scholarly journals Velocity dispersion in rocks: A laboratory technique for direct measurement of P-wave modulus at seismic frequencies

2019 ◽  
Vol 90 (2) ◽  
pp. 024501 ◽  
Author(s):  
Serhii Lozovyi ◽  
Andreas Bauer
Keyword(s):  
Direct Measurement ◽  
Velocity Dispersion ◽  
P Wave ◽  
Laboratory Technique ◽  
Seismic Frequencies

Simulation of thermoelastic waves based on the Lord-Shulman theory

Geophysics ◽  
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.

scholarly journals Velocity-attenuation model from check-shot drift trends in North Sea well data

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. D65-D74 ◽  
Author(s):  
Andrew J. Carter ◽  
Veronica A. Torres Caceres ◽  
Kenneth Duffaut ◽  
Alexey Stovas
Keyword(s):  
North Sea ◽  
Velocity Dispersion ◽  
Seismic Attenuation ◽  
P Wave ◽  
Linear Wave ◽  
Velocity Models ◽  
Velocity Attenuation ◽  
Attenuation Models ◽  
Well Data ◽  
Attenuation Values

Seismic attenuation distorts phase and narrows bandwidth in seismic surveys. It is also an exploration attribute, as, for example, gas or overpressure, may create attenuation anomalies. Compensating attenuation in imaging requires accurate models. Detailed attenuation models may be obtained using full-waveform inversion (FWI) or attenuation tomography, but their accuracy benefits from reliable starting models and/or constraints. Seismic attenuation and velocity dispersion are necessarily linked for causal linear wave propagation such that higher frequencies travel faster than lower frequencies in an attenuative medium. In publicly released well data from the Norwegian North Sea, we have observed systematic positive linear trends in check-shot drift when comparing (lower frequency) time-depth curves with (higher frequency) integrated sonic transit times. We observe velocity dispersion consistent with layers having constant seismic attenuation. Adapting a previously published method, and assuming an attenuation-dispersion relationship, we use drift gradients, measured over thick stratigraphic units, to estimate interval P-wave attenuation and tentatively interpret its variation in terms of porosity and fluid mobility. Reflectivity modeling predicts a very low attenuation contribution from peg-leg multiples. We use the attenuation values to develop a simple regional relationship between P-wave velocity and attenuation. Observed low drift gradients in some shallower units lead to an arch-shaped model that predicts low attenuation at both low and high velocities. The attenuation estimates were broadly comparable with published effective attenuation values obtained independently nearby. This general methodology for quickly deriving a regional velocity-attenuation relationship could be used anywhere that coincident velocity models are available at seismic and sonic frequencies. Such relationships can be used for fast derivation (from velocities) of starting attenuation models for FWI or tomography, constraining or linking velocity and attenuation in inversion, deriving models for attenuation compensation in time processing, or deriving background trends in screening for attenuation anomalies in exploration.

Frame moduli of unconsolidated sands and sandstones

Geophysics ◽  
1994 ◽  
Vol 59 (9) ◽  
pp. 1352-1361 ◽  
Author(s):  
James W. Spencer ◽  
Michael E. Cates ◽  
Don D. Thompson
Keyword(s):  
Poisson’S Ratio ◽  
Empirical Relation ◽  
Ultrasonic Pulse Velocity ◽  
Ultrasonic Pulse ◽  
Pulse Velocity ◽  
P Wave ◽  
Poisson's Ratio ◽  
Unconsolidated Sands ◽  
Seismic Amplitude ◽  
Seismic Frequencies

In this study, we investigate the elastic moduli of the empty grain framework (the “frame” moduli) in unconsolidated sands and consolidated sandstones. The work was done to improve the interpretation of seismic amplitude anomalies and amplitude variations with offset (AVO) associated with hydrocarbon reservoirs. We developed a laboratory apparatus to measure the frame Poisson’s ratio and Young’s modulus of unconsolidated sands at seismic frequencies (0.2 to 155 Hz) in samples approximately 11 cm long. We used ultrasonic pulse velocity measurements to measure the frame moduli of consolidated sandstones. We found that the correlation coefficient between the frame Poisson’s ratio [Formula: see text] and the mineral Poisson’s ratio [Formula: see text] is 0.84 in consolidated sandstones and only 0.28 in unconsolidated sands. The range of [Formula: see text] values in unconsolidated sands is 0.115 to 0.237 (mean = 0.187, standard deviation = 0.030), and [Formula: see text] cannot be estimated without core or log analyses. Frame moduli analyses of core samples can be used to calibrate the interpretation of seismic amplitude anomalies and AVO effects. For use in areas without core or log analyses, we developed an empirical relation that can be used to estimate [Formula: see text] in unconsolidated sands and sandstones from [Formula: see text] and the frame P‐wave modulus.

