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1
Spencer, James W., and Jacob Shine. "Seismic wave attenuation and modulus dispersion in sandstones." GEOPHYSICS 81, no. 3 (May 2016): D211—D231. http://dx.doi.org/10.1190/geo2015-0342.1.
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We have conducted laboratory experiments over the 1–200 Hz band to examine the effects of viscosity and permeability on modulus dispersion and attenuation in sandstones and also to examine the effects of partial gas or oil saturation on velocities and attenuations. Our results have indicated that bulk modulus values with low-viscosity fluids are close to the values predicted using Gassmann’s first equation, but, with increasing frequency and viscosity, the bulk and shear moduli progressively deviate from the values predicted by Gassmann’s equations. The shear moduli increase up to 1 GPa (or approximately 10%) with high-viscosity fluids. The P- and S-wave attenuations ([Formula: see text] and [Formula: see text]) and modulus dispersion with different fluids are indicative of stress relaxations that to the first order are scaling with frequency times viscosity. By fitting Cole-Cole distributions to the scaled modulus and attenuation data, we have found that there are similar P-wave, shear and bulk relaxations, and attenuation peaks in each of the five sandstones studied. The modulus defects range from 11% to 15% in Berea sandstone to 16% to 26% in the other sandstones, but these would be reduced at higher confining pressures. The relaxations shift to lower frequencies as the viscosity increased, but they do not show the dependence on permeability predicted by mesoscopic wave-induced fluid flow (WIFF) theories. Results from other experiments having patchy saturation with liquid [Formula: see text] and high-modulus fluids are consistent with mesoscopic WIFF theories. We have concluded that the modulus dispersion and attenuations ([Formula: see text] and [Formula: see text]) in saturated sandstones are caused by a pore-scale, local-flow mechanism operating near grain contacts.
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Chen, Huaizhen. "Estimating elastic properties and attenuation factor from different frequency components of observed seismic data." Geophysical Journal International 220, no. 2 (October 21, 2019): 794–805. http://dx.doi.org/10.1093/gji/ggz476.
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SUMMARY Based on an attenuation model, we first express frequency-dependent P- and S-wave attenuation factors as a function of P-wave maximum attenuation factor, and then we re-express P- and S-wave velocities in anelastic media and derive frequency-dependent stiffness parameters in terms of P-wave maximum attenuation factor. Using the derived stiffness parameters, we propose frequency-dependent reflection coefficient in terms of P- and S-wave moduli at critical frequency and P-wave maximum attenuation factor for the case of an interface separating two attenuating media. Based on the derived reflection coefficient, we establish an approach to utilize different frequency components of observed seismic data to estimate elastic properties (P- and S-wave moduli and density) and attenuation factor, and following a Bayesian framework, we construct the objective function and an iterative method is employed to solve the inversion problem. Tests on synthetic data confirm that the proposed approach makes a stable and robust estimation of unknown parameters in the case of seismic data containing a moderate noise/error. Applying the proposed approach to a real data set illustrates that a reliable attenuation factor is obtained from observed seismic data, and the ability of distinguishing oil-bearing reservoirs is improved combining the estimated elastic properties and P-wave attenuation factor.
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Sun, Junzhe, Sergey Fomel, Tieyuan Zhu, and Jingwei Hu. "Q-compensated least-squares reverse time migration using low-rank one-step wave extrapolation." GEOPHYSICS 81, no. 4 (July 2016): S271—S279. http://dx.doi.org/10.1190/geo2015-0520.1.
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Attenuation of seismic waves needs to be taken into account to improve the accuracy of seismic imaging. In viscoacoustic media, reverse time migration (RTM) can be performed with [Formula: see text]-compensation, which is also known as [Formula: see text]-RTM. Least-squares RTM (LSRTM) has also been shown to be able to compensate for attenuation through linearized inversion. However, seismic attenuation may significantly slow down the convergence rate of the least-squares iterative inversion process without proper preconditioning. We have found that incorporating attenuation compensation into LSRTM can improve the speed of convergence in attenuating media, obtaining high-quality images within the first few iterations. Based on the low-rank one-step seismic modeling operator in viscoacoustic media, we have derived its adjoint operator using nonstationary filtering theory. The proposed forward and adjoint operators can be efficiently applied to propagate viscoacoustic waves and to implement attenuation compensation. Recognizing that, in viscoacoustic media, the wave-equation Hessian may become ill-conditioned, we propose to precondition LSRTM with [Formula: see text]-compensated RTM. Numerical examples showed that the preconditioned [Formula: see text]-LSRTM method has a significantly faster convergence rate than LSRTM and thus is preferable for practical applications.
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Dobrynina, A. A., P. A. Predein, V. A. Sankov, Ts A. Tubanov, D. P. D. Sanzhieva, and E. A. Gorbunova. "SPATIAL VARIATIONS OF SEISMIC WAVE ATTENUATION IN THE SOUTH BAIKAL BASIN AND ADJACENT AREAS (BAIKAL RIFT)." Geodynamics & Tectonophysics 10, no. 1 (March 23, 2019): 147–66. http://dx.doi.org/10.5800/gt-2019-10-1-0408.
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Our detailed study of the crust and upper mantle of the South Baikal basin focused on seismic coda and seismic S-waves attenuation and estimated seismic quality factor (QS and QC), frequency parameter (n), attenuation coefficient (δ), total attenuation (QT), and the ratio of two components the total attenuation: intrinsic attenuation (Qi), and attenuation due to scattering caused by the inhomogeneities of the medium (QSC). We calculated the sizes of inhomogeneities revealed in the block medium, which put their effect on the attenuation of seismic waves in different frequency ranges. The seismic wave attenuation field was analyzed in comparison with the geological and geophysical characteristics of the medium, and a direct relationship was established between attenuation, composition and active processes in the crust and upper mantle of the studied area. According to the estimated intrinsic attenuation (Qi) and scattering attenuation (QSC) contributions into the total attenuation, intrinsic attenuation is generally dominant in the studied area, while the QSC component increases in the areas of large active faults.
5
Hao, Qi, and Tariq Alkhalifah. "An acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis." GEOPHYSICS 82, no. 1 (January 1, 2017): C9—C20. http://dx.doi.org/10.1190/geo2016-0160.1.
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Seismic-wave attenuation is an important component of describing wave propagation. Certain regions, such as gas clouds inside the earth, exert highly localized attenuation. In fact, the anisotropic nature of the earth induces anisotropic attenuation because the quasi P-wave dispersion effect should be profound along the symmetry direction. We have developed a 2D acoustic eikonal equation governing the complex-valued traveltime of quasi P-waves in attenuating, transversely isotropic media with a vertical-symmetry axis (VTI). This equation is derived under the assumption that the complex-valued traveltime of quasi P-waves in attenuating VTI media are independent of the S-wave velocity parameter [Formula: see text] in Thomsen’s notation and the S-wave attenuation coefficient [Formula: see text] in Zhu and Tsvankin’s notation. We combine perturbation theory and Shanks transform to develop practical approximations to the acoustic attenuating eikonal equation, capable of admitting an analytical description of the attenuation in homogeneous media. For a horizontal-attenuating VTI layer, we also derive the nonhyperbolic approximations for the real and imaginary parts of the complex-valued reflection traveltime. These equations reveal that (1) the quasi SV-wave velocity and the corresponding quasi SV-wave attenuation coefficient given as part of Thomsen-type notation barely affect the ray velocity and ray attenuation of quasi P-waves in attenuating VTI media; (2) combining the perturbation method and Shanks transform provides an accurate analytic eikonal solution for homogeneous attenuating VTI media; (3) for a horizontal attenuating VTI layer with weak attenuation, the real part of the complex-valued reflection traveltime may still be described by the existing nonhyperbolic approximations developed for nonattenuating VTI media, and the imaginary part of the complex-valued reflection traveltime still has the shape of nonhyperbolic curves. In addition, we have evaluated the possible extension of the proposed eikonal equation to realistic attenuating media, an alternative perturbation solution to the proposed eikonal equation, and the feasibility of applying the proposed nonhyperbolic equation for the imaginary part of the complex-valued traveltime to invert for interval attenuation parameters.
