Comparison of P‐ and S‐wave velocities and Q’S from VSP and sonic log data

Geophysics ◽  
1994 ◽  
Vol 59 (10) ◽  
pp. 1512-1529 ◽  
Author(s):  
Gopa S. De ◽  
Donald F. Winterstein ◽  
Mark A. Meadows
Keyword(s):  
Velocity Dispersion ◽  
P Wave ◽  
S Wave ◽  
S Waves ◽  
Wave Velocities ◽  
Sonic Log ◽  
Transit Times ◽  
Wave Slope ◽  
Northern Alberta ◽  
Q Values

We compared P‐ and S‐wave velocities and quality factors (Q’S) from vertical seismic profiling (VSP) and sonic log measurements in five wells, three from the southwest San Joaquin Basin of California, one from near Laredo, Texas, and one from northern Alberta. Our purpose was to investigate the bias between sonic log and VSP velocities and to examine to what degree this bias might be a consequence of dispersion. VSPs and sonic logs were recorded in the same well in every case. Subsurface formations were predominantly clastic. The bias found was that VSP transit times were greater than sonic log times, consistent with normal dispersion. For the San Joaquin wells, differences in S‐wave transit times averaged 1–2 percent, while differences in P‐wave transit times averaged 6–7 percent. For the Alberta well, the situation was reversed, with differences in S‐wave transit times being about 6 percent, while those for P‐waves were 2.5 percent. For the Texas well, the differences averaged about 4 percent for both P‐ and S‐waves. Drift‐curve slopes for S‐waves tended to be low where the P‐wave slopes were high and vice versa. S‐wave drift‐curve slopes in the shallow California wells were 5–10 μs/ft (16–33 μs/m) and the P‐wave slopes were 15–30 μs/ft (49–98 μs/m). The S‐wave slope in sandstones in the northern Alberta well was up to 50 μs/ft (164 μs/m), while the P‐wave slope was about 5 μs/ft (16 μs/m). In the northern Alberta well the slopes for both P‐ and S‐waves flattened in the carbonate. In the Texas well, both P‐ and S‐wave drifts were comparable. We calculated (Q’s) from a velocity dispersion formula and from spectral ratios. When the two Q’s agreed, we concluded that velocity dispersion resulted solely from absorption. These Q estimation methods were reliable only for Q values smaller than 20. We found that, even with data of generally outstanding quality, Q values determined by standard methods can have large uncertainties, and negative Q’s may be common.

Velocity anisotropy in shale determined from crosshole seismic and vertical seismic profile data

Geophysics ◽  
1990 ◽  
Vol 55 (4) ◽  
pp. 470-479 ◽  
Author(s):  
D. F. Winterstein ◽  
B. N. P. Paulsson
Keyword(s):  
Seismic Profile ◽  
P Wave ◽  
Isotropic Model ◽  
S Wave ◽  
Vertical Seismic Profile ◽  
Near Surface ◽  
S Waves ◽  
Velocity Anisotropy ◽  
Wave Velocities ◽  
Late Tertiary

Crosshole and vertical seismic profile (VST) data made possible accurate characterization of the elastic properties, including noticeable velocity anisotropy, of a near‐surface late Tertiary shale formation. Shear‐wave splitting was obvious in both crosshole and VSP data. In crosshole data, two orthologonally polarrized shear (S) waves arrived 19 ms in the uppermost 246 ft (75 m). Vertically traveling S waves of the VSP separated about 10 ms in the uppermost 300 ft (90 m) but remained at nearly constant separation below that level. A transversely isotropic model, which incorporates a rapid increase in S-wave velocities with depth but slow increase in P-wave velocities, closely fits the data over most of the measured interval. Elastic constants of the transvesely isotropic model show spherical P- and [Formula: see text]wave velocity surfaces but an ellipsoidal [Formula: see text]wave surface with a ratio of major to minor axes of 1.15. The magnitude of this S-wave anisotropy is consistent with and lends credence to S-wave anisotropy magnitudes deduced less directly from data of many sedimentary basins.

