable [Formula: see text] estimation and stable inverse [Formula: see text] filtering are expected to improve the resolution of seismic data and deep-layer energy. Many methods of estimating [Formula: see text] are based on an individual wavelet. However, it is difficult to extract the individual wavelet precisely from seismic reflection data. To avoid this problem, we have developed a method of directly estimating [Formula: see text] from reflection data. The core of the methodology is selecting the peak-frequency points to linear fit their logarithmic spectrum and time-frequency product. Then, we calculated [Formula: see text] according to the relationship between [Formula: see text] and the optimized slope. First, to get the peak frequency points at different times, we use the generalized S transform to produce the 2D high-precision time-frequency spectrum. According to the seismic wave attenuation mechanism, the logarithmic spectrum attenuates linearly with the product of frequency and time. Thus, the second step of the method is transforming a 2D spectrum into 1D by variable substitution. In the process of transformation, we only selected the peak frequency points to participate in the fitting process, which can reduce the impact of the interference on the spectrum. Third, we obtain the optimized slope by least-squares fitting. To demonstrate the reliability of our method, we applied it to a constant [Formula: see text] model and the real data of a work area. For the real data, we calculated the [Formula: see text] curve of the seismic trace near a well and we get the high-resolution section by using stable inverse [Formula: see text] filtering. The model and real data indicate that our method is effective and reliable for estimating the [Formula: see text] value.

Seismic wave attenuation due to fluid pressure diffusion at the mesoscopic scale: an experimental and numerical study

2021 ◽  
Author(s):  
Samuel Chapman ◽  
Jan V. M. Borgomano ◽  
Beatriz Quintal ◽  
Sally M. Benson ◽  
Jerome Fortin
Keyword(s):  
Seismic Wave ◽  
Seismic Waves ◽  
Wave Attenuation ◽  
Fluid Pressure ◽  
Fluid Distribution ◽  
Mesoscopic Scale ◽  
Seismic Wave Attenuation ◽  
X Ray ◽  
Pressure Diffusion ◽  
Attenuation And Dispersion

<p>Monitoring of the subsurface with seismic methods can be improved by better understanding the attenuation of seismic waves due to fluid pressure diffusion (FPD). In porous rocks saturated with multiple fluid phases the attenuation of seismic waves by FPD is sensitive to the mesoscopic scale distribution of the respective fluids. The relationship between fluid distribution and seismic wave attenuation could be used, for example, to assess the effectiveness of residual trapping of carbon dioxide (CO2) in the subsurface. Determining such relationships requires validating models of FPD with accurate laboratory measurements of seismic wave attenuation and modulus dispersion over a broad frequency range, and, in addition, characterising the fluid distribution during experiments. To address this challenge, experiments were performed on a Berea sandstone sample in which the exsolution of CO2 from water in the pore space of the sample was induced by a reduction in pore pressure. The fluid distribution was determined with X-ray computed tomography (CT) in a first set of experiments. The CO2 exosolved predominantly near the outlet, resulting in a heterogeneous fluid distribution along the sample length. In a second set of experiments, at similar pressure and temperature conditions, the forced oscillation method was used to measure the attenuation and modulus dispersion in the partially saturated sample over a broad frequency range (0.1 - 1000 Hz). Significant P-wave attenuation and dispersion was observed, while S-wave attenuation and dispersion were negligible. These observations suggest that the dominant mechanism of attenuation and dispersion was FPD. The attenuation and dispersion by FPD was subsequently modelled by solving Biot’s quasi-static equations of poroelasticity with the finite element method. The fluid saturation distribution determined from the X-ray CT was used in combination with a Reuss average to define a single phase effective fluid bulk modulus. The numerical solutions agree well with the attenuation and modulus dispersion measured in the laboratory, supporting the interpretation that attenuation and dispersion was due to FPD occurring in the heterogenous distribution of the coexisting fluids. The numerical simulations have the advantage that the models can easily be improved by including sub-core scale porosity and permeability distributions, which can also be determined using X-ray CT. In the future this could allow for conducting experiments on heterogenous samples.</p>

A simple and general macroscopic model for local-deformation effects in fluid-saturated porous rock

2019 ◽  
Vol 220 (3) ◽  
pp. 1893-1903
Author(s):  
Wubing Deng ◽  
Igor B Morozov
Keyword(s):  
Material Properties ◽  
Seismic Waves ◽  
Wave Attenuation ◽  
Spatial Scales ◽  
Local Deformation ◽  
Macroscopic Model ◽  
Porous Rock ◽  
Specific Flow ◽  
Frequency Independent ◽  
Consistent Manner