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LI, Q., F. SANTOSA, B. WHEELOCK, and K. GOVIL. "Modelling viscoelastic wave phenomenon by homogenisation of the poroelasticity equations." European Journal of Applied Mathematics 32, no. 5 (January 18, 2021): 846–64. http://dx.doi.org/10.1017/s0956792520000467.
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Poroelastic effects have been of great interest in the seismic literature as they have been identified as a major cause of wave attenuation in heterogeneous porous media. The observed attenuation in the seismic wave can be explained in part by energy loss to fluid motion in the pores. On the other hand, it is known that the attenuation is particularly pronounced in stratified structures where the scale of spatial heterogeneity is much smaller than the seismic wavelength. Understanding of poroelastic effects on seismic wave attenuation in heterogeneous porous media has largely relied on numerical experiments. In this work, we present a homogenisation technique to obtain an upscaled viscoelastic model that captures seismic wave attenuation when the sub-seismic scale heterogeneity is periodic. The upscaled viscoelastic model directly relates seismic wave attenuation to the material properties of the heterogeneous structure. We verify our upscaled viscoelastic model against a full poroelastic model in numerical experiments. Our homogenisation technique suggests a new approach for solving coupled equations of motion.
7
Hu, Shi Li, Jian Yong Yang, and Guan Shi Wang. "Attenuation Law of Blasting Seismic Wave Amplitude with Time and Calculation of Equivalent Elastic Modulus." Applied Mechanics and Materials 94-96 (September 2011): 178–85. http://dx.doi.org/10.4028/www.scientific.net/amm.94-96.178.
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Abstract. The characteristic frequency was generated when blasting seismic wave propagate in rock mass. The characteristic frequency played an important role in the amplitude attenuation of seismic wave with time and propagation distance. Rock mass was simplified as visco-elastic media. The time attenuation model of seismic wave amplitude was studied by wave equation and the complex number theory. Theoretical analysis demonstrates that attenuation coefficient of seismic wave amplitude with time is mainly affected by rock viscosity coefficient and elastic modulus. The attenuation coefficient decreases with increase of elastic modulus. The attenuation coefficient increases with increase of viscosity coefficient. The test method of equivalent elastic modulus of rock mass was analyzed according to model of time attenuation of seismic wave amplitude in situ. The wave velocity test verified effectiveness of the method. A new method of determining rock mass mechanical parameter was put forward.
8
Khosrovani, Hooshang, and Jose Ortega. "Seismic wave attenuation coefficient for soils." Journal of the Acoustical Society of America 108, no. 5 (November 2000): 2529. http://dx.doi.org/10.1121/1.4743358.
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Carter, Andrew J., Veronica A. Torres Caceres, Kenneth Duffaut, and Alexey Stovas. "Velocity-attenuation model from check-shot drift trends in North Sea well data." GEOPHYSICS 85, no. 2 (February 25, 2020): D65—D74. http://dx.doi.org/10.1190/geo2019-0419.1.
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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.
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Rozhko, Alexander Y. "On the spectral changes of seismic wave energy by a partially saturated crack due to the hysteresis of liquid bridges phenomenon." GEOPHYSICS 86, no. 3 (April 8, 2021): MR133—MR147. http://dx.doi.org/10.1190/geo2020-0685.1.
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Low-frequency shadows are frequently interpreted as attenuation phenomena due to partial saturation with free gas. However, several researchers have argued that shadows are not necessarily a simple attenuation phenomenon because low-frequency energy must have been added or amplified by some physical or numerical process. Attenuation alone should attenuate higher frequencies, not boost lower frequencies. The physical or numerical effects explaining this phenomenon are still debatable in the literature. To better understand the elastic wave energy’s spectral changes in partially saturated rock, we have considered the hysteresis of liquid bridges phenomena inside the crack. We determine that liquid bridges’ hysteresis leads to the nonlinear energy exchange between frequencies, explaining the wave energy boost at lower frequencies. We find that the energy exchange between different frequencies depends on the wave amplitude and the seismic wave spectrum. The low-frequency energy boost is stronger for a continuous spectrum of seismic waves, smaller for the discrete spectrum, and zero for the monochromatic spectrum of seismic waves. In addition, we find that at seismic frequencies, the attenuation 1/ Q-factor due to the friction of the contact line can be much larger than the attenuation due to viscous fluid flow inside the partially saturated crack. Our model depends on the wave amplitude and weakly depends on the wave frequency. The suggested model can help interpret the low-frequency shadows, bright spots, and attenuation anomalies frequently observed around hydrocarbon fields.
11
Pujol, J., and S. Smithson. "Seismic wave attenuation in volcanic rocks from VSP experiments." GEOPHYSICS 56, no. 9 (September 1991): 1441–55. http://dx.doi.org/10.1190/1.1443164.
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Seismic wave attenuation in the Columbia Plateau basalts and Snake River Plain volcanics was analyzed using vertical seismic profiling (VSP) data. The computation of attenuation coefficients is based on fitting a straight line to the logarithm of amplitude ratios computed for fixed values of frequency and variable depth. This approach does not require any assumptions on the dependence of Q on frequency. For the Columbia Plateau basalts, the attenuation coefficients obtained from the field data are smaller than those computed from the synthetic VSP generated using the sonic and density logs, indicating that the observed attenuation is related to scattering effects and is substantially larger than the intrinsic attenuation of basalt. Therefore, it is concluded that only a lower bound for Q can be established, in agreement with recent findings by other authors. The effective attenuation of seismic energy in basalts (about [Formula: see text] for the peak frequency) is comparable to the effective attenuation observed in sedimentary rocks (between [Formula: see text] and [Formula: see text]). Results from two VSPs recorded in the Snake River Plain volcanics using air gun and vibrator sources show some frequency‐dependent effects. The depth range analyzed covers two different lithologic units (rhyolitic rocks with interbedded volcanic sediments above more homogeneous rhyodacitic rocks). The air gun energy (with a peak frequency near 15 Hz) clearly detects a difference in the attenuating properties of the two types of rocks. The vibrator energy, on the other hand, also detects this difference, but only for the lower frequencies. For frequencies near the peak frequency (31 Hz), attenuation is almost the same in the two units. The difference in attenuation for the two types of rocks is real and cannot be explained as processing artifacts, because it can be observed for both sources by analyzing the amplitude decay in the time domain. The peak‐frequency attenuation coefficients for the lower section are [Formula: see text] and [Formula: see text] for the vibrator and air gun sources, respectively. For the upper section, the corresponding values are [Formula: see text] and [Formula: see text]. The difference in attenuation implied by the last two coefficients is probably not real, because the decay of energy in the time domain for the two sources is much closer to each other. The Columbia Plateau and Snake River Plain VSPs show that the poor quality of reflection data commonly associated with volcanic rocks cannot be explained by unusually high attenuation.
