Attenuation anisotropy in the linear-slip model: Interpretation of physical modeling data

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. WB165-WB176 ◽  
Author(s):  
Tatiana Chichinina ◽  
Irina Obolentseva ◽  
Leonid Gik ◽  
Boris Bobrov ◽  
Gerardo Ronquillo-Jarillo
Keyword(s):  
Symmetry Axis ◽  
Wave Attenuation ◽  
Joint Inversion ◽  
P Wave ◽  
Slip Model ◽  
S Wave ◽  
The Real ◽  
Complex Valued ◽  
Stack Model ◽  
Linear Slip Model

This study attempts to validate a mathematical formalism of introducing attenuation into Schoenberg’s linear slip model. This formalism is based on replacing the real-valued weaknesses by complex-valued ones. During an ultrasonic experiment, performed at a central frequency of [Formula: see text] on a plate-stack model with [Formula: see text]-thick Plexiglas™ plates, the velocity and attenuation (inverse of the quality factor [Formula: see text]) of P-, SH-, and SV-waves are measured in directions from 25° to 90° with the symmetry axis for dry and oil-saturated models and loading uniaxial pressures of 2 and [Formula: see text]. The velocity and attenuation data are fitted by the derived theoretical functions. The values of the real and imaginary parts of the complex-valued weaknesses are estimated. Thereal parts of the weaknesses, which have a clear physical meaning (they affect the weakening of the material), are three times larger for the dry model than for the oil-saturated one. The imaginary parts of the weaknesses are responsible for attenuation; their values are an order of magnitude smaller than the real parts. The derived expressions for angle-dependent velocities and attenuations can be used to distinguish between dry and oil-saturated fractures. In particular, the P-wave attenuation function in the symmetry-axis direction (normal to fracture planes) is different in dry and saturated media. The experiment shows that the plate-stack model is inhomogeneous because of the nonuniform pressure distribution, which degrades the experimental results and creates difficulties in the inversion for the complex-valued weaknesses — particularly in joint inversion of P- and S-wave data.

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

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 755-765 ◽  
Author(s):  
Xinhua Sun ◽  
Xiaoming Tang ◽  
C. H. (Arthur) Cheng ◽  
L. Neil Frazer
Keyword(s):  
Wave Attenuation ◽  
Fluid Velocity ◽  
P Wave ◽  
Reservoir Rock ◽  
Rock Properties ◽  
S Wave ◽  
Intrinsic Attenuation ◽  
Modified Method ◽  
Receiver Array ◽  
Attenuation Profiles

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

scholarly journals A method of geo-acoustic parameter inversion in shallow sea by the Bayesian theory and the acoustic pressure field

2019 ◽  
Vol 283 ◽  
pp. 06003
Author(s):  
Guangxue Zheng ◽  
Hanhao Zhu ◽  
Jun Zhu
Keyword(s):  
Sound Pressure ◽  
Pressure Field ◽  
Wave Attenuation ◽  
Acoustic Parameter ◽  
Bayesian Theory ◽  
P Wave ◽  
Shallow Sea ◽  
S Wave ◽  
Wave Velocities ◽  
Parameter Inversion

A method of geo-acoustic parameter inversion based on the Bayesian theory is proposed for the acquisition of acoustic parameters in shallow sea with the elastic seabed. Firstly, the theoretical prediction value of the sound pressure field is calculated by the fast field method (FFM). According to the Bayesian theory, we establish the misfit function between the measured sound pressure field and the theoretical pressure field. It is under the assumption of Gaussian data errors which are in line with the likelihood function. Finally, the posterior probability density (PPD) of parameters is given as the result of inversion. Our research is conducted in the light of Metropolis sample rules. Apart from numerical simulations, a scaled model experiment has been taken in the laboratory tank. The results of numerical simulations and tank experiments show that sound pressure field calculated by the result of inversion is consistent with the measured sound pressure field. Besides, s-wave velocities, p-wave velocities and seafloor density have fewer uncertainties and are more sensitive to complex sound pressure than s-wave attenuation and p-wave attenuation. The received signals calculated by inversion results are keeping with received signals in the experiment which verify the effectiveness of this method.