Separation and enhancement of split S‐waves on multicomponent shot records from the BIRPS WISPA experiment

Geophysics ◽  
1994 ◽  
Vol 59 (1) ◽  
pp. 131-139 ◽  
Author(s):  
M. Boulfoul ◽  
D. R. Watts
Keyword(s):  
Synthetic Data ◽  
P Wave ◽  
Moving Window ◽  
Wave Analysis ◽  
S Wave ◽  
Near Surface ◽  
S Waves ◽  
Wave Velocities ◽  
Wave Splitting ◽  
Explosive Source

Instantaneous rotations are combined with f-k filtering to extract coherent S‐wave events from multicomponent shot records recorded by British Institutions Reflection Profiling Syndicate (BIRPS) Weardale Integrated S‐wave and P‐wave analysis (WISPA) experiment. This experiment was an attempt to measure the Poisson’s ratio of the lower crest by measuring P‐wave and S‐wave velocities. The multihole explosive source technique did generate S‐waves although not of opposite polarization. Attempts to produce stacks of the S‐wave data are unsuccessful because S‐wave splitting in the near surface produced random polarizations from receiver group to receiver group. The delay between the split wavelets varies but is commonly between 20 to 40 ms for 10 Hz wavelets. Dix hyperbola are produced on shot records after instantaneous rotations are followed by f-k filtering. To extract the instantaneous polarization, the traces are shifted back by the length of a moving window over which the calculation is performed. The instantaneous polarization direction is computed from the shifted data using the maximum eigenvector of the covariance matrix over the computation window. Split S‐waves are separated by the instantaneous rotation of the unshifted traces to the directions of the maximum eigenvectors determined for each position of the moving window. F-K filtering is required because of the presence of mode converted S‐waves and S‐waves produced by the explosive source near the time of detonation. Examples from synthetic data show that the method of instantaneous rotations will completely separate split S‐waves if the length of the moving window over which the calculation is performed is the length of the combined split wavelets. Separation may be achieved on synthetic data for wavelet delays as small as two sample intervals.

A strategy for nonlinear elastic inversion of seismic reflection data

Geophysics ◽  
1986 ◽  
Vol 51 (10) ◽  
pp. 1893-1903 ◽  
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.

Processing, correlating, and interpreting converted shear waves from borehole data in southern Alberta

Geophysics ◽  
1990 ◽  
Vol 55 (6) ◽  
pp. 660-669 ◽  
Author(s):  
W. T. Geis ◽  
R. R. Stewart ◽  
M. J. Jones ◽  
P. E. Katapodis
Keyword(s):  
P Wave ◽  
Equation Modeling ◽  
S Wave ◽  
Borehole Data ◽  
P Waves ◽  
S Waves ◽  
Sonic Log ◽  
Lake Formation ◽  
Southern Alberta ◽  
The Time Domain

Borehole measurements coupled with phase information from Zoeppritz equation modeling has assisted in accurate correlation between a VSP converted S-wave section and both the surface and VSP P-wave sections from southern Alberta. For the most part, both the character and polarities of the sections agree; however, there are some differences. Some reflections are stronger and more distinct on the S-wave section than on the P-wave section. Spectral analysis of the time‐domain upgoing P-wave and S-wave energy shows that the frequency content of the S-waves is comparable to the P-waves. Thus, the slower velocity S-waves have a shorter wavelenght and provide better vertical resolution of some interfaces. Other upgoing S-wave modes can interfere with the P‐SV mode and contribute to the differences between the P- and S-wave sections. The match between P-wave and S-wave velocities ([Formula: see text] and [Formula: see text]), determined from VSP traveltime inversion and the full‐waveform sonic log, is best in the Paleozoic carbonate section; there is some discrepancy in Cretaceous sandstone intervals. A basal salt unit in the Paleozoic Beaverhill Lake formation has a VSP‐determined [Formula: see text] ratio of 1.97, suggesting that salt can be distinguished from carbonates using both P-wave and S-wave velocity information in this region.