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Parra, Jorge O. "The transversely isotropic poroelastic wave equation including the Biot and the squirt mechanisms: Theory and application." GEOPHYSICS 62, no. 1 (January 1997): 309–18. http://dx.doi.org/10.1190/1.1444132.
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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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Gao, Lingli, Yudi Pan, and Thomas Bohlen. "2-D multiparameter viscoelastic shallow-seismic full-waveform inversion: reconstruction tests and first field-data application." Geophysical Journal International 222, no. 1 (April 27, 2020): 560–71. http://dx.doi.org/10.1093/gji/ggaa198.
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SUMMARY 2-D full-waveform inversion (FWI) of shallow-seismic wavefields has recently become a novel way to reconstruct S-wave velocity models of the shallow subsurface with high vertical and lateral resolution. In most applications, seismic wave attenuation is ignored or considered as a passive modelling parameter only. In this study, we explore the feasibility and performance of multiparameter viscoelastic 2-D FWI in which seismic velocities and attenuation of P and S waves, respectively, and mass density are inverted simultaneously. Synthetic reconstruction experiments reveal that multiple crosstalks between all viscoelastic material parameters may occur. The reconstruction of S-wave velocity is always robust and of high quality. The parameters P-wave velocity and density exhibit weaker sensitivity and can be reconstructed more reliably by multiparameter viscoelastic FWI. Anomalies in S-wave attenuation can be recovered but with limited resolution. In a field-data application, a small-scale refilled trench is nicely delineated as a low P- and S-wave velocity anomaly. The reconstruction of P-wave velocity is improved by the simultaneous inversion of attenuation. The reconstructed S-wave attenuation reveals higher attenuation in the shallow weathering zone and weaker attenuation below. The variations in the reconstructed P- and S-wave velocity models are consistent with the reflectivity observed in a ground penetrating radar (GPR) profile.
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Chen, Gong Lian, Wen Zheng Lu, Lei Wang, and Qi Wu. "Study on Far-Field Ground Motion Characteristics." Applied Mechanics and Materials 438-439 (October 2013): 1471–73. http://dx.doi.org/10.4028/www.scientific.net/amm.438-439.1471.
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In order to study the far-field ground motion characteristics and the attenuation of seismic waves, the peak ground acceleration (velocity, displacement), time of duration and response spectrum of the seismic waves were analyzed in this paper. Through the investigation of earthquake wave propagation process, the seismic attenuation low was analyzed. This study can provide technical support for the seismic design of long period structures and related engineering application.
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Bickel, S. H., and R. R. Natarajan. "Plane‐wave Q deconvolution." GEOPHYSICS 50, no. 9 (September 1985): 1426–39. http://dx.doi.org/10.1190/1.1442011.
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Often the information content of measured signals from distance sources is hidden, because the signal distorts, weakens, and loses resolution as it propagates. For seismic energy traveling in the earth, these propagation effects can be approximated by the constant (frequency‐independent) Q model for attenuation and dispersion. For a propagating plane wave, this model leads to a spatial attenuation factor that is an unbounded function of frequency. Consequently, the broadband inverse of the constant-Q filter does not exist. For a fixed distance between the source and receiver the effects of the propagation path can be deconvolved (removed) within the seismic band by reversing the propagation of the plane wave. This propagation reversal is done by a time reversal with Q replaced by —Q, thereby changing absorption to gain in the complex wavenumber. Normally, measured seismic traces contain returns from a variety of depths. The interference of waves with different amounts of attenuation complicates the inversion process. From a superposition of plane waves with reversed propagation, a general inverse to an attenuation earth filter is proposed. To account for the increased attenuation with depth, the plane‐wave inverse filter is now time‐varying. This time‐varying inverse filter has a simple Fourier integral representation where the wavenumber is complex, and the direction of propagation is chosen such that the wave is growing rather than attenuating with distance. To control the wavelet side lobes a frequency‐domain window function (Hanning window) is applied to the trace. This two‐step plane‐wave deconvolution scheme was demonstrated to be superior to conventional deconvolution procedures. Tests with field data indicate the method is effective in removing attenuation effects from both VSP (Vertical Seismic Profile) and surface measurements. Phase distortions are eliminated and interference between events is reduced within the seismic band. This inverse is nearly exact for events where the time‐bandwidth (propagation time‐signal bandwidth) product is less than the effective Q. For depths where the time‐bandwidth product is greater than [Formula: see text] large wavelet side lobes appear. The wavelet side lobes can be partially suppressed by tapering the edges of the spectrum. However, the large side lobes of wavelets from shallow reflectors limit the bandwidth that can be recovered from the deeper events to aproximately [Formula: see text], where t is the propagation time to the event. Advances in the inversion algorithm (e.g., a Wiener filter could be used in place of the Hanning window to control side lobes) could probably improve upon our results, but in most cases even a small amount of measurement noise limits the reflection sequences to time‐bandwidth products that are less than twice the effective Q.
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Zhao, Haixia, Jinghuai Gao, Jigen Peng, and Gulan Zhang. "Modeling Attenuation of Diffusive-Viscous Wave Using Reflectivity Method." Journal of Theoretical and Computational Acoustics 27, no. 03 (September 2019): 1850030. http://dx.doi.org/10.1142/s2591728518500305.
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Seismic waves in earth materials are subject to attenuation and dispersion in a broad range of frequencies. The commonly accepted mechanism of intrinsic attenuation and dispersion is the presence of fluids in the pore space of rocks. The diffusive-viscous model was proposed to explain low-frequency seismic anomalies related to hydrocarbon reservoirs. But, the model is only a description of compressional wave. In this work, we firstly discuss the extended elastic diffusive-viscous model. Then, we extend reflectivity method to the diffusive-viscous medium. Finally, we present two numerical models to simulate the attenuation of diffusive-viscous wave in horizontal and dip multi-layered media compared with the results of viscoelastic wave. The modeling results show that the diffusive-viscous wave has strong amplitude attenuation and phase shift when it propagates across absorptive layers.
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Behura, Jyoti, and Ilya Tsvankin. "Reflection coefficients in attenuative anisotropic media." GEOPHYSICS 74, no. 5 (September 2009): WB193—WB202. http://dx.doi.org/10.1190/1.3142874.
