S Waves Research Articles

Characterization of fractured reservoir using offset VSPs: case study from the Varandei Field, Northern Russia

Anatoli A. Tikhonov (PetroAlliance), Ludmila A. Plekhodkina (Lukoil), and Enru Liu (British Geological Survey) in this technical article describe a method for the delineation of fracture-induced azimuthal anisotropic intervals in the subsurface supported by a case study with Russian data. Traditional seismic techniques of examining fracture-induced seismic anisotropy in a borehole utilize either walkaround observations of direct compressional waves (Horne 2003; Horne et al., 2002; Thompson et al., 2002), observations of vertical shear-waves with different polarizations (Brodov et al., 1991, Liu, Crampin and Queen, 1991; Winterstein, Ge, and Meadows 2001), or converted PS waves in offset VSP data (Horne et al., 2002). The walkaround VSP data allows the construction of the P-wave velocities (Vp) indicatrix. The observations of vertical shear-waves are based on shear-wave splitting or birefringence measurements. The elastic moduli are usually calculated from the kinematic parameters of seismic waves assuming the model of transversally anisotropic media with a horizontal symmetry axis. For more complicated models (for example, thin-layer section with vertical fractures leading to orthorhombic model) the 3C multi-azimuth, multi-offset VSP is used (Dewangan and Grechka, 2002). Our goal is to extract information about seismic anisotropy due to the vertical fracturing from routinely recorded offset VSP data obtained with non-directional or explosive sources. We attempt to answer the following two questions: (1) Is it possible to control the polarization of converted PS waves in order to obtain pure S1 and S2 modes? and (2), How to remove the influence of offset PS ray paths in order to estimate time delay between S1 and S2 waves? The idea of controlling the polarizations of converted down-going PS waves is based on the use of linear combinations of wavefields recorded along a vertical seismic profile from pairs of nondirectional sources located in different directions (Figure 1). We assume that the shear wave polarizations after P to S mode conversion at a given interface in horizontally layered isotropic media is contained in a vertical ray plane passing through the sources and receivers. The original technique, which uses the rotation of shear-wave polarizations proposed by Brodov et al. (1991), assumes that two different shear modes propagate along the same ray paths. However, surface seismic data use the rotation method to detect the directions of anisotropy symmetry axes using data obtained along different ray paths. This technique assumes that NMO corrections reduce different ray trajectories to the same vertical ray. We use a ray-tracing technique to remove the influence of PS ray geometry on arrival times and to reduce to vertical profile the wavefield registered from offset VSP. The initial kinematic model is built by the inversion of direct P and converted PS wave travel-times. We correct the 2D kinematic model after imaging of depth migrated seismic section.

Acoustic axes in weak triclinic anisotropy

SUMMARY Acoustic axes can exist even under an infinitesimally weak anisotropy, and occur when slowness surfaces of the S1 and S2 waves touch or intersect. The maximum number of isolated acoustic axes in weak triclinic anisotropy is 16 as in strong triclinic anisotropy. The directions of acoustic axes are calculated by solving two coupled polynomial equations in two variables. The order of the equations is 6 under strong anisotropy and reduces to 5 under weak anisotropy. The weak anisotropy approximation is particularly useful, when calculating the acoustic axes under extremely weak anisotropy with anisotropy strength less than 0.1 per cent because the equations valid for strong anisotropy might become numerically unstable and their modification, which stabilizes them, is complicated. The weak anisotropy approximation can also find applications in inversions for anisotropy from the directions of acoustic axes.

The Pragmatic Wave Equations and Their Potential Equations of a Saturated Porous Micropolar Medium

