Attenuation and dispersion of P-waves in fluid-saturated porous rocks with a distribution of coplanar cracks - scattering approach

Geophysics ◽  
2020 ◽  
pp. 1-54
Author(s):  
Yongjia Song ◽  
Jun Wang ◽  
Hengshan Hu ◽  
Bo Han
Keyword(s):  
Quality Factor ◽  
Scattering Problem ◽  
Crack Density ◽  
Relaxation Frequency ◽  
P Wave ◽  
Frequency Dependent ◽  
Low Frequencies ◽  
Attenuation And Dispersion ◽  
Dispersion And Attenuation ◽  
Coplanar Cracks

Wave-induced fluid flow (WIFF) between cracks and micro-pores is one of the major mechanisms in causing attenuation and dispersion within seismic frequency ranges. Previous non-interaction-approximation (NIA) models often assume the distribution of cracks is dilute, neglecting the influences of interacting cracks on dispersion and attenuation. To overcome this restriction, we investigate the interaction between coplanar cracks and their influences on seismic dispersion and attenuation. First, a scattering problem for a longitudinal (P) wave normally impinging on a plane with equally distributed coplanar cracks in a porous medium is solved using integral transform approach. Then, based on the solution, an effective wavenumber is derived for P-wave propagation in a porous material with coplanar cracks. It is found that the magnitude of dispersion and attenuation can significantly increase when the spacing between adjacent cracks decreases even if the crack density is unchanged. Moreover, frequency-dependent asymptotic behavior of inverse quality factor is also different from that of the NIA models at frequencies lower than the WIFF relaxation frequency. Specifically, the inverse quality factor scales with the square root of frequency at low frequencies. When the spacing between adjacent cracks is large, an additional frequency-dependent scale occurs at relatively higher frequencies (but still lower than the WIFF relaxation frequency) with inverse quality factor scales with the first power of frequency. When the spacing becomes much larger so that the interaction between the adjacent cracks is negligible, the present model exactly reduces to a NIA model for a distribution of aligned slit cracks and the first power scale can prevail attenuation within low frequencies.

scholarly journals Fluid Discrimination Based on Frequency-Dependent AVO Inversion with the Elastic Parameter Sensitivity Analysis

Geofluids ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Pu Wang ◽  
Jingye Li ◽  
Xiaohong Chen ◽  
Kedong Wang ◽  
Benfeng Wang
Keyword(s):  
Data Interpretation ◽  
Elastic Parameter ◽  
Pore Fluid ◽  
P Wave ◽  
Frequency Dependent ◽  
Avo Inversion ◽  
Fluid Factor ◽  
Dispersion Terms ◽  
Dispersion And Attenuation ◽  
Dispersion Term

Fluid discrimination is an extremely important part of seismic data interpretation. It plays an important role in the refined description of hydrocarbon-bearing reservoirs. The conventional AVO inversion based on Zoeppritz’s equation shows potential in lithology prediction and fluid discrimination; however, the dispersion and attenuation induced by pore fluid are not fully considered. The relationship between dispersion terms in different frequency-dependent AVO equations has not yet been discussed. Following the arguments of Chapman, the influence of pore fluid on elastic parameters is analyzed in detail. We find that the dispersion and attenuation of Russell fluid factor, Lamé parameter, and bulk modulus are more pronounced than those of P-wave modulus. The Russell fluid factor is most prominent among them. Based on frequency-dependent AVO inversion, the uniform expression of different dispersion terms of these parameters is derived. Then, incorporating the P-wave difference with the dispersion terms, we obtain new P-wave difference dispersion factors which can identify the gas-bearing reservoir location better compared with the dispersion terms. Field data application also shows that the dispersion term of Russell fluid factor is optimal in identifying fluid. However, the dispersion term of Russell fluid factor could be unsatisfactory, if the value of the weighting parameter associated with dry rock is improper. Then, this parameter is studied to propose a reasonable setting range. The results given by this paper are helpful for the fluid discrimination in hydrocarbon-bearing rocks.