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Such reservoir rocks as tar sands are characterized by significant attenuation and, in some cases, attenuation anisotropy. Most existing attenuation studies are focused on plane-wave attenuation coefficients, which determine the amplitude decay along the raypath of seismic waves. Here we study the influence of attenuation on PP- and PS-wave reflection coefficients for anisotropic media with the main emphasis on transversely isotropic models with a vertical symmetry axis (VTI). Concise analytic solutions obtained by linearizing the exact plane-wave reflection coefficients are verified by numerical modeling. To make a substantial contribution to reflection coefficients, attenuation must be strong, with the quality factor [Formula: see text] not exceeding 10. For such highly attenuative media, it is also necessary to take attenuation anisotropy into account if the magnitude of the Thomsen-styleattenuation-anisotropy parameters is relatively large. In general, the linearized reflection coefficients in attenuative media include velocity-anisotropy parameters but have almost “isotropic” dependence on attenuation. Our formalism also helps evaluate the influence of the inhomogeneity angle (the angle between the real and imaginary parts of the slowness vector) on the reflection coefficients. A nonzero inhomogeneity angle of the incident wave introduces additional terms into the PP- and PS-wave reflection coefficients, which makes conventional amplitude-variation-with-offset (AVO) analysis inadequate for strongly attenuative media. For instance, an incident P-wave with a nonzero inhomogeneity angle generates a mode-converted PS-wave at normal incidence, even if both half-spaces have a horizontal symmetry plane. The developed linearized solutions can be used in AVO inversion for highly attenuative (e.g., gas-sand and heavy-oil) reservoirs.
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Hao, Qi, and Tariq Alkhalifah. "An acoustic eikonal equation for attenuating orthorhombic media." GEOPHYSICS 82, no. 4 (July 1, 2017): WA67—WA81. http://dx.doi.org/10.1190/geo2016-0632.1.
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Attenuating orthorhombic models are often used to describe the azimuthal variation of the seismic wave velocity and attenuation in finely layered hydrocarbon reservoirs with vertical fractures. In addition to the P-wave related medium parameters, S-wave parameters are also present in the complex eikonal equation needed to describe the P-wave complex-valued traveltime in an attenuating orthorhombic medium, which increases the complexity of using the P-wave traveltime to invert for the medium parameters in practice. We have used the acoustic assumption to derive an acoustic eikonal equation that approximately governs the complex-valued traveltime of P-waves in an attenuating orthorhombic medium. For a homogeneous attenuating orthorhombic media, we solve the eikonal equation using a combination of the perturbation method and Shanks transform. For a horizontal attenuating orthorhombic layer, the real and imaginary parts of the complex-valued reflection traveltime have nonhyperbolic behaviors in terms of the source-receiver offset. Similar to the roles of normal moveout (NMO) velocity and anellipticity, the attenuation NMO velocity and the attenuation anellipticity characterize the variation of the imaginary part of the complex-valued reflection traveltime around zero source-receiver offset.
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Di Martino, María Del Pilar, Luca De Siena, David Healy, and Stephanie Vialle. "Petro-mineralogical controls on coda attenuation in volcanic rock samples." Geophysical Journal International 226, no. 3 (May 22, 2021): 1858–72. http://dx.doi.org/10.1093/gji/ggab198.
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SUMMARY Seismic attenuation measurements, especially those obtained from coda decay analysis, are becoming a key data source for the characterization of the heterogeneous Earth due to their sensitivity to small-scale heterogeneities. However, the relation between the scattering attenuation measured from coda waves and physical rock properties is still unclear. The goal of this study is to identify the main petrophysical and mineralogical factors controlling coda attenuation in volcanic rocks at the laboratory scale, as a necessary step before modelling seismic waves in real volcanic media. Coda wave attenuation was estimated from ultrasonic S-wave waveforms. To quantify the heterogeneity of the rocks and link them with this attenuation parameter, we performed several categorizations of the pore and grain systems of volcanic samples. Considering that seismic attenuation in rock samples can be modelled using the framework of wave propagation in random media, a statistical analysis of shear wave velocity fluctuations was performed: this analysis gives correlation lengths ranging from 0.09 to 1.20 mm, which represents the length scale of heterogeneity in the samples. The individual evaluation of the pore space and mineral content revealed that the pores of the samples (characterized by large vesicles) have a bigger effect than the grains on the heterogeneity level. We have developed a framework where intrinsic properties of the host rocks drive seismic attenuation by correlating the petro-mineralogical characteristics obtained from image data processing and analysis, with the coda attenuation measured at ultrasonic frequencies. There is conclusive evidence that porosity alone is not the primary controller of coda attenuation: it is also changed by the alteration level (i.e. oxidation, coating of the vesicles, secondary minerals) and the size of grains and pores. Among all the parameters analysed, it appears that the pore space topology is the main contributor to scattering attenuation in the volcanic samples.
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Li, Xing-Wang, Bing Zhou, Chao-Ying Bai, and Jian-Lu Wu. "Seismic complex ray tracing in 2D/3D viscoelastic anisotropic media by a modified shortest-path method." GEOPHYSICS 85, no. 6 (November 1, 2020): T331—T342. http://dx.doi.org/10.1190/geo2020-0113.1.
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In a viscoelastic anisotropic medium, velocity anisotropy and wave energy attenuation occur and are often observed in seismic data applications. Numerical investigation of seismic wave propagation in complex viscoelastic anisotropic media is very helpful in understanding seismic data and reconstructing subsurface structures. Seismic ray tracing is an effective means to study the propagation characteristics of high-frequency seismic waves. Unfortunately, most seismic ray-tracing methods and traveltime tomographic inversion algorithms only deal with elastic media and ignore the effect of viscoelasticity on the seismic raypath. We have developed a method to find the complex ray velocity that gives the seismic ray speed and attenuation in an arbitrary viscoelastic anisotropic medium, and we incorporate them with the modified shortest-path method to determine the raypath and calculate the real and imaginary traveltime (wave energy attenuation) simultaneously. We determine that the complex ray-tracing method is applicable to arbitrary 2D/3D viscoelastic anisotropic media in a complex geologic model and the computational errors of the real and imaginary traveltime are less than 0.36% and 0.59%, respectively. The numerical examples verify that the new method is an effective and powerful tool for accomplishing seismic complex ray tracing in heterogeneous viscoelastic anisotropic media.
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Bai, Jianyong, David Yingst, Robert Bloor, and Jacques Leveille. "Viscoacoustic waveform inversion of velocity structures in the time domain." GEOPHYSICS 79, no. 3 (May 1, 2014): R103—R119. http://dx.doi.org/10.1190/geo2013-0030.1.
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Because of the conversion of elastic energy into heat, seismic waves are attenuated and dispersed as they propagate. The attenuation effects can reduce the resolution of velocity models obtained from waveform inversion or even cause the inversion to produce incorrect results. Using a viscoacoustic model consisting of a single standard linear solid, we discovered a theoretical framework of viscoacoustic waveform inversion in the time domain for velocity estimation. We derived and found the viscoacoustic wave equations for forward modeling and their adjoint to compensate for the attenuation effects in viscoacoustic waveform inversion. The wave equations were numerically solved by high-order finite-difference methods on centered grids to extrapolate seismic wavefields. The finite-difference methods were implemented satisfying stability conditions, which are also presented. Numerical examples proved that the forward viscoacoustic wave equation can simulate attenuative behaviors very well in amplitude attenuation and phase dispersion. We tested acoustic and viscoacoustic waveform inversions with a modified Marmousi model and a 3D field data set from the deep-water Gulf of Mexico for comparison. The tests with the modified Marmousi model illustrated that the seismic attenuation can have large effects on waveform inversion and that choosing the most suitable inversion method was important to obtain the best inversion results for a specific seismic data volume. The tests with the field data set indicated that the inverted velocity models determined from the acoustic and viscoacoustic inversions were helpful to improve images and offset gathers obtained from migration. Compared to the acoustic inversion, viscoacoustic inversion is a realistic approach for real earth materials because the attenuation effects are compensated.