Soil is a porous medium made of rigid grains in the microscale and has an obvious grain behavior. It becomes a saturated soil when the pores between soil grains are filled with water or oil. When the porous solid skeleton is approximately taken as a micropolar medium and the fluid in the pores a point medium, the elastic pragmatic wave equations in a saturated porous micropolar medium are obtained from the results of the micropolar theory and those of Biot's pragmatic wave theory. Since the relations between the parameters of the saturated porous micropolar theory and those of the corresponding one-phase medium are obtained by means of the Greetsma theory, it has merits that the physics parameters in our dynamic equations of the saturated porous micropolar medium have a definite physics meaning and are easy to be tested in the laboratory. The dynamical equations are then simplified as the potential equations with the aid of the field theory and the dispersion equations of five elastic waves propagating in the saturated porous micropolar medium are established. Finally, the propagating characteristics of the five harmonic body waves in the saturated micropolar porous medium are investigated by the numerical methods. It is shown from the results that the dispersion curves of the velocities of P1 wave, P2 wave and shear S1 wave are similar to those in the classical saturated porous medium. When frequency is lower than the critical frequency w0, the rotation longitudinal θ wave and the rotation transverse S2 wave do not exist. When the frequency is greater than the critical frequency w0, θ wave and S2 wave both arise and their velocities decrease when frequency increases.

Strain‐induced seismic anisotropy of wadsleyite polycrystals and flow patterns in the mantle transition zone

We use forward models based on recent high‐pressure experimental data on mantle minerals to predict the seismic anisotropy produced by plastic strain of orthorhombic wadsleyite, the dominant mineral in the upper transition zone. These models predict a weak seismic anisotropy for a polycrystal of pyrolitic composition (60% wadsleyite, 40% garnet) at transition zone conditions: ∼2% for P and ∼1% for S waves for a shear strain of 1. Both P and S wave anisotropy patterns show an orthorhombic symmetry. P waves propagate faster at low angle to the shear direction and slower at high angle to the shear plane. S wave anisotropy is characterized by faster propagation of waves polarized at low angle to the shear direction. Horizontal shearing results therefore in higher velocities for horizontally propagating P waves (PH) and horizontally polarized S waves (SH), as well as in weak azimuthal variation of SV and SH velocities. On the other hand, vertical flow leads to higher velocities for vertically propagating P waves (PV) and vertically polarized S waves (SV) and to a weak azimuthal variation of SV velocity but to a roughly constant SH velocity. Analysis of global observations of seismic anisotropy in the transition zone in the light of these models supports dominant horizontal flow in the uppermost transition zone, in agreement with predictions of geodynamical models that explicitly introduce phase transitions.

Ambiguous Moment Tensors and Radiation Patterns in Anisotropic Media with Applications to the Modeling of Earthquake Mechanisms in W-Bohemia

Anisotropic material properties are usually neglected during inversions for source parameters of earthquakes. In general anisotropic media, however, moment tensors for pure-shear sources can exhibit significant non-double-couple components. Such effects may be erroneously interpreted as an indication for volumetric changes at the source. Here we investigate effects of anisotropy on seismic moment tensors and radiation patterns for pure-shear and tensile-type sources. Anisotropy can significantly influence the interpretation of the source mechanisms. For example, the orientation of the slip within the fault plane may affect the total seismic moment. Also, moment tensors due to pure-shear and tensile faulting can have similar characteristics depending on the orientation of the elastic tensor. Furthermore, the tensile nature of an earthquake can be obscured by near-source anisotropic properties. As an application, we consider effects of inhomogeneous anisotropic properties on the seismic moment tensor and the radiation patterns of a selected type of micro-earthquakes observed in W-Bohemia. The combined effects of near-source and along-path anisotropy cause characteristic amplitude distortions of the P, S1 and S2 waves. However, the modeling suggests that neither homogeneous nor inhomogeneous anisotropic properties alone can explain the observed large non-double-couple components.

Parabolic lines and caustics in homogeneous weakly anisotropic solids

The form of parabolic lines and caustics in homogeneous generally anisotropic solids can be very complicated, but simplifies considerably in homogeneous weakly anisotropic solids. Assuming sufficiently weak anisotropy, no parabolic lines appear on the S1 slowness sheet. Consequently, the corresponding wave sheet displays no caustics or triplications. Parabolic lines and caustics can appear on the S2 slowness and wave sheets, respectively, but only in directions close to conical or wedge singularities. Each conical and wedge singularity generates parabolic lines, caustics and anticaustics in its vicinity. The parabolic lines cannot touch or pass through a conical singularity, but they touch each wedge singularity. The size of the caustics and anticaustics decreases with decreasing strength of anisotropy. For infinitesimally weak anisotropy, the caustics and anticaustics contract into a single point. No parabolic lines, caustics, anticaustics and triplications can appear in transversely isotropic solids, provided the transverse isotropy is sufficiently weak.