Rock-physics modeling of ultrasonic P- and S-wave attenuation in partially frozen brine and unconsolidated sand systems and comparison with laboratory measurements

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. MR153-MR171 ◽  
Author(s):  
Linsen Zhan ◽  
Jun Matsushima
Keyword(s):  
Ultrasonic Wave ◽  
Wave Attenuation ◽  
Freezing Point ◽  
Rock Physics ◽  
Ultrasonic Waves ◽  
P Wave ◽  
Dominant Factor ◽  
S Wave ◽  
High Attenuation ◽  
Unconsolidated Sand

The nonintuitive observation of the simultaneous high velocity and high attenuation of ultrasonic waves near the freezing point of brine was previously measured in partially frozen systems. However, previous studies could not fully elucidate the attenuation variation of ultrasonic wave propagation in a partially frozen system. We have investigated the potential attenuation mechanisms responsible for previously obtained laboratory results by modeling ultrasonic wave transmission in two different partially frozen systems: partially frozen brine (two phases composed of ice and unfrozen brine) and unconsolidated sand (three phases composed of ice, unfrozen brine, and sand). We adopted two different rock-physics models: an effective medium model for partially frozen brine and a three-phase extension of the Biot model for partially frozen unconsolidated sand. For partially frozen brine, our rock-physics study indicated that squirt flow caused by unfrozen brine inclusions in porous ice could be responsible for high P-wave attenuation around the freezing point. Decreasing P-wave attenuation below the freezing point can be explained by the gradual decrease of squirt flow due to the gradual depletion of unfrozen brine. For partially frozen unconsolidated sand, our rock-physics study implied that squirt flow between ice grains is a dominant factor for P-wave attenuation around the freezing point. With decreasing temperature lower than the freezing point, the friction between ice and sand grains becomes more dominant for P-wave attenuation because the decreasing amount of unfrozen brine reduces squirt flow between ice grains, whereas the generation of ice increases the friction. The increasing friction between ice and sand grains caused by ice formation is possibly responsible for increasing the S-wave attenuation at decreasing temperatures. Then, further generation of ice with further cooling reduces the elastic contrast between ice and sand grains, hindering their relative motion; thus, reducing the P- and S-wave attenuation.

Physical modeling and analysis of P-wave attenuation anisotropy in transversely isotropic media

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. D1-D7 ◽  
Author(s):  
Yaping Zhu ◽  
Ilya Tsvankin ◽  
Pawan Dewangan ◽  
Kasper van Wijk
Keyword(s):  
Attenuation Coefficient ◽  
Symmetry Axis ◽  
Wave Attenuation ◽  
Transversely Isotropic ◽  
P Wave ◽  
Velocity Variation ◽  
Ratio Method ◽  
Fracture Detection ◽  
Wide Range ◽  
Attenuation Anisotropy

Anisotropic attenuation can provide sensitive attributes for fracture detection and lithology discrimination. This paper analyzes measurements of the P-wave attenuation coefficient in a transversely isotropic sample made of phenolic material. Using the spectral-ratio method, we estimate the group (effective) attenuation coefficient of P-waves transmitted through the sample for a wide range of propagation angles (from [Formula: see text] to [Formula: see text]) with the symmetry axis. Correction for the difference between the group and phase angles and for the angular velocity variation help us to obtain the normalized phase attenuation coefficient [Formula: see text] governed by the Thomsen-style attenuation-anisotropy parameters [Formula: see text] and [Formula: see text]. Whereas the symmetry axis of the angle-dependent coefficient [Formula: see text] practically coincides with that of the velocity function, the magnitude of the attenuation anisotropy far exceeds that of the velocity anisotropy. The quality factor [Formula: see text] increases more than tenfold from the symmetry axis (slow direction) to the isotropy plane (fast direction). Inversion of the coefficient [Formula: see text] using the Christoffel equation yields large negative values of the parameters [Formula: see text] and [Formula: see text]. The robustness of our results critically depends on several factors, such as the availability of an accurate anisotropic velocity model and adequacy of the homogeneous concept of wave propagation, as well as the choice of the frequency band. The methodology discussed here can be extended to field measurements of anisotropic attenuation needed for AVO (amplitude-variation-with-offset) analysis, amplitude-preserving migration, and seismic fracture detection.