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Gusmeroli, Alessio, Roger A. Clark, Tavi Murray, Adam D. Booth, Bernd Kulessa, and Brian E. Barrett. "Seismic wave attenuation in the uppermost glacier ice of Storglaciären, Sweden." Journal of Glaciology 56, no. 196 (2010): 249–56. http://dx.doi.org/10.3189/002214310791968485.
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AbstractWe conducted seismic refraction surveys in the upper ablation area of Storglaciären, a small valley glacier located in Swedish Lapland. We estimated seismic-wave attenuation using the spectral-ratio method on the energy travelling in the uppermost ice with an average temperature of approximately −1 °C. Attenuation values were derived between 100 and 300 Hz using the P-wave quality factor, QP, the inverse of the internal friction. By assuming constant attenuation along the seismic line we obtained mean QP = 6 ± 1. We also observed that QP varies from 8 ± 1 to 5 ± 1 from the near-offset to the far-offset region of the line, respectively. Since the wave propagates deeper at far offsets, this variation is interpreted by considering the temperature profile of the study area; far-offset arrivals sampled warmer and thus more-attenuative ice. Our estimates are considerably lower than those reported for field studies in polar ice (∼500–1700 at −28°C and 50–160 at −10°C) and, hence, are supportive of laboratory experiments that show attenuation increases with rising ice temperature. Our results provide new in situ estimates of QP for glacier ice and demonstrate a valuable method for future investigations in both alpine and polar ice.
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Kennett, B. L. N., and A. Abdullah†. "Seismic wave attenuation beneath the Australasian region." Australian Journal of Earth Sciences 58, no. 3 (April 2011): 285–95. http://dx.doi.org/10.1080/08120099.2011.550318.
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RADULIAN, M., G. F. PANZA, M. POPA, and B. GRECU. "SEISMIC WAVE ATTENUATION FOR VRANCEA EVENTS REVISITED." Journal of Earthquake Engineering 10, no. 3 (May 2006): 411–27. http://dx.doi.org/10.1080/13632460609350603.
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Fang, Y., and G. Müller. "Seismic-wave attenuation operators for arbitrary Q." Geophysical Journal International 106, no. 3 (September 1991): 703–7. http://dx.doi.org/10.1111/j.1365-246x.1991.tb06342.x.
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Müller, Tobias M., Gracjan Lambert, and Boris Gurevich. "Dynamic permeability of porous rocks and its seismic signatures." GEOPHYSICS 72, no. 5 (September 2007): E149—E158. http://dx.doi.org/10.1190/1.2749571.
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In inhomogeneous porous media, the mechanism of wave-induced fluid flow causes significant attenuation and dispersion of seismic waves. In connection with this phenomenon, we study the impact of spatial permeability fluctuations on the dynamic behavior of porous materials. This heterogeneous permeability distribution further complicates the ongoing efforts to extract flow permeability from seismic data. Based on the method of statistical smoothing applied to Biot’s equations of poroelasticity, we derive models for the dynamic-equivalent permeability in 1D and 3D randomly inhomogeneous media. The low-frequency limit of this permeability corresponds to the flow permeability governing fluid flow in porous media. We incorporate the dynamic-equivalent permeability model into the expressions for attenuation and dispersion of P-waves, also obtained by the method of smoothing. The resulting attenuation and dispersion model is confirmed by numerical computations in randomly layered poroelastic structures. The results suggest that the effect of wave-induced fluid flow can be observed in a broader frequency range than previously thought. The peak attenuation shifts along the frequency axis depending on the strength of the permeability fluctuations. We conclude that estimation of flow permeability from seismic attenuation is only possible if permeability fluctuations are properly accounted for.
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Li, Chuanhui, Kai Feng, and Xuewei Liu. "Study on p-Wave Attenuation in Hydrate-Bearing Sediments Based on BISQ Model." Journal of Geological Research 2013 (October 9, 2013): 1–8. http://dx.doi.org/10.1155/2013/176579.
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In hydrate-bearing sediments, the elastic wave attenuation characteristics depend on the elastic properties of the sediments themselves on the one hand, and on the other hand, they also depend on the hydrate occurrence state and hydrate saturation. Since the hydrate-bearing sediments always have high porosity, so they show significant porous medium characteristics. Based on the BISQ porous medium model which is the most widely used model to study the attenuation characteristics in the porous media, we focused on p-wave attenuation in hydrate-bearing sediments in Shenhu Area, South China Sea, especially in specific seismic frequency range, which lays a foundation for the identification of gas hydrates by using seismic wave attenuation in Shenhu Area, South China Sea. Our results depict that seismic wave attenuation is an effective attribute to identify gas hydrates.
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Mensah, Victor, and Arturo Hidalgo. "Modelling the effects of diffusive-viscous waves in a 3-D fluid-saturated media using two numerical approaches." Geophysical Journal International 224, no. 2 (September 24, 2020): 1443–63. http://dx.doi.org/10.1093/gji/ggaa457.
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SUMMARY The accurate numerical modelling of 3-D seismic wave propagation is essential in understanding details to seismic wavefields which are, observed on regional and global scales on the Earth’s surface. The diffusive-viscous wave (DVW) equation was proposed to study the connection between fluid saturation and frequency dependence of reflections and to characterize the attenuation property of the seismic wave in a fluid-saturated medium. The attenuation of DVW is primarily described by the active attenuation parameters (AAP) in the equation. It is, therefore, imperative to acquire these parameters and to additionally specify the characteristics of the DVW. In this paper, quality factor, Q is used to obtain the AAP, and they are compared to those of the visco-acoustic wave. We further derive the 3-D numerical schemes based on a second order accurate finite-volume scheme with a second order Runge–Kutta approximation for the time discretization and a fourth order accurate finite-difference scheme with a fourth order Runge–Kutta approximation for the time discretization. We then simulate the propagation of seismic waves in a 3-D fluid-saturated medium based on the derived schemes. The numerical results indicate stronger attenuation when compared to the visco-acoustic case.
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Wang, Yanfei, Yaxin Ning, and Yibo Wang. "Fractional Time Derivative Seismic Wave Equation Modeling for Natural Gas Hydrate." Energies 13, no. 22 (November 12, 2020): 5901. http://dx.doi.org/10.3390/en13225901.
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Simulation of the seismic wave propagation in natural gas hydrate (NGH) is of great importance. To finely portray the propagation of seismic wave in NGH, attenuation properties of the earth’s medium which causes reduced amplitude and dispersion need to be considered. The traditional viscoacoustic wave equations described by integer-order derivatives can only nearly describe the seismic attenuation. Differently, the fractional time derivative seismic wave-equation, which was rigorously derived from the Kjartansson’s constant-Q model, could be used to accurately describe the attenuation behavior in realistic media. We propose a new fractional finite-difference method, which is more accurate and faster with the short memory length. Numerical experiments are performed to show the feasibility of the proposed simulation scheme for NGH, which will be useful for next stage of seismic imaging of NGH.
