P-wave seismic attenuation by slow-wave diffusion: Effects of inhomogeneous rock properties

Recent research has established that the dominant P-wave attenuation mechanism in reservoir rocks at seismic frequencies is because of wave-induced fluid flow (mesoscopic loss). The P-wave induces a fluid-pressure difference at mesoscopic-scale inhomogeneities (larger than the pore size but smaller than the wavelength, typically tens of centimeters) and generates fluid flow and slow (diffusion) Biot waves (continuity of pore pressure is achieved by energy conversion to slow P-waves, which diffuse away from the interfaces). In this context, we consider a periodically stratified medium and investigate the amount of attenuation (and velocity dispersion) caused by different types of heterogeneities in the rock properties, namely, porosity, grain and frame moduli, permeability, and fluid properties. The most effective loss mechanisms result from porosity variations and partial saturation, where one of the fluids is very stiff and the other is very compliant, such as, a highly permeable sandstone at shallow depths, saturated with small amounts of gas (around 10% saturation) and water. Grain- and frame-moduli variations are the next cause of attenuation. The relaxation peak moves towards low frequencies as the (background) permeability decreases and the viscosity and thickness of the layers increase. The analysis indicates in which cases the seismic band is in the relaxed regime, and therefore, when the Gassmann equation can yield a good approximation to the wave velocity.

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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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Seismic attenuation: Effects of pore fluids and frictional‐sliding

Geophysics ◽

10.1190/1.1441276 ◽

1982 ◽

Vol 47 (1) ◽

pp. 1-15 ◽

Cited By ~ 268

Author(s):

Kenneth W. Winkler ◽

Amos Nur

Keyword(s):

Fluid Flow ◽

Strain Amplitude ◽

Seismic Wave ◽

Wave Attenuation ◽

Velocity Ratio ◽

Seismic Attenuation ◽

P Wave ◽

Amplitude Dependence ◽

S Wave ◽

Frictional Sliding

Seismic wave attenuation in rocks was studied experimentally, with particular attention focused on frictional sliding and fluid flow mechanisms. Sandstone bars were resonated at frequencies from 500 to 9000 Hz, and the effects of confining pressure, pore pressure, degree of saturation, strain amplitude, and frequency were studied. Observed changes in attenuation and velocity with strain amplitude are interpreted as evidence for frictional sliding at grain contacts. Since this amplitude dependence disappears at strains and confining pressures typical of seismic wave propagation in the earth, we infer that frictional sliding is not a significant source of seismic attenuation in situ. Partial water saturation significantly increases the attenuation of both compressional (P) and shear (S) waves relative to that in dry rock, resulting in greater P‐wave than S‐wave attenuation. Complete saturation maximizes S‐wave attenuation but causes a reduction in P‐wave attenuation. These effects can be interpreted in terms of wave induced pore fluid flow. The ratio of compressional to shear attenuation is found to be a more sensitive and reliable indicator of partial gas saturation than is the corresponding velocity ratio. Potential applications may exist in exploration for natural gas and geothermal steam reservoirs.

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Pore fluid effects on S-wave attenuation caused by wave-induced fluid flow

Geophysics ◽

10.1190/geo2011-0233.1 ◽

2012 ◽

Vol 77 (3) ◽

pp. L13-L23 ◽

Cited By ~ 37

Author(s):

Beatriz Quintal ◽

Holger Steeb ◽

Marcel Frehner ◽

Stefan M. Schmalholz ◽

Erik H. Saenger

Keyword(s):

Fluid Flow ◽

Wave Attenuation ◽

Pore Space ◽

Seismic Attenuation ◽

P Wave ◽

S Wave ◽

Hydrocarbon Reservoir ◽

Saturated Media ◽

Water Saturated ◽

Wave Induced

We studied seismic attenuation of P- and S-waves caused by the physical mechanism of wave-induced fluid flow at the mesoscopic scale. Stress relaxation experiments were numerically simulated by solving Biot’s equations for consolidation of 2D poroelastic media with finite-element modeling. The experiments yielded time-dependent stress-strain relations that were used to calculate the complex moduli from which frequency-dependent attenuation was determined. Our model consisted of periodically distributed circular or elliptical heterogeneities with much lower porosity and permeability than the background media, which contained 80% of the total pore space of the media. This model can represent a hydrocarbon reservoir, where the porous background is fully saturated with oil or gas and the low-porosity regions are always saturated with water. Three different saturation scenarios were considered: oil-saturated (80% oil, 20% water), gas-saturated (80% gas, 20% water), and fully water-saturated media. Varying the dry bulk and shear moduli in the background and in the heterogeneities, a consistent tendency was observed in the relative behavior of the S-wave attenuation among the different saturation scenarios. First, in the gas-saturated media the S-wave attenuation was very low and much lower than in the oil-saturated or in the fully water-saturated media. Second, at low frequencies the S-wave attenuation was significantly higher in the oil-saturated media than in the fully water-saturated media. The P-wave attenuation exhibited a more variable relative behavior among the different saturation degrees. Based on the mechanism of wave-induced fluid flow and on our numerical results, we suggest that S-wave attenuation could be used as an indicator of fluid content in a reservoir. Additionally, we observed that impermeable barriers in the background can cause a significant increase in S-wave attenuation. This suggests that S-wave attenuation could also be an indicator of permeability changes in a reservoir due to, for example, fracturing operations.

