On The Low-Frequency Elastic Response of Pierre Shale During Temperature Cycles

Summary The impact of temperature on elastic rock properties is less-studied and thus less-understood than that of pressure and stress. Thermal effects on dispersion are experimentally observed herein from seismic to ultrasonic frequencies: Young’s moduli and Poisson’s ratios plus P- and S-wave velocities are determined by forced-oscillation (FO) from 1 to 144 Hz and by pulse-transmission (PT) at 500 kHz. Despite being the dominant sedimentary rock type, shales receive less experimental attention than sandstones and carbonates. To our knowledge, no other FO studies on shale at above ambient temperatures exist. Temperature fluctuations are enforced by two temperature cycles from 20 via 40 to 60○C and vice versa. Measured rock properties are initially irreversible but become reversible with increasing number of heating and cooling segments. Rock property-sensitivity to temperature is likewise reduced. It is revealed that dispersion shifts towards higher frequencies with increasing temperature (reversible if decreased), Young’s moduli and P-wave velocity moduli and P-wave velocity maxima occur at 40○C for frequencies below 56 Hz, and S-wave velocities remain unchanged with temperature (if the first heating segment is neglected) at seismic frequencies. In comparison, ultrasonic P- and S-wave velocities are found to decrease with increasing temperatures. Behavioural differences between seismic and ultrasonic properties are attributed to decreasing fluid viscosity with temperature. We hypothesize that our ultrasonic recordings coincide with the transition-phase separating the low- and high-frequency regimes while our seismic recordings are within the low-frequency regime.

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Wavefield simulation and data-acquisition-scheme analysis for LWD acoustic tools in very slow formations

Geophysics ◽

10.1190/1.3552929 ◽

2011 ◽

Vol 76 (3) ◽

pp. E59-E68 ◽

Cited By ~ 23

Author(s):

Hua Wang ◽

Guo Tao

Keyword(s):

Wave Velocity ◽

Cutoff Frequency ◽

P Wave ◽

Flexural Wave ◽

S Wave ◽

Low Frequencies ◽

Wave Velocities ◽

Dipole System ◽

P Wave Velocity ◽

Wavefield Simulation

Propagating wavefields from monopole, dipole, and quadrupole acoustic logging-while-drilling (LWD) tools in very slow formations have been studied using the discrete wavenumber integration method. These studies examine the responses of monopole and dipole systems at different source frequencies in a very slow surrounding formation, and the responses of a quadrupole system operating at a low source frequency in a slow formation with different S-wave velocities. Analyses are conducted of coherence-velocity/slowness relationships (semblance spectra) in the time domain and of the dispersion characteristics of these waveform signals from acoustic LWD array receivers. These analyses demonstrate that, if the acoustic LWD tool is centralized properly and is operating at low frequencies (below 3 kHz), a monopole system can measure P-wave velocity by means of a “leaky” P-wave for very slow formations. Also, for very slow formations a dipole system can measure the P-wave velocity via a leaky P-wave and can measure the S-wave velocity from a formation flexural wave. With a quadrupole system, however, the lower frequency limit (cutoff frequency) of the drill-collar interference wave would decrease to 5 kHz and might no longer be neglected if the surrounding formation becomes a very slow formation, with S-wave velocities at approximately 500 m/s.

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Acoustic measurements in unconsolidated sands at low effective pressure and overpressure detection

Geophysics ◽

10.1190/1.1468600 ◽

2002 ◽

Vol 67 (2) ◽

pp. 405-412 ◽

Cited By ~ 55

Author(s):

Manika Prasad

Keyword(s):