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Yang, Jingkang, Jianhua Geng, and Luanxiao Zhao. "A frequency-decomposed nonstationary convolutional model for amplitude-versus-angle-and-frequency forward waveform modeling in attenuative media." GEOPHYSICS 85, no. 6 (October 13, 2020): T301—T314. http://dx.doi.org/10.1190/geo2019-0338.1.
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The conventional convolutional model (CCM) is widely applied to generate synthetic seismic data for numerous applications including amplitude variation with offset forward modeling, seismic well tie, and inversion. This approach assumes frequency-independent reflection coefficients and time-invariant seismic wavelets in laterally homogeneous elastic media. We have extended CCM to heterogeneous poroelastic media in which reflection coefficients are frequency dependent and the seismic wave is attenuated as it propagates. First, we decompose the seismic wavelet into monofrequency components through the Fourier transform. Then, to account for the attenuation effects at the reflection interfaces, we multiply the frequency-dependent reflection coefficients series with an attenuation function of frequency-variant quality factor [Formula: see text]. Finally, we convolve this product results with a monofrequency wavelet and sum all of the frequencies together to obtain the synthetic seismograms. The advantage of the proposed frequency-decomposed nonstationary convolutional model is that it takes into account the effects of attenuation on the wave reflections and propagation in attenuative media. In addition, it uses the frequency-dependent [Formula: see text] instead of the constant [Formula: see text] that is used by the traditional nonstationary convolutional model. The technique has been applied to amplitude-versus-angle-and-frequency forward waveform modeling in attenuative media, and it shows good agreement between synthetic and real data on seismic well ties.
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Li, Chuanhui, and Xuewei Liu. "Seismic wave attenuation in hydrate-bearing sediments based on the patchy saturation model in the Shenhu area, South China Sea." Interpretation 5, no. 3 (August 31, 2017): SM25—SM32. http://dx.doi.org/10.1190/int-2016-0139.1.
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In the Shenhu area, South China Sea, a study on P-wave attenuation in the hydrate-bearing sediments has been developed based on the Biot-Squirt (BISQ) porous medium model. However, the BISQ model has been proven to be inappropriate for the attenuation characteristics at seismic frequencies. We have adopted the patchy-saturation model, which is being increasingly considered to be more suitable for attenuation analysis at seismic frequencies in porous media, to study P-wave attenuation in the hydrate-bearing sediments in the Shenhu area, South China Sea. The theoretical modeling indicates that the P-wave attenuation at seismic frequencies is observed to decrease when the sediments contain gas hydrates. In the case studies in the Shenhu area, the interval inverse [Formula: see text]-factors from seismic reflection data were estimated, and the results indicate good agreement with the theoretical modeling.
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Parra, Jorge O. "Poroelastic model to relate seismic wave attenuation and dispersion to permeability anisotropy." GEOPHYSICS 65, no. 1 (January 2000): 202–10. http://dx.doi.org/10.1190/1.1444711.
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A transversely isotropic model with a horizontal axis of symmetry, based on the Biot and squirt‐flow mechanisms, predicts seismic waves in poroelastic media. The model estimates velocity dispersion and attenuation of waves propagating in the frequency range of crosswell and high‐resolution reverse vertical seismic profiling (VSP) (250–1250 Hz) for vertical permeability values much greater than horizontal permeability parameters. The model assumes the principal axes of the stiffness constant tensor are aligned with the axes of the permeability and squirt‐flow tensors. In addition, the unified Biot and squirt‐flow mechanism (BISQ) model is adapted to simulate cracks in permeable media. Under these conditions, the model simulations demonstrate that the preferential direction of fluid flow in a reservoir containing fluid‐filled cracks can be determined by analyzing the phase velocity and attenuation of seismic waves propagating at different azimuth and incident angles. As a result, the fast compressional wave can be related to permeability anisotropy in a reservoir. The model results demonstrate that for a fast quasi-P-wave propagating perpendicular to fluid‐filled cracks, the attenuation is greater than when the wave propagates parallel to the plane of the crack. Theoretical predictions and velocity dispersion of inter‐well seismic waves in the Kankakee Limestone Formation at the Buckhorn test site (Illinois) demonstrate that the permeable rock matrix surrounding a low‐velocity heterogeneity contains vertical cracks.
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SUN, YUE-FENG, JOHN T. KUO, and YU-CHIUNG TENG. "EFFECTS OF POROSITY ON SEISMIC ATTENUATION." Journal of Computational Acoustics 02, no. 01 (March 1994): 53–69. http://dx.doi.org/10.1142/s0218396x94000051.
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Effects of porosity on the attenuation of wave propagation are studied. The effects of pore fluids and porous structures are significant on changing the shapes of propagating wavelets. The waveform change of a propagating wavelet is much more sensitive to porosity than intrinsic attenuation. The attenuation occurred in natural rocks may largely due to these porous effects in addition to the internal friction of the solid represented by the intrinsic quality factor Q. The waveform of a propagating wavelet is quantitatively associated with attenuation, porosity, and fluid content, and is characterized by three parameters: the porosity ϕ, the quality factor Q, and the center frequency f0. Estimations of attenuation, porosity, and fluid content can be made by optimal wavelet analysis. High-resolution mapping of subsurface structures can be achieved by solving the integral equation with the nonlinear optimization of the time-variant wavelets. The inversion and the optimization schemes have been applied to study the porous sea floor and the crustal axial magma chamber (AMC) on the East Pacific Rise. These results provide porosity, attenuation information, and the highly resolved wave events, for further evaluation of compressional and shear wave velocities and other physical properties such as crack density and aspect ratio.
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Ba, Jing, José M. Carcione, and Weitao Sun. "Seismic attenuation due to heterogeneities of rock fabric and fluid distribution." Geophysical Journal International 202, no. 3 (July 23, 2015): 1843–47. http://dx.doi.org/10.1093/gji/ggv255.
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Abstract The study of the influence of rock fabric and porefluid distribution on the seismic wavefield is important for the prediction and detection of reservoir properties such as lithology and fluid saturation. Wave-induced local fluid flow (WILFF), which is affected by local heterogeneities of the pore structure and fluid saturation, is believed to be the main mechanism to explain the measured attenuation levels at different frequency bands. These two types of heterogeneity affect seismic waves as a combined WILFF process. In this work, we consider a double-porosity system, each part with a different compressibility and patchy saturation, and derive the wave equations from Hamilton's principle. A plane-wave analysis yields the properties of the classical P-wave and those of the four slow waves. The examples show that patchy fluid saturation dominates the peak frequency of the relaxation mechanism. The relation between seismic anelasticity (velocity dispersion and attenuation) and saturation depends on frequency and on the geometrical features of the two heterogeneities. The proposed theory constitutes the comprehensive description for wave propagation process through reservoirs rocks of shallow Earth and porous media in general, to estimate fluid content and distribution.
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Chen, Huaizhen, Kristopher A. Innanen, and Tiansheng Chen. "Estimating P- and S-wave inverse quality factors from observed seismic data using an attenuative elastic impedance." GEOPHYSICS 83, no. 2 (March 1, 2018): R173—R187. http://dx.doi.org/10.1190/geo2017-0183.1.