Inversion of reflection traveltimes for transverse isotropy

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1095-1107 ◽  
Author(s):  
Ilya Tsvankin ◽  
Leon Thomsen
Keyword(s):  
Wave Velocity ◽  
Vertical Velocity ◽  
Joint Inversion ◽  
Transverse Isotropy ◽  
Taylor Series Expansion ◽  
High Sensitivity ◽  
Transversely Isotropic ◽  
P Wave ◽  
S Wave ◽  
Quartic Term

In anisotropic media, the short‐spread stacking velocity is generally different from the root‐mean‐square vertical velocity. The influence of anisotropy makes it impossible to recover the vertical velocity (or the reflector depth) using hyperbolic moveout analysis on short‐spread, common‐midpoint (CMP) gathers, even if both P‐ and S‐waves are recorded. Hence, we examine the feasibility of inverting long‐spread (nonhyperbolic) reflection moveouts for parameters of transversely isotropic media with a vertical symmetry axis. One possible solution is to recover the quartic term of the Taylor series expansion for [Formula: see text] curves for P‐ and SV‐waves, and to use it to determine the anisotropy. However, this procedure turns out to be unstable because of the ambiguity in the joint inversion of intermediate‐spread (i.e., spreads of about 1.5 times the reflector depth) P and SV moveouts. The nonuniqueness cannot be overcome by using long spreads (twice as large as the reflector depth) if only P‐wave data are included. A general analysis of the P‐wave inverse problem proves the existence of a broad set of models with different vertical velocities, all of which provide a satisfactory fit to the exact traveltimes. This strong ambiguity is explained by a trade‐off between vertical velocity and the parameters of anisotropy on gathers with a limited angle coverage. The accuracy of the inversion procedure may be significantly increased by combining both long‐spread P and SV moveouts. The high sensitivity of the long‐spread SV moveout to the reflector depth permits a less ambiguous inversion. In some cases, the SV moveout alone may be used to recover the vertical S‐wave velocity, and hence the depth. Success of this inversion depends on the spreadlength and degree of SV‐wave velocity anisotropy, as well as on the constraints on the P‐wave vertical velocity.

Seismic wave attenuation and modulus dispersion in sandstones

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. D211-D231 ◽  
Author(s):  
James W. Spencer ◽  
Jacob Shine
Keyword(s):  
Wave Attenuation ◽  
High Viscosity ◽  
P Wave ◽  
S Wave ◽  
Local Flow ◽  
Shear Moduli ◽  
Low Viscosity ◽  
Confining Pressures ◽  
Wave Induced ◽  
Dispersion And Attenuation

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.

The effects of pore‐fluid salinity on ultrasonic wave propagation in sandstones

Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 928-934 ◽  
Author(s):  
Simon M. Jones ◽  
Clive McCann ◽  
Timothy R. Astin ◽  
Jeremy Sothcott
Keyword(s):  
Wave Propagation ◽  
Ultrasonic Wave ◽  
Wave Attenuation ◽  
Clay Content ◽  
Seismic Wave Propagation ◽  
Ultrasonic Pulse ◽  
Pore Fluid ◽  
P Wave ◽  
S Wave ◽  
Shear Moduli