Wave Velocity ◽

P Wave ◽

Acoustic Measurements ◽

S Wave ◽

Deepwater Drilling ◽

Unconsolidated Sands ◽

Wave Velocities ◽

P Wave Velocity ◽

Shallow Water Flows ◽

Low Pressures

Shallow water flows and over‐pressured zones are a major hazard in deepwater drilling projects. Their detection prior to drilling would save millions of dollars in lost drilling costs. I have investigated the sensitivity of seismic methods for this purpose. Using P‐wave information alone can be ambiguous, because a drop in P‐wave velocity (Vp) can be caused both by overpressure and by presence of gas. The ratio of P‐wave velocity to S‐wave velocity (Vp/Vs), which increases with overpressure and decreases with gas saturation, can help differentiate between the two cases. Since P‐wave velocity in a suspension is slightly below that of the suspending fluid and Vs=0, Vp/Vs and Poisson's ratio must increase exponentially as a load‐bearing sediment approaches a state of suspension. On the other hand, presence of gas will also decrease Vp but Vs will remain unaffected and Vp/Vs will decrease. Analyses of ultrasonic P‐ and S‐wave velocities in sands show that the Vp/Vs ratio, especially at low effective pressures, decreases rapidly with pressure. At very low pressures, Vp/Vs values can be as large as 100 and higher. Above pressures greater than 2 MPa, it plateaus and does not change much with pressure. There is significant change in signal amplitudes and frequency of shear waves below 1 MPa. The current ultrasonic data shows that Vp/Vs values can be invaluable indicators of low differential pressures.

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EXPERIMENTAL EVALUATION OF ULTRASONIC VELOCITIES AND ANISOTROPY IN THE TUSCALOOSA MARINE SHALE FORMATION

Interpretation ◽

10.1190/int-2019-0268.1 ◽

2020 ◽

pp. 1-62 ◽

Cited By ~ 2

Author(s):

Jamal Ahmadov ◽

Mehdi Mokhtari

Keyword(s):

Wave Velocity ◽

Mineralogical Composition ◽

Organic Content ◽

P Wave ◽

S Wave ◽

Velocity Anisotropy ◽

Wave Velocities ◽

Marine Shale ◽

P Wave Velocity ◽

Degree Of Anisotropy

Tuscaloosa Marine Shale (TMS) formation is a clay- and organic-rich emerging shale play with a considerable amount of hydrocarbon resources. Despite the substantial potential, there have been only a few wells drilled and produced in the formation over the recent years. The analyzed TMS samples contain an average of 50 wt% total clay, 27 wt% quartz and 14 wt% calcite and the mineralogy varies considerably over the small intervals. The high amount of clay leads to pronounced anisotropy and the frequent changes in mineralogy result in the heterogeneity of the formation. We studied the compressional (VP) and shear-wave (VS) velocities to evaluate the degree of anisotropy and heterogeneity, which impact hydraulic fracture growth, borehole instabilities, and subsurface imaging. The ultrasonic measurements of P- and S-wave velocities from five TMS wells are the best fit to the linear relationship with R2 = 0.84 in the least-squares criteria. We observed that TMS S-wave velocities are relatively lower when compared to the established velocity relationships. Most of the velocity data in bedding-normal direction lie outside constant VP/VS lines of 1.6–1.8, a region typical of most organic-rich shale plays. For all of the studied TMS samples, the S-wave velocity anisotropy exhibits higher values than P-wave velocity anisotropy. In the samples in which the composition is dominated by either calcite or quartz minerals, mineralogy controls the velocities and VP/VS ratios to a great extent. Additionally, the organic content and maturity account for the velocity behavior in the samples in which the mineralogical composition fails to do so. The results provide further insights into TMS Formation evaluation and contribute to a better understanding of the heterogeneity and anisotropy of the play.

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Determining P- and S-wave velocities and Q-values from single ultrasound transmission measurements performed on cylindrical rock samples: it’s possible, when…

10.5194/egusphere-egu2020-9178 ◽

2020 ◽

Author(s):

Marc S. Boxberg ◽

Mandy Duda ◽

Katrin Löer ◽

Wolfgang Friederich ◽

Jörg Renner

Keyword(s):