Effects of ellipsoidal heterogeneities on wave propagation in partially saturated double-porosity rocks

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. WC71-WC81 ◽  
Author(s):  
Weitao Sun ◽  
Fansheng Xiong ◽  
Jing Ba ◽  
José M. Carcione
Keyword(s):  
Wave Propagation ◽  
Aspect Ratio ◽  
Wave Velocity ◽  
Velocity Dispersion ◽  
Laboratory Data ◽  
P Wave ◽  
Lagrange Equations ◽  
Wave Dissipation ◽  
P Wave Velocity ◽  
The Impact

Reservoir rocks are heterogeneous porous media saturated with multiphase fluids, in which strong wave dissipation and velocity dispersion are closely associated with fabric heterogeneities and patchy saturation at different scales. The irregular solid inclusions and fluid patches are ubiquitous in nature, whereas the impact of geometry on wave dissipation is still not well-understood. We have investigated the dependence of wave attenuation and velocity on patch geometry. The governing equations for wave propagation in a porous medium, containing fluid/solid heterogeneities of ellipsoidal triple-layer patches, are derived from the Lagrange equations on the basis of the potential and kinetic energies. Harmonic functions describe the wave-induced local fluid flow of an ellipsoidal patch. The effects of the aspect ratio on wave velocity are illustrated with numerical examples and comparisons with laboratory measurements. The results indicate that the P-wave velocity dispersion and attenuation depend on the aspect ratio of the ellipsoidal heterogeneities, especially in the intermediate frequency range. In the case of Fort Union sandstone, the P-wave velocity increases toward an upper bound as the aspect ratio decreases. The example of a North Sea sandstone clearly indicates that introducing ellipsoidal heterogeneities gives a better description of laboratory data than that based on spherical patches. The unexpected high-velocity values previously reported and ascribed to sample heterogeneities are explained by varying the aspect ratio of the inclusions (or patches).

Comparison of P‐ and S‐wave velocities and Q’S from VSP and sonic log data

Geophysics ◽  
1994 ◽  
Vol 59 (10) ◽  
pp. 1512-1529 ◽  
Author(s):  
Gopa S. De ◽  
Donald F. Winterstein ◽  
Mark A. Meadows
Keyword(s):  
Velocity Dispersion ◽  
P Wave ◽  
S Wave ◽  
S Waves ◽  
Wave Velocities ◽  
Sonic Log ◽  
Transit Times ◽  
Wave Slope ◽  
Northern Alberta ◽  
Q Values

We compared P‐ and S‐wave velocities and quality factors (Q’S) from vertical seismic profiling (VSP) and sonic log measurements in five wells, three from the southwest San Joaquin Basin of California, one from near Laredo, Texas, and one from northern Alberta. Our purpose was to investigate the bias between sonic log and VSP velocities and to examine to what degree this bias might be a consequence of dispersion. VSPs and sonic logs were recorded in the same well in every case. Subsurface formations were predominantly clastic. The bias found was that VSP transit times were greater than sonic log times, consistent with normal dispersion. For the San Joaquin wells, differences in S‐wave transit times averaged 1–2 percent, while differences in P‐wave transit times averaged 6–7 percent. For the Alberta well, the situation was reversed, with differences in S‐wave transit times being about 6 percent, while those for P‐waves were 2.5 percent. For the Texas well, the differences averaged about 4 percent for both P‐ and S‐waves. Drift‐curve slopes for S‐waves tended to be low where the P‐wave slopes were high and vice versa. S‐wave drift‐curve slopes in the shallow California wells were 5–10 μs/ft (16–33 μs/m) and the P‐wave slopes were 15–30 μs/ft (49–98 μs/m). The S‐wave slope in sandstones in the northern Alberta well was up to 50 μs/ft (164 μs/m), while the P‐wave slope was about 5 μs/ft (16 μs/m). In the northern Alberta well the slopes for both P‐ and S‐waves flattened in the carbonate. In the Texas well, both P‐ and S‐wave drifts were comparable. We calculated (Q’s) from a velocity dispersion formula and from spectral ratios. When the two Q’s agreed, we concluded that velocity dispersion resulted solely from absorption. These Q estimation methods were reliable only for Q values smaller than 20. We found that, even with data of generally outstanding quality, Q values determined by standard methods can have large uncertainties, and negative Q’s may be common.

