P-wave attenuation and dispersion in a fluid-saturated rock with aligned rectangular cracks

Elastic upscaling of thinly layered rocks typically is performed using the established Backus averaging technique. Its poroelastic extension applies to thinly layered fluid-saturated porous rocks and enables the use of anisotropic effective medium models that are valid in the low- and high-frequency limits for relaxed and unrelaxed pore-fluid pressures, respectively. At intermediate frequencies, wave-induced interlayer flow causes attenuation and dispersion beyond that described by Biot’s global flow and microscopic squirt flow. Several models quantify frequency-dependent, normal-incidence P-wave propagation in layered poroelastic media but yield no prediction for arbitrary angles of incidence, or for S-wave-induced interlayer flow. It is shown that generalized models for P-SV-wave attenuation and dispersion as a result of interlayer flow can be constructed by unifying the anisotropic Backus limits with existing P-wave frequency-dependent interlayer flow models. The construction principle is exact and is based on the symmetry properties of the effective elastic relaxation tensor governing the pore-fluid pressure diffusion. These new theories quantify anisotropic P- and SV-wave attenuation and velocity dispersion. The maximum SV-wave attenuation is of the same order of magnitude as the maximum P-wave attenuation and occurs prominently around an angle of incidence of [Formula: see text]. For the particular case of a periodically layered medium, the theoretical predictions are confirmed through numerical simulations.

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Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks — A review

Geophysics ◽

10.1190/1.3463417 ◽

2010 ◽

Vol 75 (5) ◽

pp. 75A147-75A164 ◽

Cited By ~ 457

Author(s):

Tobias M. Müller ◽

Boris Gurevich ◽

Maxim Lebedev

Keyword(s):

Fluid Flow ◽

Velocity Dispersion ◽

Wave Attenuation ◽

Field Measurements ◽

Theoretical Models ◽

Seismic Attenuation ◽

P Wave ◽

Induced Flow ◽

Wave Induced ◽

Attenuation And Dispersion

One major cause of elastic wave attenuation in heterogeneous porous media is wave-induced flow of the pore fluid between heterogeneities of various scales. It is believed that for frequencies below [Formula: see text], the most important cause is the wave-induced flow between mesoscopic inhomogeneities, which are large compared with the typical individual pore size but small compared to the wavelength. Various laboratory experiments in some natural porous materials provide evidence for the presence of centimeter-scale mesoscopic heterogeneities. Laboratory and field measurements of seismic attenuation in fluid-saturated rocks provide indications of the role of the wave-induced flow. Signatures of wave-induced flow include the frequency and saturation dependence of P-wave attenuation and its associated velocity dispersion, frequency-dependent shear-wave splitting, and attenuation anisotropy. During the last four decades, numerous models for attenuation and velocity dispersion from wave-induced flow have been developed with varying degrees of rigor and complexity. These models can be categorized roughly into three groups ac-cording to their underlying theoretical framework. The first group of models is based on Biot’s theory of poroelasticity. The second group is based on elastodynamic theory where local fluid flow is incorporated through an additional hydrodynamic equation. Another group of models is derived using the theory of viscoelasticity. Though all models predict attenuation and velocity dispersion typical for a relaxation process, there exist differences that can be related to the type of disorder (periodic, random, space dimension) and to the way the local flow is incorporated. The differences manifest themselves in different asymptotic scaling laws for attenuation and in different expressions for characteristic frequencies. In recent years, some theoretical models of wave-induced fluid flow have been validated numerically, using finite-difference, finite-element, and reflectivity algorithms applied to Biot’s equations of poroelasticity. Application of theoretical models to real seismic data requires further studies using broadband laboratory and field measurements of attenuation and dispersion for different rocks as well as development of more robust methods for estimating dissipation attributes from field data.

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P-wave attenuation and dispersion in a porous medium permeated by aligned fractures—a new poroelastic approach

Journal of Geophysics and Engineering ◽

10.1088/1742-2132/9/2/115 ◽

2012 ◽

Vol 9 (2) ◽

pp. 115-126 ◽

Cited By ~ 2

Author(s):

Jixin Deng ◽

Shouli Qu ◽

Shixing Wang ◽

Shengwang Zhu ◽

Xuben Wang

Keyword(s):

Porous Medium ◽

Wave Attenuation ◽

P Wave ◽

Attenuation And Dispersion

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Incorporating capillarity into models for P-wave attenuation and dispersion in partially saturated rocks

10.1190/segam2014-0370.1 ◽

2014 ◽

Author(s):

Qiaomu Qi* ◽

Tobias M. Müller ◽

J. German Rubino

Keyword(s):

Wave Attenuation ◽

P Wave ◽

Partially Saturated ◽

Attenuation And Dispersion

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The effect of viscoelasticity and microplasticity on the P- wave attenuation in dry and water-saturated sandstone: An experimental study

International Journal of Rock Mechanics and Mining Sciences ◽

10.1016/j.ijrmms.2021.104771 ◽

2021 ◽

Vol 142 ◽

pp. 104771

Author(s):

Eduard Mashinskii ◽

Nazanin Nourifard

Keyword(s):

Experimental Study ◽

Wave Attenuation ◽

P Wave ◽

Water Saturated

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The transversely isotropic poroelastic wave equation including the Biot and the squirt mechanisms: Theory and application

Geophysics ◽

10.1190/1.1444132 ◽

1997 ◽

Vol 62 (1) ◽

pp. 309-318 ◽

Cited By ~ 47

Author(s):

Jorge O. Parra

Keyword(s):