Anisotropic P-SV-wave dispersion and attenuation due to inter-layer flow in thinly layered porous rocks

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. WA135-WA145 ◽  
Author(s):  
Fabian Krzikalla ◽  
Tobias M. Müller
Keyword(s):  
Wave Attenuation ◽  
Fluid Pressure ◽  
Pore Fluid ◽  
P Wave ◽  
Angle Of Incidence ◽  
Porous Rocks ◽  
Frequency Dependent ◽  
Symmetry Properties ◽  
Wave Induced ◽  
Attenuation And Dispersion

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

scholarly journals Frequency-dependent attenuation and dispersion caused by squirt flow: Three-dimensional numerical study

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. MR129-MR145 ◽  
Author(s):  
Yury Alkhimenkov ◽  
Eva Caspari ◽  
Boris Gurevich ◽  
Nicolás D. Barbosa ◽  
Stanislav Glubokovskikh ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Analytical Solution ◽  
Analytical Solutions ◽  
Numerical Study ◽  
Numerical Models ◽  
Pore Space ◽  
Fluid Pressure ◽  
Frequency Dependent ◽  
Attenuation And Dispersion ◽  
Dispersion And Attenuation

Seismic waves may exhibit significant dispersion and attenuation in reservoir rocks due to pore-scale fluid flow. Fluid flow at the microscopic scale is referred to as squirt flow and occurs in very compliant pores, such as grain contacts or microcracks, that are connected to other stiffer pores. We have performed 3D numerical simulations of squirt flow using a finite-element approach. Our 3D numerical models consist of a pore space embedded into a solid grain material. The pore space is represented by a flat cylinder (a compliant crack) whose edge is connected with a torus (a stiff pore). Grains are described as a linear isotropic elastic material, whereas the fluid phase is described by the quasistatic linearized compressible Navier-Stokes momentum equation. We obtain the frequency-dependent effective stiffness of a porous medium and calculate dispersion and attenuation due to fluid flow from a compliant crack to a stiff pore. We compare our numerical results against a published analytical solution for squirt flow and analyze the effects of its assumptions. Previous interpretation of the squirt flow phenomenon based mainly on analytical solutions is verified, and some new physical effects are identified. The numerical and analytical solutions agree only for the simplest model in which the edge of the crack is subjected to zero fluid pressure boundary condition while the stiff pore is absent. For the more realistic model that includes the stiff pore, significant discrepancies are observed. We identify two important aspects that need improvement in the analytical solution: the calculation of the frame stiffness moduli and the frequency dependence of attenuation and dispersion at intermediate frequencies.

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

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 309-318 ◽  
Author(s):  
Jorge O. Parra
Keyword(s):  
Wave Equation ◽  
Fluid Flow ◽  
Analytical Solution ◽  
Seismic Waves ◽  
Transversely Isotropic ◽  
P Wave ◽  
Fluid Properties ◽  
Permeability Anisotropy ◽  
Attenuation And Dispersion ◽  
Maximum Permeability

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

Application of bandlimited anelastic models to wave propagation in highly attenuative media

1995 ◽  
Vol 85 (5) ◽  
pp. 1359-1372
Author(s):  
Hsi-Ping Liu
Keyword(s):  
Wave Propagation ◽  
Quality Factor ◽  
Lower Limit ◽  
Relaxation Function ◽  
Function Approach ◽  
Creep Function ◽  
Frequency Range ◽  
Quality Factors ◽  
Low Frequencies ◽  
Near Surface