On the effects of a dipping axis of symmetry on shear wave splitting measurements in a transversely isotropic medium

SUMMARY We derive the explicit expressions for the phase velocities and polarizations of quasi-shear waves propagating in a transversely isotropic medium. The normal to the plane defined by the phase normal and the symmetry axis gives the exact polarization of S1, while the polarization of S2 also depends on the elastic parameters of the medium and is thus more complicated. Therefore, we propose that the polarization of the slow S1 wave, instead of the fast S2 wave, as is common practice, should be determined from seismic data. For a dipping fast axis of symmetry, a 360 ◦ periodic variation of the apparent slow axis is predicted, with an amplitude given by arctan(tanθ/tan θ0), where θ is the incidence angle and θ 0 the angle between the symmetry axis and the vertical. For a significant dip of the symmetry axis (larger than 20 ◦ ) and for large incidence angles these variations should be observable in shear wave splitting measurements. This suggests that SKKS, and S waves generated by deep earthquakes, which are characterized by larger incidence angles in comparison to SKS waves, should be able to constrain a possible dip of the symmetry axis. In contrast, constraining the dip of the symmetry axis from the delay times turns out to be much more difficult owing to their complicated (and non-linear) dependence on azimuth and on the elastic parameters.

FES99: A Global Tide Finite Element Solution Assimilating Tide Gauge and Altimetric Information

An improved version of the global hydrodynamic tide solutions [finite element solutions (FESs) FES94, FES95.2.1, and FES98] has been developed, implemented, and validated. The new model is based on the resolution of the tidal barotropic equations on a global finite element grid without any open boundary condition, which leads to solutions independent of in situ data (no open boundary conditions and no assimilation). The accuracy of these ‘‘free’’ solutions is improved by assimilating tide gauge and TOPEX/Poseidon (T/P) altimeter information through a representer assimilation method. This leads to the FES99 version of this model. For the eight main constituents of the tidal spectrum (M 2 ,S 2 ,N 2 ,K 2 ,2 N 2 ,K 1 ,O 1, and Q1), about 700 tide gauges and 687 T/P altimetric measurements are assimilated. An original algorithm is developed to calculate the tidal harmonic constituents at crossover points of the T/P altimeter database. Additional work is performed for the S2 wave by reconsidering the inverse barometer correction. To complete the spectrum, 19 minor constituents have been added by admittance. The accuracy of FES99 is evaluated against the former FESs. First, it is compared to two tide gauge datasets: ST95 (95 open-ocean measurements) and ST739 (739 coastal measurements). For ST95, the root-sum square of the differences between observations and solutions is reduced from 2.8 (FES95.2.1) to 2.4 cm (FES99), a gain of 17% in overall accuracy. Second, the variance of the sea surface variability is calculated and compared for FES95.2.1, FES98, and FES99 at the T/P and the European Remote Sensing Satellite (ERS-2) crossover data points. FES99 performed best, with a residual standard deviation for the independent ERS-2 dataset of 13.5 cm (15.2 cm for FES95.2.1). Third, tidal predictions are implemented for the FESs to provide along-track estimates of the sea surface variability for T/P and ERS-2. Compared to ERS-2, FES99 residuals are 11.8 cm (12.4 cm for FES95.2.1). All the accuracy tests show that FES99 is a significant improvement compared to former FESs both in the deep ocean and along coasts.

Three dimensional simulation of tide and tidal current characteristics in the East China Sea

With the fine horizontal (5ˈ × 5ˈ) and vertical (15 levels) grids, a three-dimensional model, imbedded a closure turbulence sub-model, was used to calculate the barotropic tides and tidal currents in the Bohai Sea, Yellow Sea, and East China Sea. The computational results are in good agreement with the observed M2, S2, K1 and O1 tides in the domain. Comparison with fifty tide gauges showed that the averaged absolute differences between the simulated and observed amplitudes are only 3.95, 2.96, 2.5 and 1.78 cm for the M2, S2, K1 and O1 tidal waves, respectively. The averaged phase-lag differences of the four tides are 6.88, 6.96, 5.96 and 6.16°. The model reproduces well the tidal charts and this characteristic is discussed in detail. Comparison with 13 current stations, gave averaged absolute deviations between the calculated and observed harmonic constant of the eastern and northern tidal current of 〚6.53, 20.4, 7.55, 24.9〛; 〚3.24, 24.2, 2.89, 22.8〛; 〚2.98, 22.4, 3.6, 25.9〛; 〚2.39, 35.8, 2.01 cm s –1, 22.6°〛 for M2, S2, K1 and O1, respectively. The calculated structures of the tidal current ellipse in the vertical are in fair agreement with the observations. The surface distributions of the tidal current ellipse in the four tidal systems and the maximum current distributions are discussed in detail.