Wave Equation ◽

Fluid Flow ◽

Analytical Solution ◽

Seismic Waves ◽

Transversely Isotropic ◽

P Wave ◽

Fluid Properties ◽

Permeability Anisotropy ◽

Attenuation And Dispersion ◽

Maximum Permeability

The transversely isotropic poroelastic wave equation can be formulated to include the Biot and the squirt‐flow mechanisms to yield a new analytical solution in terms of the elements of the squirt‐flow tensor. The new model gives estimates of the vertical and the horizontal permeabilities, as well as other measurable rock and fluid properties. In particular, the model estimates phase velocity and attenuation of waves traveling at different angles of incidence with respect to the principal axis of anisotropy. The attenuation and dispersion of the fast quasi P‐wave and the quasi SV‐wave are related to the vertical and the horizontal permeabilities. Modeling suggests that the attenuation of both the quasi P‐wave and quasi SV‐wave depend on the direction of permeability. For frequencies from 500 to 4500 Hz, the quasi P‐wave attenuation will be of maximum permeability. To test the theory, interwell seismic waveforms, well logs, and hydraulic conductivity measurements (recorded in the fluvial Gypsy sandstone reservoir, Oklahoma) provide the material and fluid property parameters. For example, the analysis of petrophysical data suggests that the vertical permeability (1 md) is affected by the presence of mudstone and siltstone bodies, which are barriers to vertical fluid movement, and the horizontal permeability (1640 md) is controlled by cross‐bedded and planar‐laminated sandstones. The theoretical dispersion curves based on measurable rock and fluid properties, and the phase velocity curve obtained from seismic signatures, give the ingredients to evaluate the model. Theoretical predictions show the influence of the permeability anisotropy on the dispersion of seismic waves. These dispersion values derived from interwell seismic signatures are consistent with the theoretical model and with the direction of propagation of the seismic waves that travel parallel to the maximum permeability. This analysis with the new analytical solution is the first step toward a quantitative evaluation of the preferential directions of fluid flow in reservoir formation containing hydrocarbons. The results of the present work may lead to the development of algorithms to extract the permeability anisotropy from attenuation and dispersion data (derived from sonic logs and crosswell seismics) to map the fluid flow distribution in a reservoir.

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P- and S-wave attenuation logs from monopole sonic data

Geophysics ◽

10.1190/1.1444774 ◽

2000 ◽

Vol 65 (3) ◽

pp. 755-765 ◽

Cited By ~ 37

Author(s):

Xinhua Sun ◽

Xiaoming Tang ◽

C. H. (Arthur) Cheng ◽

L. Neil Frazer

Keyword(s):

Wave Attenuation ◽

Fluid Velocity ◽

P Wave ◽

Reservoir Rock ◽

Rock Properties ◽

S Wave ◽

Intrinsic Attenuation ◽

Modified Method ◽

Receiver Array ◽

Attenuation Profiles

In this paper, a modification of an existing method for estimating relative P-wave attenuation is proposed. By generating synthetic waveforms without attenuation, the variation of geometrical spreading related to changes in formation properties with depth can be accounted for. With the modified method, reliable P- and S-wave attenuation logs can be extracted from monopole array acoustic waveform log data. Synthetic tests show that the P- and S-wave attenuation values estimated from synthetic waveforms agree well with their respective model values. In‐situ P- and S-wave attenuation profiles provide valuable information about reservoir rock properties. Field data processing results show that this method gives robust estimates of intrinsic attenuation. The attenuation profiles calculated independently from each waveform of an eight‐receiver array are consistent with one another. In fast formations where S-wave velocity exceeds the borehole fluid velocity, both P-wave attenuation ([Formula: see text]) and S-wave attenuation ([Formula: see text]) profiles can be obtained. P- and S-wave attenuation profiles and their comparisons are presented for three reservoirs. Their correlations with formation lithology, permeability, and fractures are also presented.

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Simulation of thermoelastic waves based on the Lord-Shulman theory

Geophysics ◽

10.1190/geo2020-0515.1 ◽

2021 ◽

Vol 86 (3) ◽

pp. T155-T164

Author(s):

Wanting Hou ◽

Li-Yun Fu ◽

José M. Carcione ◽

Zhiwei Wang ◽

Jia Wei

Keyword(s):

Thermal Conductivity ◽

Expansion Coefficient ◽

Velocity Dispersion ◽

Wave Attenuation ◽

Splitting Method ◽

Grazing Incidence ◽

P Wave ◽

Staggered Grid ◽

Thermal Mode ◽

P Waves

Thermoelasticity is important in seismic propagation due to the effects related to wave attenuation and velocity dispersion. We have applied a novel finite-difference (FD) solver of the Lord-Shulman thermoelasticity equations to compute synthetic seismograms that include the effects of the thermal properties (expansion coefficient, thermal conductivity, and specific heat) compared with the classic forward-modeling codes. We use a time splitting method because the presence of a slow quasistatic mode (the thermal mode) makes the differential equations stiff and unstable for explicit time-stepping methods. The spatial derivatives are computed with a rotated staggered-grid FD method, and an unsplit convolutional perfectly matched layer is used to absorb the waves at the boundaries, with an optimal performance at the grazing incidence. The stability condition of the modeling algorithm is examined. The numerical experiments illustrate the effects of the thermoelasticity properties on the attenuation of the fast P-wave (or E-wave) and the slow thermal P-wave (or T-wave). These propagation modes have characteristics similar to the fast and slow P-waves of poroelasticity, respectively. The thermal expansion coefficient has a significant effect on the velocity dispersion and attenuation of the elastic waves, and the thermal conductivity affects the relaxation time of the thermal diffusion process, with the T mode becoming wave-like at high thermal conductivities and high frequencies.

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