Wave Velocity ◽

P Wave ◽

S Wave ◽

Standard Material ◽

Rock Samples ◽

Intrinsic Attenuation ◽

Finite Element Software ◽

Wave Velocities ◽

P Wave Velocity

Determining elastic wave velocities and intrinsic attenuation of cylindrical rock samples by transmission of ultrasound signals appears to be a simple experimental task, which is performed routinely in a range of geoscientific and engineering applications requiring characterization of rocks in field and laboratory. P- and S-wave velocities are generally determined from first arrivals of signals excited by specifically designed transducers. A couple of methods exist for determining the intrinsic attenuation, most of them relying either on a comparison between the sample under investigation and a standard material or on investigating the same material for various geometries.Of the three properties of interest, P-wave velocity is certainly the least challenging one to determine, but dispersion phenomena lead to complications with the consistent identification of frequency-dependent first breaks. The determination of S-wave velocities is even more hampered by converted waves interfering with the S-wave arrival. Attenuation estimates are generally subject to higher uncertainties than velocity measurements due to the high sensitivity of amplitudes to experimental procedures. The achievable accuracy of determining S-wave velocity and intrinsic attenuation using standard procedures thus appears to be limited.We pursue the determination of velocity and attenuation of rock samples based on full waveform modeling and inversion. Assuming the rock sample to be homogeneous - an assumption also underlying standard analyses - we quantify P-wave velocity, S-wave velocity and intrinsic P- and S-wave attenuation from matching a single ultrasound trace with a synthetic one numerically modelled using the spectral finite-element software packages SPECFEM2D and SPECFEM3D. We find that enough information on both velocities is contained in the recognizable reflected and converted phases even when nominal P-wave sensors are used. Attenuation characteristics are also inherently contained in the relative amplitudes of these phases due to their different travel paths. We present recommendations for and results from laboratory measurements on cylindrical samples of aluminum and rocks with different geometries that we also compare with various standard analysis methods. The effort put into processing for our approach is particularly justified when accurate values and/or small variations, for example in response to changing P-T-conditions, are of interest or when the amount of sample material is limited.

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Estimating shear‐wave velocities from P-wave and converted‐wave data

Geophysics ◽

10.1190/1.1444556 ◽

1999 ◽

Vol 64 (2) ◽

pp. 504-507 ◽

Cited By ~ 1

Author(s):

Franklyn K. Levin

Keyword(s):

Wave Velocity ◽

Seismic Data ◽

P Wave ◽

S Wave ◽

Converted Wave ◽

Wave Data ◽

Wave Velocities ◽

Shear Wave Velocities ◽

P Wave Velocity ◽

Growing Body

Tessmer and Behle (1988) show that S-wave velocity can be estimated from surface seismic data if both normal P-wave data and converted‐wave data (P-SV) are available. The relation of Tessmer and Behle is [Formula: see text] (1) where [Formula: see text] is the S-wave velocity, [Formula: see text] is the P-wave velocity, and [Formula: see text] is the converted‐wave velocity. The growing body of converted‐wave data suggest a brief examination of the validity of equation (1) for velocities that vary with depth.

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Seismological studies in a rock body at Chalk River, Ontario and their relation to fractures

Canadian Journal of Earth Sciences ◽

10.1139/e82-133 ◽

1982 ◽

Vol 19 (8) ◽

pp. 1535-1547 ◽

Cited By ~ 1

Author(s):

C. Wright

Keyword(s):

Wave Velocity ◽

Test Site ◽

P Wave ◽

Seismic Velocities ◽

S Wave ◽

P Waves ◽

Rock Body ◽

Near Surface ◽

Wave Velocities ◽

P Wave Velocity

Seismological experiments have been undertaken at a test site near Chalk River, Ontario that consists of crystalline rocks covered by glacial sediments. Near-surface P and S wave velocity and amplitude variations have been measured along profiles less than 2 km in length. The P and S wave velocities were generally in the range 4.5–5.6 and 2.9–3.2 km/s, respectively. These results are consistent with propagation through fractured gneiss and monzonite, which form the bulk of the rock body. The P wave velocity falls below 5.0 km/s in a region where there is a major fault and in an area of high electrical conductivity; such velocity minima are therefore associated with fracture systems. For some paths, the P and 5 wave velocities were in the ranges 6.2–6.6 and 3.7–4.1 km/s, respectively, showing the presence of thin sheets of gabbro. Temporal changes in P travel times of up to 1.4% over a 12 h period were observed where the sediment cover was thickest. The cause may be changes in the water table. The absence of polarized SH arrivals from specially designed shear wave sources indicates the inhomogeneity of the test site. A Q value of 243 ± 53 for P waves was derived over one relatively homogeneous profile of about 600 m length. P wave velocity minima measured between depths of 25 and 250 m in a borehole correlate well with the distribution of fractures inferred from optical examination of borehole cores, laboratory measurements of seismic velocities, and tube wave studies.