Effect of barotropic tidal rectification on low‐frequency circulation near the shelf break in the northern Bay of Biscay

Current meter data collected in the Bay of Biscay are used with a barotropic model to study the effect of the tidal rectification on the low‐frequency circulation near the shelf break. Data collected at two different locations are analyzed and show that the tidal forcing terms and the low‐frequency circulation are completely different at the two locations. In order to obtain a quantitative interpretation of these differences, a tidal forcing with both M2 and S2 waves is introduced in a barotropic tidal rectification model. We focus on the rectification process due to the “stretching of the water columns” alone, in the realistic case of large‐amplitude topography. A first theoretical result is that the bichromatic forcing generates a nonlinear variation of the residual current which depends on only one nondimensional parameter. This parameter is a function of the barotropic flow and of the wave frequencies. A second result is that the low‐frequency circulation generated by such a rectification process (including the two waves) is twice as large in spring tide than in neap tide. Finally, the model applied to both moorings confirms that the tidal rectification is much weaker at one mooring, the northwest one, than at the other, where the tidal rectification can explain 50% of the observed low‐frequency circulation.

Internal tides observed at 2°S–156°E by in situ and TOPEX/POSEIDON data during the Coupled Ocean‐Atmosphere Response Experiment (COARE)

During the enhanced monitoring phase of the Coupled Ocean‐Atmosphere Experiment (COARE), semidiurnal baroclinic tides were observed. At 2°S–156°E (1739 m depth) the Tropical Atmosphere‐Ocean (TAO) mooring outfitted with additional sensors from surface to bottom provides an interesting tool for describing the internal tides. M2, S2, and N2 baroclinic components were detected, explaining 59% of the semidiurnal variance on surface dynamic height. At the semidiurnal frequency, vertical displacements of isopycnals, highly variable in time, can reach 30 m and are mostly a combination of the M2, S2, and N2 internal waves. The two first baroclinic modes explain 70% of the variance in vertical displacement. M2 and S2 internal waves have different vertical structure: M2 resembles the first baroclinic mode and S2 resembles the second baroclinic mode. The M2 and S2 internal waves projected on their respective baroclinic mode are highly related to the modeled barotropic tide. Two TOPEX/POSEIDON tracks cross over the mooring every 10 days, and the internal wave signature can be expected in sea level along the tracks despite the weakness of the signal. Sea level spectra along both ascending and descending tracks show the existence of energy around the 250 km and the 120 km wavelength, respectively, which is in accordance with a first baroclinic wave propagating northeastward, as suggested in previous studies. From wavelet transform, the baroclinic tide signatures on the ascending (descending) track are centered around 2.5°S (3.5°S) with a 1° (2°) latitudinal extension, respectively, limited to the Ontong Java Plateau. We confirm the northeastward propagation of the baroclinic tides, and their source could be a series of islands parallel to the Kilinailau Trench or the large sloping topography between the Kilinailau Trench and the Ontong Java Plateau.

Resonance Theory of Elastic Head Waves Propagating in a Solid Layer in Tight Contact With a Thick Solid Base

The boundary value problem of elastic wave propagation in the case of a plane solid layer I in tight contact with a thick solid base II with a monopole sonic source placed in layer I is treated analytically by the standing wave method. Solution in the form of contour integrals with the amplitudes in 2 x 2 matrix form are obtained. An inspection of the solution shows that it contains all well-known component waves except the head waves. Particular interest is put on these latter waves. Three kinds of head waves (P, S, and S1) are obtained. The S1 wave is newly predicted, which propagates with the shear wave velocity of the soft layer I. It may be considered as the candidate for the "late S wave" observed in earthquakes. The resonance frequencies of the three head waves are obtained, and the motion of the free surface is also described for the three cases.