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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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Spatio-temporal variation of Anaelastic and Scattering Seismic Attenuation during the 2016-2017 Central Italy Seismic Sequence

10.5194/egusphere-egu21-8802 ◽

2021 ◽

Author(s):

Simona Gabrielli ◽

Aybige Akinci ◽

Ferdinando Napolitano ◽

Luca De Siena ◽

Edoardo Del Pezzo ◽

...

Keyword(s):

Wave Attenuation ◽

Central Italy ◽

Temporal Variations ◽

Seismic Attenuation ◽

Coda Wave ◽

Seismic Sequence ◽

Rock Fracturing ◽

Low Frequencies ◽

Main Shocks ◽

Stress Changes

Between August and October 2016, the Central Apennines in Italy have been struck by a long-lasting seismic sequence, known as the Amatrice (Mw 6.0) - Visso (Mw 5.9) - Norcia (Mw 6.5) sequence. The cascading ruptures occurred in this sequence have been considered connected to the fluid migration in the fault network, as suggested by previous studies. The behaviour of fluids in the crust is crucial to understand earthquakes occurrence and stress changes since fluids reduce fault stability. It has long been understood that the seismic attenuation is strongly controlled by the structural irregularity and heterogeneities; micro-cracks and cavities, either fluid-filled or dry, temperature and pressure variations cause a decrease in seismic wave amplitude and pulse broadening. Hence seismic attenuation imagining is a powerful tool to be a relevant provenance of information about the influence and abundance of fluids in a seismic sequence.The aim of this work is to separate scattering and absorption contributions to the total attenuation of coda waves and to provide their spatial and temporal variations at different frequency bands of these quantities using two datasets: the first one comprising 592 earthquakes occurred before the sequence (March 2013-August 2016) and the second one comprising 763 events (ML > 2.8) from the Amatrice-Visso-Norcia sequence. Scattering and absorption have been measured through peak-delay and coda-wave attenuation parameters (the latter inverted using frequency-dependent sensitivity kernels).The preliminary results show a clear difference between the pre-sequence and sequence images, mainly at low frequencies (1.5 Hz), where we can define a spatial increase of scattering with time attributed to rock fracturing and fluid circulation. The coda attenuation tomography also demonstrates a clear variation between the pre-sequence and the sequence over series of time windows being before and after the largest main shocks of the seismic sequence, with an increase of the attenuation in space with decreasing time. The peak delay indicates a high scattering area corresponding to the Gran Sasso massif and L&#8217;Aquila zone, where an important seismic sequence (Mw 6.3) occurred in 2009.

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P-Wave Attenuation Mechanism of Calcareous Sand under Explosion

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.580-583.268 ◽

2014 ◽

Vol 580-583 ◽

pp. 268-272

Author(s):

Xue Yong Xu ◽

Sheng Jie Di ◽

Wan Qiang Cheng ◽

Wei Li ◽

Wen Bo Du

Keyword(s):

Wave Attenuation ◽

Earth Pressure ◽

Physical And Mechanical Properties ◽

P Wave ◽

Calcareous Sand ◽

The Earth ◽

Composition And Structure ◽

Attenuation Mechanism ◽

Blasting Load ◽

Many Particles

Calcareous sand is a special marine geotechnical medium that exhibits interesting physical and mechanical properties resulting from its composition and structure. In the current paper, the blasting compression wave (P-wave) attenuation mechanism of calcareous sand under explosion was studied through explosion experiments. The decay law of the P-wave was obtained based on the earth pressure at different distances from the blast center. The results show that, the broken, compress, and damage zones were formed under the effect of blasting load, many particles were broken near the blasting zone. Calcareous sand exhibits strong absorption and attenuation effects on the P-wave because of its particle breakage characteristics.