SUMMARY Wave-induced fluid flows (WIFF) can be viewed as cases of broader local-deformation (LD) phenomena and represent the principal causes of seismic-wave attenuation in fluid-saturated porous rock. Most existing WIFF models refer to greatly simplified microstructures and specific flow patterns, such as planar divergent flows within thin cracks (squirt flows, SF) or flows within patchy-saturation zones. However, such microstructures represent only idealized mathematical models that may be impossible to consistently identify within a given rock. At the same time, most details of such microstructures are insignificant for seismic waves, which are only sensitive to averaged properties of the medium. To perform microstructure-independent modelling of LD effects, we develop a simple yet general approach based entirely on a macroscopic local-deformation variable. This variable is broadly analogous to Biot's fluid content and is illustrated for two specific microstructural models. The macroscopic model is Biot-consistent and uses only time- and frequency-independent material properties. Both local and global (Biot's) pore flows and all types of waves and deformations are explained in a rigorous and consistent manner. The model allows constraining a minimal set of material properties responsible for all observed elastic and anelastic effects in porous rock. Because of making no assumptions about the microstructures and their spatial scales, this approach should comprise at least some of the existing WIFF models. In particular, this model accurately reproduces all attenuation and velocity dispersion spectra predicted by a broadly used SF model. The model also contains effects not considered previously, such as bulk viscosity of pore fluid and viscous coupling between the rock frame and fluid-filled pores. The model offers straightforward extensions to multiple porosities and cases of viscous fluids in primary pores. Based on the resulting differential equations, physically consistent schemes for numerical modelling of seismic wavefields can be developed for porous rock with arbitrary LD effects.

Huge wave attenuation in partially saturated fractured reservoirs

2007 ◽  
Vol 2007 (1) ◽  
pp. 1-3
Author(s):  
Miroslav Brajanovski ◽  
Tobias Müller
Keyword(s):  
Wave Attenuation ◽  
Fractured Reservoirs ◽  
Partially Saturated

The Study of Statistical Model of Mass Liquid Drop during Metal Spray Forming Process

2005 ◽  
Vol 475-479 ◽  
pp. 2819-2822 ◽  
Author(s):  
Yin Zhang ◽  
Jun Fei Fan ◽  
You Duo He ◽  
San Bing Ren ◽  
Jing Guo Zhang ◽  
...  
Keyword(s):  
Statistical Model ◽  
Initial Velocity ◽  
Liquid Drop ◽  
Simulation Method ◽  
Deposition Process ◽  
Spray Forming ◽  
Liquid Droplets ◽  
Forming Process ◽  
Whole Space ◽  
Metal Spray

Through the probability simulation method, the statistical model of mass metal liquid droplets during metal spray forming process was developed and the ejecting process of molten steel was studied. The distribution of metal liquid droplets, their different initial velocity and the original appear location during spray forming were obtained based on the above computation. After made statistic and analyzed on large number of metal liquid droplets, the forming and motion of liquid drop in whole space were defined in detail, which provided the precondition and reference for further study of liquid droplets deposition process on substrate.

scholarly journals Statistical characterization of gas-patch distributions in partially saturated rocks

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. WA51-WA64 ◽  
Author(s):  
Julianna Toms-Stewart ◽  
Tobias M. Müller ◽  
Boris Gurevich ◽  
Lincoln Paterson
Keyword(s):  
Correlation Function ◽  
Autocorrelation Function ◽  
Correlation Length ◽  
Wave Attenuation ◽  
Length Scales ◽  
Gas Saturation ◽  
Partially Saturated ◽  
Statistical Measures ◽  
Fluid Saturation ◽  
Limestone Sample

Reservoir rocks are often saturated by two or more fluid phases forming complex patterns on all length scales. The objective of this work is to quantify the geometry of fluid phase distribution in partially saturated porous rocks using statistical methods and to model the associated acoustic signatures. Based on X-ray tomographic images at submillimeter resolution obtained during a gas-injection experiment, the spatial distribution of the gas phase in initially water-saturated limestone samples are constructed. Maps of the continuous variation of the percentage of gas saturation are computed and associated binary maps obtained through a global thresholding technique. The autocorrelation function is derived via the two-point probability function computed from the binary gas-distribution maps using Monte Carlo simulations.The autocorrelation function can be approximated well by a single Debye correlation function or a superposition of two such functions. The characteristic length scales and show sensitivity (and hence significance) with respect to the percentage of gas saturation. An almost linear decrease of the Debye correlation length occurs with increasing gas saturation. It is concluded that correlation function and correlation length provide useful statistical information to quantify fluid-saturation patterns and changes in these patterns at the mesoscale. These spatial statistical measures are linked to a model that predicts compressional wave attenuation and dispersion from local, wave-induced fluid flow in randomly heterogeneous poroelastic solids. In particular, for a limestone sample, with flow permeability of 5 darcies and an average gas saturation of [Formula: see text], significant [Formula: see text]-wave attenuation is predicted at ultrasonic frequencies.