The relation between seismic P‐ and S‐wave velocity dispersion in saturated rocks

Geophysics ◽  
1994 ◽  
Vol 59 (1) ◽  
pp. 87-92 ◽  
Author(s):  
Gary Mavko ◽  
Diane Jizba
Keyword(s):  
Wave Velocity ◽  
Large Scale ◽  
Velocity Dispersion ◽  
Seismic Velocity ◽  
Ultrasonic Velocities ◽  
S Wave ◽  
Local Flow ◽  
Wave Velocities ◽  
Shear Compliance

Seismic velocity dispersionin fluid-saturated rocks appears to be dominated by tow mecahnisms: the large scale mechanism modeled by Biot, and the local flow or squirt mecahnism. The tow mechanisms can be distuinguished by the ratio of P-to S-wave dispersions, or more conbeniently, by the ratio of dynamic bulk to shear compliance dispersions derived from the wave velocities. Our formulation suggests that when local flow denominates, the dispersion of the shear compliance will be approximately 4/15 the dispersion of the compressibility. When the Biot mechanism dominates, the constant of proportionality is much smaller. Our examination of ultrasonic velocities from 40 sandstones and granites shows that most, but not all, of the samples were dominated by local flow dispersion, particularly at effective pressures below 40 MPa.

scholarly journals How Nanopores Influence Dry-Frame VP Pressure Sensitivity

2021 ◽  
Vol 9 ◽  
Author(s):  
Rohit Raj ◽  
Priyank Jaiswal ◽  
Yulun Wang ◽  
G. Michael Grammer ◽  
Ralf J. Weger
Keyword(s):  
Fluid Model ◽  
Confining Pressure ◽  
P Wave ◽  
Pore Shape ◽  
Pressure Sensitivity ◽  
S Wave ◽  
Shape Distribution ◽  
Transit Times ◽  
Three Samples ◽  
The Individual

This paper investigates how nanopore size distribution influences dry-frame P-wave velocity (VP) pressure sensitivity. The study uses a set of twenty-three samples belonging to a single vertical core from the Mississippian-age Meramec formation of the mid-continent US. Individual samples had their facies interpreted, composition estimated, He-gas porosity (ΦHe) determined, and P-wave and S-wave transit times systematically measured for dry core-plugs in a 5–40 MPa loading and unloading cycle. Data from the unloading cycle were linearized in the log scale, and the slope of the best fitting line was considered as a representative of the dry-frame VP pressure sensitivity. A series of photomicrographs from each sample were analyzed using image processing methods to obtain the shape and size of the individual pores, which were mostly in the nanopore (10−6–10–9 m) scale. At the outset, the pore-shape distribution plots were used to identify and discard samples with excessive cracks and complex pores. When the remaining samples were compared, it was found that within the same facies and pore-shape distribution subgroups VP pressure sensitivity increased as the dominant pore-size became smaller. This was largely independent of ΦHe and composition. The paper postulates that at the nanopore scale in the Meramec formation, pores are mostly isolated, and an increase in the confining pressure increased the bulk moduli of the fluids in the isolated pores, which in turn increased the VP pressure sensitivity. The study proposes incorporating this effect quantitatively through a dual-fluid model where the part of the fluid in unconnected pores is considered compressible while the remaining is considered incompressible. Results start to explain the universal observation of why the presence of microporosity quintessentially enhances VP pressure sensitivity.

Numerical simulation of azimuthal acoustic logging in a borehole penetrating a rock formation boundary

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. D283-D291 ◽  
Author(s):  
Peng Liu ◽  
Wenxiao Qiao ◽  
Xiaohua Che ◽  
Xiaodong Ju ◽  
Junqiang Lu ◽  
...  
Keyword(s):  
Domain Model ◽  
P Wave ◽  
S Wave ◽  
Angle Variation ◽  
P Waves ◽  
Acoustic Logging ◽  
S Waves ◽  
Rock Formation ◽  
Logging Tool ◽  
Difference Time

We have developed a new 3D acoustic logging tool (3DAC). To examine the azimuthal resolution of 3DAC, we have evaluated a 3D finite-difference time-domain model to simulate a case in which the borehole penetrated a rock formation boundary when the tool worked at the azimuthal-transmitting-azimuthal-receiving mode. The results indicated that there were two types of P-waves with different slowness in waveforms: the P-wave of the harder rock (P1) and the P-wave of the softer rock (P2). The P1-wave can be observed in each azimuthal receiver, but the P2-wave appears only in the azimuthal receivers toward the softer rock. When these two types of rock are both fast formations, two types of S-waves also exist, and they have better azimuthal sensitivity compared with P-waves. The S-wave of the harder rock (S1) appears only in receivers toward the harder rock, and the S-wave of the softer rock (S2) appears only in receivers toward the softer rock. A model was simulated in which the boundary between shale and sand penetrated the borehole but not the borehole axis. The P-wave of shale and the S-wave of sand are azimuthally sensitive to the azimuth angle variation of two formations. In addition, waveforms obtained from 3DAC working at the monopole-transmitting-azimuthal-receiving mode indicate that the corresponding P-waves and S-waves are azimuthally sensitive, too. Finally, we have developed a field example of 3DAC to support our simulation results: The azimuthal variation of the P-wave slowness was observed and can thus be used to reflect the azimuthal heterogeneity of formations.