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A strategy for nonlinear elastic inversion of seismic reflection data

Geophysics ◽

10.1190/1.1442046 ◽

1986 ◽

Vol 51 (10) ◽

pp. 1893-1903 ◽

Cited By ~ 561

Author(s):

Albert Tarantola

Keyword(s):

Wave Velocity ◽

Seismic Reflection ◽

Wave Impedance ◽

P Wave ◽

S Wave ◽

Seismic Reflection Data ◽

S Waves ◽

Wave Velocities ◽

Reflection Data ◽

P Wave Velocity

The problem of interpretation of seismic reflection data can be posed with sufficient generality using the concepts of inverse theory. In its roughest formulation, the inverse problem consists of obtaining the Earth model for which the predicted data best fit the observed data. If an adequate forward model is used, this best model will give the best images of the Earth’s interior. Three parameters are needed for describing a perfectly elastic, isotropic, Earth: the density ρ(x) and the Lamé parameters λ(x) and μ(x), or the density ρ(x) and the P-wave and S-wave velocities α(x) and β(x). The choice of parameters is not neutral, in the sense that although theoretically equivalent, if they are not adequately chosen the numerical algorithms in the inversion can be inefficient. In the long (spatial) wavelengths of the model, adequate parameters are the P-wave and S-wave velocities, while in the short (spatial) wavelengths, P-wave impedance, S-wave impedance, and density are adequate. The problem of inversion of waveforms is highly nonlinear for the long wavelengths of the velocities, while it is reasonably linear for the short wavelengths of the impedances and density. Furthermore, this parameterization defines a highly hierarchical problem: the long wavelengths of the P-wave velocity and short wavelengths of the P-wave impedance are much more important parameters than their counterparts for S-waves (in terms of interpreting observed amplitudes), and the latter are much more important than the density. This suggests solving the general inverse problem (which must involve all the parameters) by first optimizing for the P-wave velocity and impedance, then optimizing for the S-wave velocity and impedance, and finally optimizing for density. The first part of the problem of obtaining the long wavelengths of the P-wave velocity and the short wavelengths of the P-wave impedance is similar to the problem solved by present industrial practice (for accurate data interpretation through velocity analysis and “prestack migration”). In fact, the method proposed here produces (as a byproduct) a generalization to the elastic case of the equations of “prestack acoustic migration.” Once an adequate model of the long wavelengths of the P-wave velocity and of the short wavelengths of the P-wave impedance has been obtained, the data residuals should essentially contain information on S-waves (essentially P-S and S-P converted waves). Once the corresponding model of S-wave velocity (long wavelengths) and S-wave impedance (short wavelengths) has been obtained, and if the remaining residuals still contain information, an optimization for density should be performed (the short wavelengths of impedances do not give independent information on density and velocity independently). Because the problem is nonlinear, the whole process should be iterated to convergence; however, the information from each parameter should be independent enough for an interesting first solution.

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Impact of change in pore-fill material on P-wave velocity

Geophysics ◽

10.1190/geo2014-0160.1 ◽

2014 ◽

Vol 79 (6) ◽

pp. D399-D407 ◽

Cited By ~ 12

Author(s):

Nishank Saxena ◽

Gary Mavko

Keyword(s):

Shear Modulus ◽

Wave Velocity ◽

P Wave ◽

Exact Equation ◽

Fluid Substitution ◽

Seismic Velocities ◽

S Wave ◽

Wave Velocities ◽

Fill Material ◽

P Wave Velocity

The problem of predicting the change in seismic velocities (P-wave and S-wave) upon the change in pore-fill material properties is commonly known as substitution. For isotropic rocks, P- and S-wave velocities are fundamentally linked to the effective P-wave and shear moduli. The change in the S-wave velocity or shear modulus upon fluid substitution can be predicted with Gassmann’s equations starting only with the initial S-wave velocity. However, predicting changes in P-wave velocity or the P-wave modulus requires knowledge of the initial P- and S-wave velocities. We initiated a rigorous derivation of the P-wave modulus for fluid and solid substitution in monomineralic isotropic rocks for cases in which an estimate of the S-wave velocity or shear modulus is not available. For the general case of solid substitution, the exact equation for the P-wave modulus depends on parameters that are usually unknown. However, for fluid substitution, fewer parameters are required. As Poisson’s ratio increases for the mineral in the rock frame, the dependence of exact substitution on these unknown parameters decreases. As a result, in the absence of shear velocity, P-wave modulus fluid substitution can, for example, be performed with higher confidence for rocks with a calcite or dolomite frame than it can for rocks with quartz frame. We evaluated a recipe for applying the new P-wave modulus fluid substitution. This improves on existing work and is recommended for practice.