Abstract Because of its simple form, a bandlimited, four-parameter anelastic model that yields nearly constant midband Q for low-loss materials is often used for calculating synthetic seismograms. The four parameters used in the literature to characterize anelastic behavior are τ1, τ2, Qm, and MR in the relaxation-function approach (s1 = 1/τ1 and s2 = 1/τ2 are angular frequencies defining the bandwidth, MR is the relaxed modulus, and Qm is approximately the midband quality factor when Qm ≫ 1); or τ1, τ2, Qm, and MR in the creep-function approach (s1 = 1/τ1 and s2 = 1/τ2 are angular frequencies defining the bandwidth, and Qm is approximately the midband quality factor when Qm ≫ 1). In practice, it is often the case that, for a particular medium, the quality factor Q(ω0) and phase velocity c(ω0) at an angular frequency ω0 (s1 < ω0 < s2; s1 < ω0 < s2) are known from field measurements. If values are assigned to τ1 and τ2 (τ2 < τ1), or to τ1 and τ2 (τ2 < τ1), then the two remaining parameters, Qm and MR, or Qm and MR, can be obtained from Q(ω0). However, for highly attenuative media, e.g., Q(ω0) ≦ 5, Q(ω) can become highly skewed and negative at low frequencies (for the relaxation-function approach) or at high frequencies (for the creep-function approach) if this procedure is followed. A negative Q(ω) is unacceptable because it implies an increase in energy for waves propagating in a homogeneous and attenuative medium. This article shows that given (τ1, τ2, ω0) or (τ1, τ2, ω0), a lower limit of Q(ω0) exists for a bandlimited, four-parameter anelastic model. In the relaxation-function approach, the minimum permissible Q(ω0) is given by ln [(1 + ω20τ21)/(1 + ω20τ22)]/{2 arctan [ω0(τ1 − τ2)/(1 + ω20τ1τ2)]}. In the creep-function approach, the minimum permissible Q(ω0) is given by {2 ln (τ1/τ2) − ln [(1 + ω20τ21)/(1 + ω20τ22)]}/{2 arctan [ω0(τ1 − τ2)/(1 + ω20τ1τ2)]}. The more general statement that, for a given set of relaxation mechanisms, a lower limit exists for Q(ω0) is also shown to hold. Because a nearly constant midband Q cannot be achieved for highly attenuative media using a four-parameter anelastic model, a bandlimited, six-parameter anelastic model that yields a nearly constant midband Q for such media is devised; an expression for the minimum permissible Q(ω0) is given. Six-parameter anelastic models with quality factors Q ∼ 5 and Q ∼ 16, constant to 6% over the frequency range 0.5 to 200 Hz, illustrate this result. In conformity with field observations that Q(ω) for near-surface earth materials is approximately constant over a wide frequency range, the bandlimited, six-parameter anelastic models are suitable for modeling wave propagation in highly attenuative media for bandlimited time functions in engineering and exploration seismology.

Regional Lg attenuation for the continental United States

1997 ◽  
Vol 87 (3) ◽  
pp. 606-619 ◽  
Author(s):  
Harley M. Benz ◽  
Arthur Frankel ◽  
David M. Boore
Keyword(s):  
United States ◽  
Frequency Band ◽  
Southern California ◽  
Basin And Range ◽  
Northeastern United States ◽  
Basin And Range Province ◽  
Frequency Dependent ◽  
Low Frequencies ◽  
Central United States ◽  
Q Function

Abstract Measurements of the Fourier amplitude spectra of Lg phases recorded at high frequency (0.5 to 14.0 Hz) by broadband seismic stations are used to determine regional attenuation relationships for southern California, the Basin and Range Province, the central United States, and the northeastern United States and southeastern Canada. Fourier spectral amplitudes were measured every quarter octave from Lg phases windowed between 3.0 and 3.7 km sec−1 and recorded in the distance range of 150 to 1000 km. Attenuation at each frequency is determined by assuming a geometrical spreading exponent of 0.5 and inverting for Q and source and receiver terms. Both southern California and the Basin and Range Province are well described by low Lg Q and frequency-dependent attenuation. Lg spectral amplitudes in southern California are fit at low frequencies (0.625 to 0.875 Hz) by a constant Lg Q of 224 and by a frequency-dependent Lg Q function Q = 187−7+7f0.55(±0.03) in the frequency band 1.0 to 7.0 Hz. The Basin and Range Province is characterized by a constant Lg Q of 192 for frequencies of 0.5 to 0.875 Hz and by the frequency-dependent Lg Q function Q = 235−11+11f0.56(±0.04) in the frequency band 1.0 to 5.0 Hz. A change in frequency dependence above 5.0 Hz is possible due to contamination of the Lg window by Pn and Sn phases. Lg spectral amplitudes in the central United States are fit by a mean frequency-independent Lg Q of 1291 for frequencies of 1.5 to 7.0 Hz, while a frequency-dependent Lg Q of Q = 1052−83+91(f/1.5)0.22(±0.06) fits the Lg spectral amplitudes for the northeastern United States and southeastern Canada over the passband 1.5 to 14.0 Hz. Attenuation measurements for these areas were restricted to frequencies >1.5 Hz due to larger microseismic noise levels at the lower frequencies.

