On S-wave directivity patterns

Geophysics ◽  
1984 ◽  
Vol 49 (6) ◽  
pp. 822-825 ◽  
Author(s):  
Walter L. Pilant
Keyword(s):  
Free Surface ◽  
Plane Wave ◽  
Three Dimensional ◽  
Complex Numbers ◽  
S Wave ◽  
S Waves ◽  
Time Harmonic ◽  
Source Case ◽  
Directivity Patterns ◽  
Impulsive Source

Plane‐wave directivity patterns for both P- and S-waves approaching a free surface are well known (Knopoff et al., 1957, Figure 3–5). These have been shown to apply in a reciprocal manner to time‐harmonic S-waves emanating from vertical and horizontal sources (Miller and Pursey, 1954; Cherry, 1962) in both two‐dimensional (2-D) and three‐dimensional (3-D) cases. Knopoff and Gilbert (1959) showed that the plane‐wave directivity patterns also apply to the first motions seen in the impulsive‐source case (3-D) and Pilant (1979, sec. 9–6) showed that they held in the equivalent 2-D problem. Theoretical expressions for these patterns are given by Pilant (ibid) as [Formula: see text] and [Formula: see text] where [Formula: see text] is measured from the vertical and the positive z-axis is into the medium. The x-axis lies along the free surface and the quantity [Formula: see text]. For angles greater than critical [Formula: see text], the proper expression for the square root is given by [Formula: see text] Thus for angles of incidence (or take‐off) greater than [Formula: see text], both [Formula: see text] and [Formula: see text] become complex numbers and lead to phase‐shift induced waveform changes as the S-waves interact with the free surface. The functions [Formula: see text] and [Formula: see text] are shown in Figure 1 for the angular range 34–37 degrees which includes the angle [Formula: see text] degrees. For this example, [Formula: see text] corresponding to a Poisson’s ratio equal to one‐quarter. The null in [Formula: see text] and the maximum in [Formula: see text] are clearly seen.

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.

Coupling PSE and FLUENT to Predict Laminar-Turbulent Transition in Boundary Layers

2013 ◽  
Vol 432 ◽  
pp. 168-172
Author(s):  
Y. Zhou ◽  
Y.H. Fang
Keyword(s):  
Flat Plate ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Basic Flow ◽  
Two Dimensional ◽  
S Wave ◽  
S Waves ◽  
Turbulent Transition ◽  
Transition Criterion ◽  
Laminar Turbulent Transition

In this paper, the coupling method of PSE and FLUENT was experimented for predicting the laminar-turbulent transition. The software FLUENT was used to get the basic flow over a flat plate. A two-dimensional T-S wave and a pair of three-dimensional T-S waves were fed in at the entrance. The transition criterion was verified by DNS results. The availability of the coupling methodology has been evaluated.

SP- and SS-imaging for 3D elastic reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. A1-A6 ◽  
Author(s):  
Xufei Gong ◽  
Qizhen Du ◽  
Qiang Zhao
Keyword(s):  
Three Dimensional ◽  
Scalar Wave ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Sh Waves ◽  
S Waves ◽  
Time Migration ◽  
Underlying Principle ◽  
Imaging Conditions

Three-dimensional elastic reverse time migration has been confronted with the problem of generating scalar images with vector S-waves. The underlying principle for solving this problem is to convert the vector S-waves into scalars. Previous methods were mainly focused on PS-imaging, but they usually cannot work properly on SP- and SS-cases. The complexity of SP- and SS-imaging arises from the fact that the incident S-wave has unpredictable relationship with the raypath plane. We have suggested that S-wave should be treated separately as SV- and SH-waves, which keep predictable relationships with the raypath plane. First, the elastic wavefield is separated into P- and S-waves using the Helmholtz decomposition. Then, we evaluate the normal direction of the raypath plane at each imaging grid. Next, we separate the vector S-wave obtained with curl operator into SH- and SV-waves, both of which are scalars. Finally, correlation imaging conditions are implemented to those scalar wave modes to produce scalar SV-P, SV-SV, and SH-SH images.