scholarly journals Coal Seam Roof: Lithology and Influence on the Enrichment of Coalbed Methane

2019 ◽  
Vol 23 (4) ◽  
pp. 359-364
Author(s):  
Yunlan He ◽  
Xikai Wang ◽  
Hongjie Sun ◽  
Zhenguo Xing ◽  
Shan Chong ◽  
...  
Keyword(s):  
Coal Seam ◽  
Coalbed Methane ◽  
Low Frequency ◽  
Propagation Speed ◽  
Wave Impedance ◽  
P Wave ◽  
Borehole Data ◽  
Seismic Frequencies ◽  
Argillaceous Siltstone ◽  
Gas Bearing

To identify the lithology of coal seam roof and explore the influence of these roofs on the enrichment of coalbed methane, low-frequency rock petrophysics experiments, seismic analyses and gas-bearing trend analyses were performed. The results show that the sound wave propagation speed in rock at seismic frequencies was lower than that at ultrasound frequencies. Additionally, the P-wave velocities of gritstone, fine sandstone, argillaceous siltstone and mudstone were 1,651 m/s, 2,840 m/s, 3,191 m/s and 4,214 m/s, respectively. The surface properties of the coal seam roofs were extracted through 3D seismic wave impedance inversion. The theoretical P-wave impedance was calculated after the tested P-wave velocity was determined. By matching the theoretical P-wave impedance of the four types of rocks with that of the coal seam roofs, we identified the lithology of the roofs. By analyzing known borehole data, we found that the identified lithology was consistent with that revealed by the data. By comparing and analyzing the coal seam roof lithology and the gas-bearing trends in the study area, we discovered that the coal seam roof lithology was related to the enrichment of coalbed methane. In the study area, areas with high gas contents mainly coincided with roof zones composed of mudstone and argillaceous siltstone, and those with low gas contents were mainly associated with fine sandstone roof areas. Thus, highly compact areas of coal seam roof are favorable for the formation and preservation of coalbed methane. 

scholarly journals Prediction of sweet spots in tight sandstone reservoirs based on anisotropic frequency-dependent AVO inversion

2021 ◽  
Vol 18 (5) ◽  
pp. 664-680
Author(s):  
Xilin Qin ◽  
Zhixian Gui ◽  
Fei Yang ◽  
Yuanyuan Liu ◽  
Wei Jin ◽  
...  
Keyword(s):  
Velocity Dispersion ◽  
Fractured Reservoirs ◽  
P Wave ◽  
Inversion Method ◽  
Tight Sandstone ◽  
Anisotropic Parameter ◽  
Frequency Dependent ◽  
Anisotropy Parameters ◽  
Fluid Detection ◽  
Parameter Dispersion

Abstract The frequency-dependent amplitude-versus-offset (FAVO) method has become a practical method for fluid detection in sand reservoirs. At present, most FAVO inversions are based on the assumption that reservoirs are isotropy, but the application effect is not satisfactory for fractured reservoirs. Hence, we analyse the frequency variation characteristics of anisotropy parameters in tight sandstone reservoirs based on a new petrophysical model, and propose a stepwise anisotropic FAVO inversion method to extract frequency-dependent attributes from prestack seismic field data. First, we combine the improved Brie's law with the fine-fracture model to analyse frequency-dependent characteristics of velocities and Thomsen anisotropy parameters at different gas saturations and fracture densities. Then, we derive an anisotropic FAVO inversion algorithm based on Rüger's approximation formula and propose a stepwise anisotropic FAVO inversion method to obtain the dispersions of anisotropy parameters. Finally, we propose a method that combines the inversion spectral decomposition with the stepwise anisotropy FAVO inversion and apply it to tight sand reservoirs in the Xinchang area. We use P-wave velocity dispersion and anisotropy parameter ε dispersion to optimise favourable areas. Numerical analysis results show that velocity dispersion of the P-wave is sensitive to fracture density, which can be used for fracture prediction in fractured reservoirs. In contrast, anisotropic parameter dispersion is sensitive to gas saturation and can be used for fluid detection. The seismic data inversion results show that velocity dispersion of the P-wave and anisotropic parameter dispersion are sensitive to fractured reservoirs in the second member of Xujiahe Group, which is consistent with logging interpretation results.

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

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. 75A147-75A164 ◽  
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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