Multiscale fracture density analysis at Stromboli Volcano, Italy: implications to flank stability

2021 ◽  
Author(s):  
Thomas Alcock ◽  
Sergio Vinciguerra ◽  
Phillip Benson ◽  
Federico Vagnon
Keyword(s):  
Electrical Resistivity ◽  
Wave Velocity ◽  
Rift Zone ◽  
Pulse Generator ◽  
Average Length ◽  
Crack Density ◽  
P Wave ◽  
Fracture Density ◽  
Stromboli Volcano ◽  
P Wave Velocity

<p>Stromboli volcano has experienced four sector collapses over the past 13 thousand years, resulting in the formation of the Sciara del Fuoco (SDF) horseshoe-shaped depression and an inferred NE / SW striking rift zone across the SDF and the western sector of the island. These events have resulted in the formation of steep depressions on the slopes on the volcano where episodes of instability are continuously being observed and recorded. This study aims to quantify the fracture density inside and outside the rift zone to identify potential damaged zones that could reduce the edifice strength and promote fracturing. In order to do so we have carried out a multiscale analysis, by integrating satellite observations, field work and seismic and electrical resistivity analyses on cm scales blocks belonging to 11 lava units from the main volcanic cycles that have built the volcano edifice, ie. Paleostromboli, Nestromboli and Vancori. 0.5 m resolution Pleiades satellite data has been first used to highlight 23635 distinct linear features across the island. Fracture density has been calculated using Fracpaq based on the Mauldon et al (2001) method to determine the average fracture density of a given area on the basis of the average length of drawn segments within a predetermined circular area. 41.8 % of total fracture density is found around intrusions and fissures, with the summit area and the slopes of SDF having the highest average fracture density of 5.279  . Density, porosity, P- wave velocity in dry and wet conditions and electrical resistivity (in wet conditions) were measured  via an ultrasonic pulse generator and acquisition system (Pundit) and an on purpose built measuring quadrupole on cm scale blocks of lavas collected from both within and outside the proposed rift zone to assess the physical state and the crack damage of the different lava units.  Preliminary results show that P-wave velocity between ~ 2.25 km/s < Vp < 5km/s decreases with porosity while there is high variability electrical resistivity with 21.7 < ρ < 590 Ohm * m. This is presumably due to the lavas texture and the variable content of bubble/vesicles porosity and crack damage, that is reflected by an effective overall porosity between 0 and 9 %. Higher porosity is generally mirrored by lower p-wave velocity values. Neostromboli blocks show the most variability in both P-wave velocity and electrical resistivity. Further work will assess crack density throughout optical analyses and systematically investigate the UCS and elastic moduli. This integrated approach is expected to provide a multiscale fracture density and allow to develop further laboratory testing on how slip surfaces can evolve to a flank collapse at Stromboli.</p>

scholarly journals Impact of frequency-dependent anisotropy on azimuthal P-wave reflections

2018 ◽  
Vol 15 (6) ◽  
pp. 2530-2544 ◽  
Author(s):  
Zhaoyu Jin ◽  
Mark Chapman ◽  
Giorgos Papageorgiou ◽  
Xiaoyang Wu
Keyword(s):  
P Wave ◽  
Wave Reflections ◽  
Frequency Dependent
Sign in / Sign up

Export Citation Format

Share Document