Atmospheric tides in the area of Thessaloniki

The tidal changes of the barometric pressure in the area of Thessaloniki, Greece were investigated by analyzing a sample of 10.75 years of hourly measurements. The tidal analysis showed that the signal-to-noise ratio varies from 16.8 to 1 for the long period waves (Sa, Ssa, Mm, Mf). For the short period constituents, the corresponding quantity was negligible with the exception of the diurnal P1, S1, K1 and semidiurnal waves S2, K2 where values of 14, 93, 15 and 61 and 7 were found respectively. The amplitude and the phase difference of the above tidal waves were determined with an accuracy of 0.008–0.18 hPa and 1–3 ° correspondingly. There is a considerable correlation of the surface temperature to the changes of the pressure affecting mainly the Ssa, S1 and S2 waves. The barometric changes computed in the area of Thessaloniki using the amplitude and phase difference determined through the tidal analysis reach a maximum amplitude equal to 10 hPa per year. It is also shown that the tidal changes of the barometric pressure in the test area correspond to about 37% of the total changes. A Fourier analysis of the daily mean values of the barometric pressure for the last 44 years showed significant amplitudes of the power spectral density (PSD) at the non-tidal periods of 8 and 52.6 days.

Attenuation of P- and S-waves as a method of distinguishing gas and condensate from oil and water : T. Klimentos, Geophysics, 60(2), 1995, pp 447–458

Attenuation of P- and S-waves as a method of distinguishing gas and condensate from oil and water : T. Klimentos, Geophysics, 60(2), 1995, pp 447–458

Backward-wave model of the high-frequency enhancement or quasiresonance in the backscattering from spherical shells.

For certain elastic plates in a vacuum, the group velocity near the mode threshold of a Lamb wave becomes negative and the average power flow is directed opposite the phase velocity. This is known as a backward wave. It is proposed that backward leaky Lamb waves on thin fluid loaded shells contribute to the high-frequency enhancement that has been noted recently by several researchers. Though the ka of that enhancement lies close to that of the longitudinal or thickness resonance, ray models of the internal reverberations do not adequately describe the structure in the form function where the group velocity of the s1 wave can be negative [S. G. Kargl and P. L. Marston, J. Acoust. Soc. Am. 89, 2545–2558 (1991)]. In the backward-ray model a leaky wave with a phase velocity in the clockwise direction propagates energy in the counterclockwise direction. As a result, energy is leaked off toward the source without having circumnavigated the backside of the shell, having propagated an angle of only 2θl on the shell where sin θl=c/cl. The contribution to the backscattering has the approximate magnitude ‖f0,l‖ ≊‖ Gl‖exp (−2θlβl) and only occurs where the radiation damping βl is large. Some discrepancies in previous ray models for thick and thin shells are partially accounted for and a prompt surface ray mechanism for tone burst scattering is evident. [Work supported by ONR.]

Analysis of seismic SV waves in the core's penumbra

Vertically‐polarized S‐waves (SV) attenuate rapidly as they diffract around the Earth's core, whereas horizontally‐polarized S‐waves (SH) propagate to large distances in the core shadow zone. The amplitude decay of diffracted SV signals is so strong that few studies have been made of these phases, despite their acute sensitivity to velocity structure just above the core‐mantle boundary. We analyze SV signals in the penumbra of the core's shadow, finding systematic waveform complexities indicative of local stratification and apparent anisotropy at the base of the mantle, with implications for the dynamic processes in this internal boundary layer.

Motility Effects of Electrical Anterior Sacral Nerve Root Stimulation of the Parasympathetic Supply of the Left Colon and Anorectum in Paraplegic Subjects

The extent and nature of colonic and anorectal motility responses to S2, S3, and S4 anterior nerve root stimulation were studied in seven paraplegic patients with a Brindley electromicturition sacral implant. After sequential S2, S3 and S4 stimulation wave height activity was increased above basal from the transverse colon to the rectum. The mean motility index response to sequential stimulation was greatest at the splenic flexure. The greatest peak wave height and mean motility index response to individual anterior nerve root stimulation was to S3, which could empty the left colon by a distal motility gradient. S4 anterior root stimulation increased the intrarectal pressure and also raised the anal canal pressure to high levels.