The present state of seismic data acquisition: One view

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2443-2451 ◽  
Author(s):  
Stanley J. Laster
Keyword(s):  
Data Acquisition ◽  
Seismic Data ◽  
Three Dimensional ◽  
Artificial Satellites ◽  
S Wave ◽  
Positioning Systems ◽  
S Waves ◽  
Exploration And Production ◽  
Seismic Data Acquisition ◽  
Marine Applications

Seismic data acquisition in the mid‐1980s is briefly reviewed. In terms of hardware, the trend has been toward an increased number of data channels in both land and marine applications. This has led to the development of digital telemetry systems. Positioning systems, particularly for marine work, have made use of artificial satellites. The perceived need for S‐wave information has led to development of S‐wave sources such as the horizontal vibrator. S‐waves in a few cases have been used to validate hydrocarbon indicators on seismic records. There has been a distinct trend toward three‐dimensional (3-D) seismic recording, both on land and at sea, and for both exploration and production applications.

Measurement of Q−1 for S waves in mudstone at Chikura, Japan: Comparison of incident and reflected phases in borehole seismograms

1992 ◽  
Vol 82 (1) ◽  
pp. 148-163
Author(s):  
Yoshimitsu Fukushima ◽  
Shigeo Kinoshita ◽  
Haruo Sato
Keyword(s):  
Principal Axis ◽  
Three Dimensional ◽  
Ground Surface ◽  
Head Wave ◽  
S Wave ◽  
Sh Waves ◽  
S Waves ◽  
Confidence Levels ◽  
Kanto Region ◽  
Ray Path

Abstract Seismograms from small events in the southern Kanto region have been recorded by a seismometer installed in a 732-m-deep borehole at Chikura observatory, Japan, where mudstone of early Pliocene age is found from the ground surface to the bottom of the borehole. Strong phases occurring 1.5 ∼ 1.6 sec after the S-wave arrival were interpreted as reflections at the ground surface. Ray path directions of the incident S waves were determined from the minimum principal axis of the three-dimensional trajectory ellipsoid, which represents the particle motion for a head wave of S phase. Transverse horizontal SH components were used to estimate the Q−1 value for S waves. Assuming the free surface acted as an 100% reflector for the SH waves and the incident SH phase as an input and the reflected phase as an output, we calculated system functions. The Q−1 value was measured from the transfer characteristics between the incident and the reflected phases in a single seismogram, thus no corrections were necessary for source or site (including instrument) effects. If we applied a power law model, the following relationship was obtained from the regression analyses of 20 events: log 10 ( Q − 1 ) = ( − 0.52 ± 0.48 ) ⋅ log 10 ( f ) − ( 1.28 ± 0.22 ) ( 1.0 < f < 5.0 Hz ) , where f is frequency in Hz and error values are the 95% confidence levels of the regression coefficients.

Effects of surface corrugation on the stability of a zero-pressure-gradient boundary layer

2014 ◽  
Vol 741 ◽  
pp. 228-251 ◽  
Author(s):  
Mochamad Dady Ma’mun ◽  
Masahito Asai ◽  
Ayumu Inasawa
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Three Dimensional ◽  
Two Dimensional ◽  
S Wave ◽  
Flow Distortion ◽  
Oblique Waves ◽  
Surface Corrugation ◽  
S Waves ◽  
Displacement Thickness