Fluid distribution effect on sonic attenuation in partially saturated limestones

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 154-160 ◽  
Author(s):  
Thierry Cadoret ◽  
Gary Mavko ◽  
Bernard Zinszner
Keyword(s):  
Wave Attenuation ◽  
Water Saturation ◽  
High Water ◽  
Fluid Distribution ◽  
Computer Assisted ◽  
Fluid Content ◽  
Partially Saturated ◽  
Fluid Saturation ◽  
Distribution Effect ◽  
Saturation Method

Extensional and torsional wave‐attenuation measurements are obtained at a sonic frequency around 1 kHz on partially saturated limestones using large resonant bars, 1 m long. To study the influence of the fluid distribution, we use two different saturation methods: drying and depressurization. When water saturation (Sw) is higher than 70%, the extensional wave attenuation is found to depend on whether the resonant bar is jacketed. This can be interpreted as the Biot‐Gardner‐White effect. The experimental results obtained on jacketed samples show that, during a drying experiment, extensional wave attenuation is influenced strongly by the fluid content when Sw is between approximately 60% and 100%. This sensitivity to fluid saturation vanishes when saturation is obtained through depressurization. Using a computer‐assisted tomographic (CT) scan, we found that, during depressurization, the fluid distribution is homogeneous at the millimetric scale at all saturations. In contrast, during drying, heterogeneous saturation was observed at high water‐saturation levels. Thus, we interpret the dependence of the extensional wave attenuation upon the saturation method as principally caused by a fluid distribution effect. Torsional attenuation shows no sensitivity to fluid saturation for Sw between 5% and 100%.

Wave propagation and directionality in two-dimensional periodic lattices considering shear deformations

2022 ◽  
pp. 239779142110694
Author(s):  
Soroush Sepehri ◽  
Mahmoud Mosavi Mashhadi ◽  
Mir Masoud Seyyed Fakhrabadi
Keyword(s):  
Wave Propagation ◽  
Shear Deformation ◽  
Wave Attenuation ◽  
Softening Effect ◽  
Aspect Ratios ◽  
Lattice Materials ◽  
Out Of Plane ◽  
Plane Direction ◽  
Bloch’S Theorem ◽  
Euler Bernoulli Beam

The effects of shear deformation on analysis of the wave propagation in periodic lattices are often assumed negligible. However, this assumption is not always true, especially for the lattices made of beams with smaller aspect ratios. Therefore, in the present paper, the effect of shear deformation on wave propagation in periodic lattices with different topologies is studied and their wave attenuation and directionality performances are compared. Current experimental limitations make the researchers focus more on the wave propagation in the direction perpendicular to the plane of periodicity in micro/nanoscale lattice materials while for their macro/mesoscale counterparts, in-plane modes can also be analyzed as well as the out-of-plane ones. Four well-known topologies of hexagonal, triangular, square, and Kagomé are considered in the current paper and their wave propagation is investigated both in the plane of periodicity and in the out-of-plane direction. The finite element method is used to formulate the governing equations and Bloch’s theorem is used to solve the dispersion relations. To investigate the effect of shear deformation, both the Timoshenko and Euler-Bernoulli beam theories are implemented. The results indicate that including shear deformation in wave propagation has a softening effect on the band diagrams of wave propagation and moves the dispersion branches to lower frequencies. It can also reveal some bandgaps that are not predicted without considering the shear deformation.

scholarly journals The response of a seasonal snow cover to explosive loading

1994 ◽  
Vol 19 ◽  
pp. 49-54 ◽  
Author(s):  
Jerome B. Johnson ◽  
Daniel J. Solie ◽  
Stephen A. Barrett
Keyword(s):  
Snow Cover ◽  
Seismic Waves ◽  
Wave Attenuation ◽  
Plane Waves ◽  
Propagation Distance ◽  
Explosive Loading ◽  
Spherical Waves ◽  
Seasonal Snow ◽  
Seasonal Snow Cover ◽  
Explosive Detonation

An explosive detonation in snow produces high intensity shock waves that are rapidly attenuated by momentum spreading as the snow is compacted. Our experimental measurements and numerical calculations indicate that the maximum shock-wave attenuation in seasonal snow (250 kgm−3) is proportional to between x−1.6 and x−3 for plane waves and x−3 for spherical waves (x is the propagation distance). Outside the region of shock-compacted snow or in air over snow, stresses are transmitted as acoustic/seismic waves. Attenuation of these waves depends on snow permeability and the effective modulus of the ice frame and is proportional to about x−0.7 for plane waves in seasonal snow and to about x−1 for spherical waves in air over seasonal snow. Increasing the scaled detonation height of an explosive up to 2mkgf−1/3 above a snow cover increases the far field (scaled distances greater than about 8m kgf−1/3 snow surface pressures. Scaled detonation heights greater than about 2mkgf−1/3 have little additional effect.

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