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P- and S-wave inverse quality factors quantify seismic wave attenuation, which is related to several key reservoir parameters (porosity, saturation, and viscosity). Estimating the inverse quality factors from observed seismic data provides additional and useful information during gas-bearing reservoir prediction. First, we have developed an approximate reflection coefficient and attenuative elastic impedance (QEI) in terms of the inverse quality factors, and then we established an approach to estimate elastic properties (P- and S-wave impedances, and density) and attenuation (P- and S-wave inverse quality factors) from seismic data at different incidence angles and frequencies. The approach is implemented as a two-step inversion: a model-based and damped least-squares inversion for QEI, and a Bayesian Markov chain Monte Carlo inversion for the inverse quality factors. Synthetic data tests confirm that P- and S-wave impedances and inverse quality factors are reasonably estimated in the case of moderate data error or noise. Applying the established approach to a real data set is suggestive of the robustness of the approach, and furthermore that physically meaningful inverse quality factors can be estimated from seismic data acquired over a gas-bearing reservoir.
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Peacock, Sheila, Clive McCann, Jeremy Sothcott, and Timothy R. Astin. "Experimental measurements of seismic attenuation In microfractured sedimentary rock." GEOPHYSICS 59, no. 9 (September 1994): 1342–51. http://dx.doi.org/10.1190/1.1443693.
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Ultrasonic compressional‐ and shear‐wave attenuation in water‐saturated Carrara Marble increase with increasing crack density and decreasing effective pressure. Between 0.4 and 1.0 MHz, empirical linear relationships between 1/Q and crack density CD were found to be: CD = 1.96 ± 0.63 × 1/Q, for compressional waves and CD = 6.7 ± 1.5 × 1/Q, for shear waves.
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Klimentos, T., and C. McCann. "Relationships among compressional wave attenuation, porosity, clay content, and permeability in sandstones." GEOPHYSICS 55, no. 8 (August 1990): 998–1014. http://dx.doi.org/10.1190/1.1442928.
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Anelastic attenuation is the process by which rocks convert compressional waves into heat and thereby modify the amplitude and phase of the waves. Understanding the causes of compressional wave attenuation is important in the acquisition, processing, and interpretation of high‐resolution seismic data, and in deducing the physical properties of rocks from seismic data. We have measured the attenuation coefficients of compressional waves in 42 sandstones at a confining pressure of 40 MPa (equivalent to a depth of burial of about 1.5 km) in a frequency range from 0.5 to 1.5 MHz. The compressional wave measurements were made using a pulse‐echo method in which the sample (5 cm diameter, 1.8 cm to 3.5 cm long) was sandwiched between perspex (lucite) buffer rods inside the high‐pressure rig. The attenuation of the sample was estimated from the logarithmic spectral ratio of the signals (corrected for beam spreading) reflected from the top and base of the sample. The results show that for these samples, compressional wave attenuation (α, dB/cm) at 1 MHz and 40 MPa is related to clay content (C, percent) and porosity (ϕ, percent) by α=0.0315ϕ+0.241C−0.132 with a correlation coefficient of 0.88. The relationship between attenuation and permeability is less well defined: Those samples with permeabilities less than 50 md have high attenuation coefficients (generally greater than 1 dB/cm) while those with permeabilities greater than 50 md have low attenuation coefficients (generally less than 1 dB/cm) at 1 MHz at 40 MPa. These experimental data can be accounted for by modifications of the Biot theory and by consideration of the Sewell/Urick theory of compressional wave attenuation in porous, fluid‐saturated media.
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Mörig, R., and H. Burkhardt. "Experimental evidence for the Biot‐Gardner theory." GEOPHYSICS 54, no. 4 (April 1989): 524–27. http://dx.doi.org/10.1190/1.1442679.
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Seismic wave attenuation has been a subject of interest during the last 40 years because it may be of use in interpreting seismic data. From this attenuation parameter, more detailed information about the lithology of the subsurface may be deduced if we understand the absorption mechanisms by which dissipation of seismic energy is governed. We are, therefore, studying in the laboratory the effects of different parameters such as porosity, permeability, pore fluid, and saturation state on the absorption of seismic waves in porous rocks over a wide spectrum ranging from seismic to ultrasonic frequencies (Burkhardt et al., 1986).
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Carcione, José M., and Stefano Picotti. "P-wave seismic attenuation by slow-wave diffusion: Effects of inhomogeneous rock properties." GEOPHYSICS 71, no. 3 (May 2006): O1—O8. http://dx.doi.org/10.1190/1.2194512.
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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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MARI, Jean-Luc, Gilles POREL, and Frederick DELAY. "Contribution of Full Wave Acoustic Logging to the Detection and Prediction of Karstic Bodies." Water 12, no. 4 (March 27, 2020): 948. http://dx.doi.org/10.3390/w12040948.
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A 3D seismic survey was done on a near surface karstic reservoir located at the hydrogeological experimental site (HES) of the University of Poitiers (France). The processing of the 3D data led to obtaining a 3D velocity block in depth. The velocity block was converted in pseudo porosity. The resulting 3D seismic pseudo-porosity block reveals three high-porosity, presumably-water-productive layers, at depths of 30–40, 85–87 and 110–115 m. This paper shows how full wave acoustic logging (FWAL) can be used to validate the results obtained from the 3D seismic survey if the karstic body has a lateral extension over several seismic. If karstic bodies have a small extension, FWAL in open hole can be fruitfully used to: detect highly permeable bodies, thanks to measurements of acoustic energy and attenuation; detect the presence of karstic bodies characterized by a very strong attenuation of the different wave trains and a loss of continuity of acoustic sections; confirm the results obtained by vertical seismic profile (VSP) data. The field example also shows that acoustic attenuation of the total wavefield as well as conversion of downward-going P-wave in Stoneley waves observed on VSP data are strongly correlated with the presence of flow.
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Jia, Fan, Hongyang Cheng, Sihong Liu, and Vanessa Magnanimo. "Elastic wave velocity and attenuation in granular material." EPJ Web of Conferences 249 (2021): 11001. http://dx.doi.org/10.1051/epjconf/202124911001.
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Discrete Elements Method simulations are carried out to investigate waves propagation in isotropic, frictional granular media. The focus is on the effects of confining pressure, microstructure and input frequency on both wave velocity and attenuation. The latter is described via the seismic quality factor Q and three different measurement approaches are compared, in time and frequency domain. The simulation data validate previous findings on the scaling of wave velocity with confining pressure and coordination number. The quality factor Q shows a non-monotonic behavior with input frequency.
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Dvorkin, Jack, and Richard Uden. "Seismic wave attenuation in a methane hydrate reservoir." Leading Edge 23, no. 8 (August 2004): 730–32. http://dx.doi.org/10.1190/1.1786892.
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Edwards, Benjamin, Donat Fäh, and Domenico Giardini. "Attenuation of seismic shear wave energy in Switzerland." Geophysical Journal International 185, no. 2 (March 25, 2011): 967–84. http://dx.doi.org/10.1111/j.1365-246x.2011.04987.x.
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Berryman, James G. "Seismic wave attenuation in fluid-saturated porous media." Pure and Applied Geophysics PAGEOPH 128, no. 1-2 (March 1988): 423–32. http://dx.doi.org/10.1007/bf01772607.