Petrophysical interpretation of increasingly refined seismic data from subsurface formations requires a more fundamental understanding of seismic wave propagation in sedimentary rocks. We consider the variation of ultrasonic wave velocity and attenuation in sandstones with pore‐fluid salinity and show that wave propagation is modified in proportion to the clay content of the rock and the salinity of the pore fluid. Using an ultrasonic pulse reflection technique (590–890 kHz), we have measured the P-wave and S-wave velocities and attenuations of 15 saturated sandstones with variable effective pressure (5–60 MPa) and pore‐fluid salinity (0.0–3.4 M). In clean sandstones, there was close agreement between experimental and Biot model values of [Formula: see text], but they diverged progressively in rocks containing more than 5% clay. However, this effect is small: [Formula: see text] changed by only 0.6% per molar change in salinity for a rock with a clay content of 29%. The variation of [Formula: see text] with brine molarity exhibited Biot behavior in some samples but not in others; there was no obvious relationship with clay content. P-wave attenuation was independent of pore‐fluid salinity, while S-wave attenuation was weakly dependent. The velocity data suggest the frame bulk and shear moduli of sandstones are altered by changes in the pore‐fluid salinity. One possible mechanism is the formation damage caused by clay swelling and migration of fines in low‐molarity electrolytes. The absence of variation between the attenuation in water‐saturated and brine‐saturated samples indicates the attenuation mechanism is relatively unaffected by changes in the frame moduli.

Simultaneous inversion of PP and PS seismic data

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. R1-R10 ◽  
Author(s):  
Helene Hafslund Veire ◽  
Martin Landrø
Keyword(s):  
Seismic Data ◽  
Reservoir Characterization ◽  
Model Building ◽  
Joint Inversion ◽  
P Wave ◽  
Inversion Method ◽  
System Of Equations ◽  
S Wave ◽  
Data Set ◽  
Simultaneous Inversion

Elastic parameters derived from seismic data are valuable input for reservoir characterization because they can be related to lithology and fluid content of the reservoir through empirical relationships. The relationship between physical properties of rocks and fluids and P-wave seismic data is nonunique. This leads to large uncertainties in reservoir models derived from P-wave seismic data. Because S- waves do not propagate through fluids, the combined use of P-and S-wave seismic data might increase our ability to derive fluid and lithology effects from seismic data, reducing the uncertainty in reservoir characterization and thereby improving 3D reservoir model-building. We present a joint inversion method for PP and PS seismic data by solving approximated linear expressions of PP and PS reflection coefficients simultaneously using a least-squares estimation algorithm. The resulting system of equations is solved by singular-value decomposition (SVD). By combining the two independent measurements (PP and PS seismic data), we stabilize the system of equations for PP and PS seismic data separately, leading to more robust parameter estimation. The method does not require any knowledge of PP and PS wavelets. We tested the stability of this joint inversion method on a 1D synthetic data set. We also applied the methodology to North Sea multicomponent field data to identify sand layers in a shallow formation. The identified sand layers from our inverted sections are consistent with observations from nearby well logs.

scholarly journals Azimuthal Attenuation Elastic Impedance Inversion for Fluid and Fracture Characterization Based on Modified Linear-Slip Theory

Geofluids ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18
Author(s):  
Xinpeng Pan ◽  
Guangzhi Zhang ◽  
Yian Cui
Keyword(s):  
Porous Medium ◽  
Wave Attenuation ◽  
Real Data ◽  
Seismic Attenuation ◽  
P Wave ◽  
Inversion Method ◽  
S Wave ◽  
Fracture Characterization ◽  
Fractured Porous Medium ◽  
Elastic Impedance

The seismic attenuation should be considered while accounting for the effect of anisotropy on the seismic wave propagating through a saturated fractured porous medium. Based on the modified linear-slip theory and anisotropic Gassmann’s equation, we derive an analytical expression for a linearized PP-wave reflection coefficient and an azimuthal attenuation elastic impedance (AAEI) equation in terms of fluid/porosity term, shear modulus, density, dry normal and tangential fracture weaknesses, and compressional (P-wave) and shear (S-wave) attenuation parameters in a weak-attenuation isotropic background rock containing one single set of vertical aligned fractures. We then propose an AAEI inversion method to characterize the characteristics of fluids and fractures using two kinds of constrained regularizations in such a fractured porous medium. The proposed approach is finally confirmed by both the synthetic and real data sets acquired over a saturated fractured porous reservoir.

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