S-WAVES IN THE SPECTRA OF CATACLYSMIC BINARIES

S-WAVES IN THE SPECTRA OF CATACLYSMIC BINARIES

Neuronal pathways for the lingual reflex in the Japanese toad.

1. Anuran tongue is controlled by visual stimuli for releasing the prey-catching behavior ('snapping') and also by the intra-oral stimuli for eliciting the lingual reflex. To elucidate the neural mechanisms controlling tongue movements, we analyzed the neuronal pathways from the glossopharyngeal (IX) afferents to the hypoglossal (XII) tongue-muscle motoneurons. 2. Field potentials were recorded from the bulbar dorsal surface over the fasciculus solitarius (fsol) to the electrical stimulation of the ipsilateral IX nerve. They were composed of three successive negative waves: S1, S2 and N wave. The S1 and S2 waves followed successive stimuli applied at short intervals (10 ms or less), whereas the N wave was strongly suppressed at intervals shorter than 500 ms. Furthermore, the S1 wave had lower threshold than the S2 wave. 3. Orthodromic action potentials were intra-axonally recorded from IX afferent fibers in the fsol to the ipsilateral IX nerve stimuli. Two peaks found in the latency distribution histogram of these action potentials well coincided with the negative peaks of the S1 and the S2 waves of the simultaneously recorded field potentials. Therefore, the S1 and S2 waves should represent the compound action potentials of two groups of the IX afferent fibers with different conduction velocities. 4. Ipsilateral IX nerve stimuli elicited excitatory postsynaptic potentials (EPSPs) in the tongue-protractor motoneurons (PMNs) and the tongue-retractor motoneurons (RMNs). Inhibitory postsynaptic potentials were not observed. 5. The EPSPs recorded in PMNs had mean onset latencies of 6.4 ms measured from the negative peaks of the S1 wave. The EPSPs were facilitated when paired submaximal stimuli were applied at intervals shorter than 20 ms, but were suppressed at intervals longer than 30 ms. Furthermore, the EPSPs were spatially facilitated when peripherally split two bundles of the IX nerve were simultaneously stimulated. 6. On the other hand, the EPSPs recorded in RMNs had shorter onset latencies, averaging 2.5 ms. In 14 of 43 RMNs, early and late EPSP components could be reliably discriminated. The thresholds for the early EPSP components were as low as those for the S1 waves, whereas for the late EPSP components the thresholds were usually higher than those for the S2 waves.(ABSTRACT TRUNCATED AT 400 WORDS)

Separation of S‐wave and P‐wave reflections offshore western Florida

Hard water‐bottom marine environments, such as offshore western Florida, have presented particular problems in the acquisition and processing of seismic reflection data. One problem has been the limited angle of incidence (less than critical) available to P‐wave penetration into the subsurface. Mode conversion from P‐wave to S‐waves (SV), however, is quite efficient over a broad range of angles of incidence. After the success of a previously reported physical model experiment, an experimental line was acquired offshore western Florida. The 19 mile line, located approximately 100 miles west of Key West, Florida, was shot and processed. Three key factors have contributed to the successful recording of mode‐converted S‐wave reflections: (1) recognition of the effect of the group length on attenuation of energy arriving at large angles of incidence; (2) tau‐p processing techniques that allow separation of energy by angle of incidence; and (3) velocity filtering over a range of hyperbolic normal‐moveout (NMO) velocities as part of the forward tau‐p transform. These three factors, two of them data processing techniques, have allowed separation of P‐ and S‐wave energy in the marine environment. Overall, S‐wave reflections have been unambiguously identified to a reflection time of 2 sec and may be interpreted to a reflection time of 2 sec. Integrating an S‐wave section with P‐wave interpretations of offshore Florida data allows an independent confirmation of structural events. This independent confirmation may be more significant than improvements in the P‐wave data quality alone. Lateraly stable [Formula: see text] values are computed in intervals 1500 to 5000 ft thick and to S‐wave reflection times as great as 3 sec. The opportunity of [Formula: see text], interpretations for lithologic identification, gas thickness estimates, and general stratigraphic trap exploration makes mode‐converted shear waves a new tool in this area.