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Kacin, Selcuk, Murat Ozturk, Umur Korkut Sevim, Bayram Ali Mert, Zafer Ozer, Oguzhan Akgol, Emin Unal, and Muharrem Karaaslan. "Seismic metamaterials for low-frequency mechanical wave attenuation." Natural Hazards 107, no. 1 (February 11, 2021): 213–29. http://dx.doi.org/10.1007/s11069-021-04580-5.
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Zhang, Wei, and Shi Hai Chen. "The Prediction of Blast Vibration." Applied Mechanics and Materials 353-356 (August 2013): 357–60. http://dx.doi.org/10.4028/www.scientific.net/amm.353-356.357.
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Blasting on large mounts of experiments, we construct mathematical model of seismic wave of blast with systems response method and predict waveform of blast seismic wave. The model can reflect the influence of seismic wave from several kinds of factors and can simulate the attenuation low of amplitude and frequency in the whole process of blast seismic wave. It not only simulates better for simple blast seismic wave, but also can get consistent result in simulating porous blast seismic wave.
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Behura, Jyoti, Mike Batzle, Ronny Hofmann, and John Dorgan. "Heavy oils: Their shear story." GEOPHYSICS 72, no. 5 (September 2007): E175—E183. http://dx.doi.org/10.1190/1.2756600.
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Heavy oils are important unconventional hydrocarbon resources with huge reserves and are usually exploited through thermal recovery processes. These thermal recovery processes can be monitored using seismic techniques. Shear-wave properties, in particular, are expected to be most sensitive to the changes in the heavy-oil reservoir because heavy oils change from being solid-like at low temperatures to fluid-like at higher temperatures. To understand their behavior, we measure the complex shear modulus (and thus also the attenuation) of a heavy-oil-saturated rock and the oil extracted from it within the seismic frequency band in the laboratory. The modulus and quality factor [Formula: see text] of the heavy-oil-saturated rock show a moderate dependence on frequency, but are strongly influenced by temperature. The shear-wave velocity dispersion in these rocks is significant at steam-flooding temperatures as the oil inside the reservoir losesviscosity. At room temperatures, the extracted heavy oil supports a shear wave, but with increasing temperature, its shear modulus decreases rapidly, which translates to a rapid drop in the shear modulus of the heavy-oil-saturated rock as well. At these low to intermediate temperatures [Formula: see text], an attenuation peak corresponding to the viscous relaxation of the heavy oil is encountered (also resulting in significant shear-wave velocity dispersion, well described by the Cole-Cole model). Thus, shear-wave attenuation in heavy-oil rocks can be significantly large and is caused by both the melting and viscous relaxation of the heavy oil. At yet higher temperatures, the lighter components of the heavy oil are lost, making the oil stiffer and less attenuative. The dramatic changes in shear velocities and attenuation in heavy oils should be clearly visible in multicomponent seismic data, and suggest that these measurements can be qualitatively and quantitatively used in seismic monitoring of thermal recovery processes.
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Chen, Yangkang, Weilin Huang, Yatong Zhou, Wei Liu, and Dong Zhang. "Plane-wave orthogonal polynomial transform for amplitude-preserving noise attenuation." Geophysical Journal International 222, no. 3 (June 20, 2020): 1789–804. http://dx.doi.org/10.1093/gji/ggaa188.
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SUMMARY Amplitude-preserving data processing is an important and challenging topic in many scientific fields. The amplitude-variation details in seismic data are especially important because the amplitude variation is directly related with the subsurface wave impedance and fluid characteristics. We propose a novel seismic noise attenuation approach that is based on local plane-wave assumption of seismic events and the amplitude preserving capability of the orthogonal polynomial transform (OPT). The OPT is a way for representing spatially correlative seismic data as a superposition of polynomial basis functions, by which the random noise is distinguished from the useful energy by the high orthogonal polynomial coefficients. The seismic energy is the most correlative along the structural direction and thus the OPT is optimally performed in a flattened gather. We introduce in detail the flattening operator for creating the flattened dimension, where the OPT can be applied subsequently. The flattening operator is created by deriving a plane-wave trace continuation relation following the plane-wave equation. We demonstrate that both plane-wave trace continuation and OPT can well preserve the strong amplitude variation existing in seismic data. In order to obtain a robust slope estimation performance in the presence of noise, a robust slope estimation approach is introduced to substitute the traditional method. A group of synthetic, pre-stack and post-stack field seismic data are used to demonstrate the potential of the proposed framework in realistic applications.
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Zhu, Tieyuan. "Numerical simulation of seismic wave propagation in viscoelastic-anisotropic media using frequency-independent Q wave equation." GEOPHYSICS 82, no. 4 (July 1, 2017): WA1—WA10. http://dx.doi.org/10.1190/geo2016-0635.1.
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Seismic anisotropy is the fundamental phenomenon of wave propagation in the earth’s interior. Numerical modeling of wave behavior is critical for exploration and global seismology studies. The full elastic (anisotropy) wave equation is often used to model the complexity of velocity anisotropy, but it ignores attenuation anisotropy. I have presented a time-domain displacement-stress formulation of the anisotropic-viscoelastic wave equation, which holds for arbitrarily anisotropic velocity and attenuation [Formula: see text]. The frequency-independent [Formula: see text] model is considered in the seismic frequency band; thus, anisotropic attenuation is mathematically expressed by way of fractional time derivatives, which are solved using the truncated Grünwald-Letnikov approximation. I evaluate the accuracy of numerical solutions in a homogeneous transversely isotropic (TI) medium by comparing with theoretical [Formula: see text] and [Formula: see text] values calculated from the Christoffel equation. Numerical modeling results show that the anisotropic attenuation is angle dependent and significantly different from the isotropic attenuation. In synthetic examples, I have proved its generality and feasibility by modeling wave propagation in a 2D TI inhomogeneous medium and a 3D orthorhombic inhomogeneous medium.
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Qi, Qiaomu, Arthur C. H. Cheng, and Yunyue Elita Li. "Determination of formation shear attenuation from dipole sonic log data." GEOPHYSICS 84, no. 3 (May 1, 2019): D73—D79. http://dx.doi.org/10.1190/geo2018-0006.1.
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ABSTRACT Formation S-wave attenuation, when combined with compressional attenuation, serves as a potential hydrocarbon indicator for seismic reservoir characterization. Sonic flexural wave measurements provide a direct means for obtaining the in situ S-wave attenuation at log scale. The key characteristic of the flexural wave is that it propagates at the formation shear slowness and experiences shear attenuation at low frequency. However, in a fast formation, the dipole log consists of refracted P- and S-waves in addition to the flexural wave. The refracted P-wave arrives early and can be removed from the dipole waveforms through time windowing. However, the refracted S-wave, which is often embedded in the flexural wave packet, is difficult to separate from the dipole waveforms. The additional energy loss associated with the refracted S-wave results in the estimated dipole attenuation being higher than the shear attenuation at low frequency. To address this issue, we have developed a new method for accurately determining the formation shear attenuation from the dipole sonic log data. The method uses a multifrequency inversion of the frequency-dependent flexural wave attenuation based on energy partitioning. We first developed our method using synthetic data. Application to field data results in a shear attenuation log that is consistent with lithologic interpretation of other available logs.