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Local and regional P-wave spectral attenuation model for Iran

Geophysical Journal International ◽

10.1093/gji/ggaa450 ◽

2020 ◽

Vol 224 (1) ◽

pp. 241-256

Author(s):

Ehsan Moradian Bajestani ◽

Anooshiravan Ansari ◽

Ehsan Karkooti

Keyword(s):

Wave Attenuation ◽

Vertical Component ◽

P Wave ◽

P Waves ◽

Attenuation Model ◽

Hypocentral Distance ◽

Anelastic Attenuation ◽

Curve Versus ◽

Path Coverage ◽

Spectral Attenuation

SUMMARY A robust frequency-dependent local and regional P-wave attenuation model is estimated for continental paths in the Iranian Plateau. In order to calculate the average attenuation parameters, 46 337 vertical-component waveforms related to 9267 earthquakes, which are recorded at the Iranian Seismological Center (IRSC) stations, have been selected in the distance range 10–1000 km. The majority of the event's magnitudes are less than 4.5. This collection of records provides high spatial ray path coverage. Results indicate that the shape of attenuation P-wave curve versus distance is not uniform and has three distinct sections with hinges at 90 and 175 km. A trilinear model for attenuation of P-wave amplitude in the frequency range 1–10 Hz is proposed in this study. Fourier spectral amplitudes are found to decay as R−1.2 (where R is hypocentral distance), corresponding to geometric spreading within 90 km from the source. There is a section from 90 to 175 km, where the attenuation is described as R0.8, and the attenuation is described well beyond 175 km by R−1.3. Moreover, the average quality factor for Pg and Pn waves (QPg and QPn), related to anelastic attenuation is obtained as Qpg= (54.2 ± 2.6)f(1.0096±0.07) and Qpn= (306.8 ± 7.4)f (0.51±0.05). There is a good agreement between the results of the model and observations. Also, the attenuation model shows compatibility with the recent regional studies. From the results it turns out that the amplitude of P waves attenuates more rapidly in comparison with the global models in local distances.

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Incorporating mechanisms of fluid pressure relaxation into inclusion‐based models of elastic wave velocities

Geophysics ◽

10.1190/1.1598110 ◽

2003 ◽

Vol 68 (4) ◽

pp. 1173-1181 ◽

Cited By ~ 3

Author(s):

S. Richard Taylor ◽

Rosemary J. Knight

Keyword(s):

Elastic Wave ◽

Water Saturation ◽

Laboratory Data ◽

Fluid Pressure ◽

P Wave ◽

Porous Rocks ◽

Low Frequencies ◽

Wave Velocities ◽

Exact Agreement ◽

Flow Through

Our new method incorporates fluid pressure communication into inclusion‐based models of elastic wave velocities in porous rocks by defining effective elastic moduli for fluid‐filled inclusions. We illustrate this approach with two models: (1) flow between nearest‐neighbor pairs of inclusions and (2) flow through a network of inclusions that communicates fluid pressure throughout a rock sample. In both models, we assume that pore pressure gradients induce laminar flow through narrow ducts, and we give expressions for the effective bulk moduli of inclusions. We compute P‐wave velocities and attenuation in a model sandstone and illustrate that the dependence on frequency and water‐saturation agrees qualitatively with laboratory data. We consider levels of water saturation from 0 to 100% and all wavelengths much larger than the scale of material heterogeneity, obtaining near‐exact agreement with Gassmann theory at low frequencies and exact agreement with inclusion‐based models at high frequencies.

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A direct comparison between vibrational resonance and pulse transmission data for assessment of seismic attenuation in rock

Geophysics ◽

10.1190/1.1442771 ◽

1990 ◽

Vol 55 (1) ◽

pp. 51-60 ◽

Cited By ~ 26

Author(s):

Dane P. Blair

Keyword(s):

Elastic Scattering ◽

Wave Attenuation ◽

Seismic Attenuation ◽

Experimental Results ◽

P Wave ◽

Whole Body ◽

Frequency Range ◽

Vibrational Resonance ◽

Fine Grained ◽

Pulse Transmission

For the same volume of rock, I compare the attenuation obtained by seismic pulse transmission over the frequency range 1–150 kHz with that obtained by vibrational resonance techniques over the frequency range 1–50 kHz. The initial studies were performed on a rectangular block of medium‐grained granite which was large enough to permit the installation of a seismic pulse transmission array over a 1.8 m path length, yet small enough to permit whole‐body resonance. A Q of 82, for the P wave, was derived from the vibrational resonance results, whereas a Q of 15 was derived from the pulse transmission results. In light of models proposed for the viscoelastic, geometric, and elastic scattering attenuation mechanisms, the experimental results suggest that this large discrepancy in Q values is due to elastic scattering by grain clusters (rather than individual grains) within the granite. Scattering is significant in the high‐frequency pulse transmission tests, but is considered insignificant in the lower frequency resonance tests. Furthermore, this scattering is represented approximately by a constant-Q loss mechanism, which makes it difficult to separate unambiguously elastic scattering and viscoelastic losses. Subsequent studies performed on a large block of fine‐grained norite yield a resonance Q of 89 and a pulse Q of approximately 102 and suggest a negligible scattering loss for this material. The experimental results for the norite imply that the constant-Q theory of seismic pulse attenuation provides a reasonable description of wave attenuation in a dry, fine‐grained crystalline rock over the frequency range 1–150 kHz.

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