AbstractThe effects of surface corrugation with small amplitude on the growth of Tollmien–Schlichting (T–S) waves were examined experimentally in a zero-pressure-gradient boundary layer. Two- and three-dimensional corrugations of sinusoidal geometry with wavelengths of the same order as that of the two-dimensional T–S wave were considered. The corrugation amplitudes were one order of magnitude smaller than the boundary-layer displacement thickness. Streamwise growth of T–S waves on the corrugated walls was compared with that in the boundary layer on the smooth surface. A distinct difference was found in the destabilizing effect between the two- and three-dimensional corrugations. The two-dimensional corrugation significantly enhanced the growth of two-dimensional T–S waves even when the corrugation amplitude was only ∼10% of the displacement thickness. On decreasing the corrugation amplitude, the growth rate of two-dimensional T–S waves asymptotically approached that in the smooth-wall case. On the other hand, the three-dimensional corrugation had only a small influence on the growth of two-dimensional T–S waves even when the corrugation amplitude was as large as 20% of the displacement thickness. For three-dimensional corrugations, however, a pair of oblique waves was generated and developed by an interaction between the two-dimensional T–S wave and the corrugation-induced mean-flow distortion for the corrugation wavelength considered. On increasing the corrugation amplitude, the oblique waves generated were increased in amplitude and thus significantly influenced the secondary instability process.

RADIATION OF BODY WAVES FROM NEAR‐SURFACE EXPLOSIVE SOURCES

Geophysics ◽  
1966 ◽  
Vol 31 (6) ◽  
pp. 1057-1065 ◽  
Author(s):  
I. N. Gupta ◽  
C. Kisslinger
Keyword(s):  
Free Surface ◽  
Body Waves ◽  
Radiation Patterns ◽  
S Wave ◽  
Near Surface ◽  
S Waves ◽  
Nuclear Explosions ◽  
Plexiglas Sheet ◽  
Chemical Explosions ◽  
Seismic Models

Amplitude distributions obtained from field observations of the azimuthal distribution of motion from cratering shots near a vertical face in a limestone section yielded data on radiation into a half‐space. These effects have been approximately reproduced in the laboratory by means of two‐dimensional seismic models. Small chemical explosions were fired on or near the edge of a large plexiglas sheet and the radiation of both P and S waves observed. Shots on the edge of the model sheet produce P and S radiation patterns expected from a normal downward impulse on the free surface. The radiation patterns from cratering shots may be qualitatively explained by the combined action on the free surface of a normal downward stress and a pair of horizontal stresses (dipole without moment) at the source point. The observed data are not sufficient for verifying theoretical S wave distributions. Observations of SV amplitudes from nuclear explosions could yield useful information concerning the relation between the angle at which the waves leave the source and the distance at which the wave emerges.

Prediction of Ship Motions Via a Three-Dimensional Time-Domain Method Following a Quad-Tree Adaptive Mesh Technique

2020 ◽  
Vol 27 (1) ◽  
pp. 29-38
Author(s):  
Teng Zhang ◽  
Junsheng Ren ◽  
Lu Liu
Keyword(s):  
Free Surface ◽  
Incident Wave ◽  
Time Domain ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Wave Profile ◽  
Time Domain Method ◽  
Ship Motions ◽  
Quad Tree ◽  
Mesh Technique

AbstractA three-dimensional (3D) time-domain method is developed to predict ship motions in waves. To evaluate the Froude-Krylov (F-K) forces and hydrostatic forces under the instantaneous incident wave profile, an adaptive mesh technique based on a quad-tree subdivision is adopted to generate instantaneous wet meshes for ship. For quadrilateral panels under both mean free surface and instantaneous incident wave profiles, Froude-Krylov forces and hydrostatic forces are computed by analytical exact pressure integration expressions, allowing for considerably coarse meshes without loss of accuracy. And for quadrilateral panels interacting with the wave profile, F-K and hydrostatic forces are evaluated following a quad-tree subdivision. The transient free surface Green function (TFSGF) is essential to evaluate radiation and diffraction forces based on linear theory. To reduce the numerical error due to unclear partition, a precise integration method is applied to solve the TFSGF in the partition computation time domain. Computations are carried out for a Wigley hull form and S175 container ship, and the results show good agreement with both experimental results and published results.

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