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Improved estimation method for dynamic bulk moduli of sandstones subjected to hydrostatic stress.

10.5194/egusphere-egu21-3588 ◽

2021 ◽

Author(s):

Nazanin Nourifard ◽

Elena Pasternak ◽

Maxim Lebedev

Keyword(s):

Hydrostatic Pressure ◽

Wave Velocity ◽

Hydrostatic Stress ◽

Estimation Method ◽

P Wave ◽

S Wave ◽

Dynamic Moduli ◽

Fixed Rate ◽

Wave Velocities ◽

P Wave Velocity

We designed and modified an experimental method to simultaneously measure the stress-strain (static moduli) and stress dependence of S and P-wave velocities of rocks (sandstone) under hydrostatic pressure by a Hoek&#8217;s cell. Dynamic moduli were calculated from the direct measurement of ultrasonic P- and S-wave velocities at a central dominant frequency of 1 MHz, while static moduli was recorded by strain gauges. The hydrostatic pressure was applied with a fixed rate at 1MPa/minute. We observed that the dynamic bulk moduli can be up to 44% higher than the static moduli in sandstones with porosity ranging from 8% to 24%. The results are in agreement with the existing empirical equations for soft rocks. Our experimental results demonstrate that the dynamic bulk&#8217;s modulus ranges from 4-13GPa, while the static bulk modulus ranges from 2-11GPa. We measured dynamic Young&#8217;s modulus and Poisson&#8217;s ratio at four different time periods (before applying the stress, right after the unloading, 20 days, and 60 days after the experiment) to investigate the effect of time on stress relaxation and eventually on the properties of the sandstones. All the samples showed an increase of Young&#8217;s modulus right after the stress application and then a gradual decrease of this value over time because of this relaxation; however, most of the samples could not reach the original state due to irreversible deformation at micro-level. Dynamic moduli show greater sensitivity to the irreversible deformations as compared to static moduli (even within the elastic limits). Dynamic moduli of porous material are also more sensitive to the microstructure than the static ones. Independent P and S-wave measurement for this study showed that the estimation of the S-wave velocity from the recorded P-wave velocity is not an accurate procedure and introduces a big error in the final calculation of the dynamic moduli. It also confirmed that by registering an accurate P-wave velocity the UCS (Unconfined Compressive Strength) value can be accurately estimated for sandstones. This demonstrates the great potential of dynamic studies as a non-destructive method to estimate this value for porous materials.

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Seismic velocities in transversely isotropic media, II

Geophysics ◽

10.1190/1.1441039 ◽

1980 ◽

Vol 45 (1) ◽

pp. 3-17 ◽

Cited By ~ 18

Author(s):

Franklyn K. Levin

Keyword(s):

Wave Velocity ◽

Transversely Isotropic ◽

P Wave ◽

Seismic Velocities ◽

Sh Wave ◽

S Wave ◽

Wave Velocities ◽

P Wave Velocity ◽

Surface Spread ◽

Isotropic Solids

P‐wave, SV‐wave, and SH‐wave velocities are computed for transversely isotropic solids formed from two isotropic solids. The combinations are shale‐sandstone and shale‐limestone solids of an earlier paper (Levin, 1979), but one velocity of the nonshale component is allowed to vary over the range of Poisson’s ratios σ = 0 to σ = 0.45, i.e., from a rigid solid to a near‐liquid. When the S‐wave velocity of either the sandstone or limestone is varied, the ratio of horizontal P‐wave velocity to vertical P‐wave velocity goes through a maximum as σ increases and subsequently falls to values less than unity as σ approaches 0.5. The P‐wave velocity that would be found with a short surface spread also goes through a maximum and, at σ = 0.5, is less than the P‐wave velocity of either isotropic component. SV‐wave velocities found for data from a short spread are unreasonably large; SH‐wave velocities decrease monotonically as σ increases, but the ratio of horizontal SH‐wave velocity to vertical SH‐wave velocity goes through a minimum of unity.

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