Seismic velocities in transversely isotropic media, II

Geophysics ◽  
1980 ◽  
Vol 45 (1) ◽  
pp. 3-17 ◽  
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.

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

1982 ◽  
Vol 19 (8) ◽  
pp. 1535-1547 ◽  
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.

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

Geophysics ◽  
2014 ◽  
Vol 79 (6) ◽  
pp. D399-D407 ◽  
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.

Seismic velocities in transversely isotropic media

Geophysics ◽  
1979 ◽  
Vol 44 (5) ◽  
pp. 918-936 ◽  
Author(s):  
Franklyn K. Levin
Keyword(s):  
Physical Properties ◽  
Wave Velocity ◽  
Transversely Isotropic ◽  
P Wave ◽  
Seismic Velocities ◽  
Sh Wave ◽  
Near Surface ◽  
P Wave Velocity ◽  
Unconsolidated Material ◽  
Two Component

When a sedimentary earth section is layered on a scale much finer than the wavelength of seismic waves, the waves average the physical properties of the layers; a seismic wave acts as if it were traveling in a single, transversely isotropic solid. We compute the velocities with which P‐waves, SV‐waves, and SH‐waves travel in transversely isotropic solids formed from two‐component solids and find the corresponding moveout velocities from [Formula: see text] plots. The combinations studied are sandstone and shale, shale and limestone, water sand and gas sand, and gypsum and unconsolidated material, one set of typical physical properties being selected for each component of a combination. A reflector at 1524 m and a geophone spread of 0–3048 m are assumed. The moveout velocity for an SH‐wave is always the velocity for a wave traveling in the horizontal direction. The P‐wave moveout velocity found from surface seismic data can be anywhere from the vertical P‐wave velocity to values between those for vertical and horizontal travel; the actual value depends on the elastic parameters and the spread length used for velocity determination. If the two components of the solid have the same Poisson’s ratio, the velocity from surface‐recorded data is the vertical P‐wave velocity. For this case, SH‐wave anisotropy can be computed. SV‐wave data usually do not have hyperbolic time‐distance curves, and the moveout velocity found varies with spread length. Surprisingly, the water sand‐gas sand combination gives a medium with negligible anistropy. A two‐component combination of gypsum in weathered material gives rise to [Formula: see text] plots that seem to explain the unusual behavior of near‐surface SV‐waves seen in field studies reported by Jolly (1956).

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

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. E59-E68 ◽  
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.

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

Geophysics ◽  
2002 ◽  
Vol 67 (2) ◽  
pp. 405-412 ◽  
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.

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

2020 ◽  
pp. 1-62 ◽  
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.

The effects of transverse isotropy on reflection amplitude versus offset

Geophysics ◽  
1987 ◽  
Vol 52 (4) ◽  
pp. 564-567 ◽  
Author(s):  
J. Wright
Keyword(s):  
Wave Velocity ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
S Wave ◽  
Reflection Amplitude ◽  
Amplitude Versus Offset ◽  
Transversely Isotropic Media ◽  
P Wave Velocity ◽  
Isotropic Media

Studies have shown that elastic properties of materials such as shale and chalk are anisotropic. With the increasing emphasis on extraction of lithology and fluid content from changes in reflection amplitude with shot‐to‐group offset, one needs to know the effects of anisotropy on reflectivity. Since anisotropy means that velocity depends upon the direction of propagation, this angular dependence of velocity is expected to influence reflectivity changes with offset. These effects might be particularly evident in deltaic sand‐shale sequences since measurements have shown that the P-wave velocity of shales in the horizontal direction can be 20 percent higher than the vertical P-wave velocity. To investigate this behavior, a computer program was written to find the P- and S-wave reflectivities at an interface between two transversely isotropic media with the axis of symmetry perpendicular to the interface. Models for shale‐chalk and shale‐sand P-wave reflectivities were analyzed.

Experimental study of fracture size effect on elastic-wave velocity dispersion and anisotropy

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. C49-C59 ◽  
Author(s):  
Da Shuai ◽  
Jianxin Wei ◽  
Bangrang Di ◽  
Sanyi Yuan ◽  
Jianyong Xie ◽  
...  
Keyword(s):  
Wave Velocity ◽  
Seismic Velocity ◽  
Effective Medium Theory ◽  
Transversely Isotropic ◽  
Elastic Wave Velocity ◽  
P Wave ◽  
S Wave ◽  
P Wave Velocity ◽  
Fracture Size ◽  
Good Agreement

We have designed transversely isotropic models containing penny-shaped rubber inclusions, with the crack diameters ranging from 2.5 to 6.2 mm to study the influence of fracture size on seismic velocity under controlled conditions. Three pairs of transducers with different frequencies (0.5, 0.25, and 0.1 MHz) are used for P- and S-wave ultrasonic sounding, respectively. The P-wave measurements indicate that the scattering effect is dominant when the waves propagate perpendicular to the fractures. Our experimental results demonstrate that when the wavelength-to-crack-diameter ratio ([Formula: see text]) is larger than 14, the P-wave velocity can be described predominantly by the effective medium theory. Although the ratio is larger than four, the S-wave velocity is close to the equivalent medium results. When [Formula: see text] < 14 or [Formula: see text] is < 4, the elastic velocity is dominated by scattering. The magnitudes of the Thomsen anisotropic parameters [Formula: see text] and [Formula: see text] are scale and frequency dependent on the assumption that the transversely isotropic models are vertical transversely isotropic medium. Furthermore, we compare the experimental velocities with the Hudson theory. The results illustrate that there is a good agreement between the observed P-wave velocity and the Hudson theory when [Formula: see text] > 7 in the directions parallel and perpendicular to the fractures. For small fracture diameters, however, the P-wave velocity perpendicular to the fractures predicted from the Hudson theory is not accurate. When [Formula: see text] < 4, there is good agreement between the experimental fast S-wave velocity and the Hudson theory, whereas the experimental slow S-wave velocity diverges with the Hudson theory. When [Formula: see text] > 4, the deviation of fast and slow S-wave velocities with the Hudson prediction is stable.

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

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

&lt;p&gt;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.&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;

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

Geophysics ◽  
1999 ◽  
Vol 64 (2) ◽  
pp. 504-507 ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document