Shallow velocity structure and poisson's ratio at the Tarzana, California, strong-motion accelerometer site

1996 ◽  
Vol 86 (6) ◽  
pp. 1704-1713 ◽  
Author(s):  
R. D. Catchings ◽  
W. H. K. Lee
Keyword(s):  
Urban Areas ◽  
Velocity Structure ◽  
Strong Motion ◽  
P Wave ◽  
S Wave ◽  
Near Surface ◽  
Velocity Models ◽  
Wave Velocities ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

Abstract The 17 January 1994, Northridge, California, earthquake produced strong ground shaking at the Cedar Hills Nursery (referred to here as the Tarzana site) within the city of Tarzana, California, approximately 6 km from the epicenter of the mainshock. Although the Tarzana site is on a hill and is a rock site, accelerations of approximately 1.78 g horizontally and 1.2 g vertically at the Tarzana site are among the highest ever instrumentally recorded for an earthquake. To investigate possible site effects at the Tarzana site, we used explosive-source seismic refraction data to determine the shallow (<70 m) P-and S-wave velocity structure. Our seismic velocity models for the Tarzana site indicate that the local velocity structure may have contributed significantly to the observed shaking. P-wave velocities range from 0.9 to 1.65 km/sec, and S-wave velocities range from 0.20 and 0.6 km/sec for the upper 70 m. We also found evidence for a local S-wave low-velocity zone (LVZ) beneath the top of the hill. The LVZ underlies a CDMG strong-motion recording site at depths between 25 and 60 m below ground surface (BGS). Our velocity model is consistent with the near-surface (<30 m) P- and S-wave velocities and Poisson's ratios measured in a nearby (<30 m) borehole. High Poisson's ratios (0.477 to 0.494) and S-wave attenuation within the LVZ suggest that the LVZ may be composed of highly saturated shales of the Modelo Formation. Because the lateral dimensions of the LVZ approximately correspond to the areas of strongest shaking, we suggest that the highly saturated zone may have contributed to localized strong shaking. Rock sites are generally considered to be ideal locations for site response in urban areas; however, localized, highly saturated rock sites may be a hazard in urban areas that requires further investigation.

Green's function of the Lord–Shulman thermo-poroelasticity theory

2020 ◽  
Vol 221 (3) ◽  
pp. 1765-1776 ◽  
Author(s):  
Jia Wei ◽  
Li-Yun Fu ◽  
Zhi-Wei Wang ◽  
Jing Ba ◽  
José M Carcione
Keyword(s):  
Plane Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Heterogeneous Media ◽  
Numerical Algorithms ◽  
Heat Diffusion ◽  
P Wave ◽  
Wave Analysis ◽  
S Wave ◽  
S Waves

SUMMARY The Lord–Shulman thermoelasticity theory combined with Biot equations of poroelasticity, describes wave dissipation due to fluid and heat flow. This theory avoids an unphysical behaviour of the thermoelastic waves present in the classical theory based on a parabolic heat equation, that is infinite velocity. A plane-wave analysis predicts four propagation modes: the classical P and S waves and two slow waves, namely, the Biot and thermal modes. We obtain the frequency-domain Green's function in homogeneous media as the displacements-temperature solution of the thermo-poroelasticity equations. The numerical examples validate the presence of the wave modes predicted by the plane-wave analysis. The S wave is not affected by heat diffusion, whereas the P wave shows an anelastic behaviour, and the slow modes present a diffusive behaviour depending on the viscosity, frequency and thermoelasticity properties. In heterogeneous media, the P wave undergoes mesoscopic attenuation through energy conversion to the slow modes. The Green's function is useful to study the physics in thermoelastic media and test numerical algorithms.

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