REFLECTION OF AN ACOUSTICAL PRESSURE PULSE FROM A LIQUID‐SOLID PLANE BOUNDARY

Geophysics ◽  
1956 ◽  
Vol 21 (1) ◽  
pp. 71-87 ◽  
Author(s):  
T. W. Spencer
Keyword(s):  
Surface Wave ◽  
Poisson’S Ratio ◽  
Velocity Ratio ◽  
Elastic Solid ◽  
Vertical Axis ◽  
Vertical Displacement ◽  
Poisson's Ratio ◽  
Plane Boundary ◽  
The Laplace Transform ◽  
Compressional Velocity

The problem treated is concerned with predicting the transient response of a system composed of a liquid layer, bounded above by a vacuum and below by a perfectly elastic solid, when excited by an arbitrary pressure applied uniformly over the surface of a spherical cavity located in the fluid. The Laplace transform of the displacement response is expressed in terms of an integral which is expanded in such a way that each term describes the contribution from one of the image sources. Each term may be evaluated exactly at points located on a vertical axis passing through the source. The final expression for the vertical displacement at axial points is composed of the acoustic, after‐flow, and correction terms. In solids for which Poisson’s ratio is greater than one third the initial variation of the correction is toward positive values (corresponding to motion directed toward the interface). For Poisson’s ratio less than one third the initial variation may be either positive or negative depending on the magnitude of the compressional velocity ratio. A surface wave is shown to exist regardless of the choice of parameters. The surface wave velocity is always less than it would be in the absence of the liquid.

The impact of a rigid circular cylinder on an elastic solid

1962 ◽  
Vol 255 (1053) ◽  
pp. 153-191 ◽  
Keyword(s):  
Laplace Transform ◽  
Elastic Body ◽  
Contact Area ◽  
Elastic Solid ◽  
Coupled System ◽  
Poisson's Ratio ◽  
Normal Displacement ◽  
Plane Boundary ◽  
The Laplace Transform ◽  
Perfect Adherence

A method is described for approximating to any degree of accuracy the solution of the following problem: An elastic body which is bounded by a plane on one side, but extends to infinity otherwise, is hit by a circular disk of given mass, radius, and initial speed perpendicular to the plane boundary. The whole surface of the disk enters into contact with the elastic body at the same time and stays in contact at all its points from then on. The disk is assumed to be rigid, i.e. it does not allow the particles of the elastic body in the contact area to move relative to each other in a direction perpendicular to the plane boundary. For the relative motion of these particles parallel to the face of the disk several conditions are considered, representing perfect lubrication, various degrees of viscous friction and perfect adherence. With the help of various Mellin transformations a method is indicated which leads to an expansion of the motion in powers of the Laplace transform variable. The case of perfect adherence needs some special consideration, and a simple approximation for the static problem is found. The case of perfect lubrication is then treated in more detail by a different method which replaces the condition of constant normal displacement in the contact area by an equivalent number of requirements for certain averages over the normal displacement in the contact area. The condition of rigidity for the disk is not exactly satisfied, but it is possible to judge the accuracy of the approximation (with the help of asymptotic expansions in the Laplace transform variable) at the initial time, when discrepancies are largest. The concept of ‘mode of vibration’ is introduced. Any transient in the coupled system of elastic body and rigid disk can be described as superposition of modes, each of which is an exponentially damped harmonic oscillation of the coupled system with a frequency and damping constant independent of the particular transient. The motion of the impinging disk is then seen to be dominated mostly by the lowest mode, provided the mass of the disk is not too small. The displacement perpendicular to the boundary outside of the contact area has been calculated. This calculation is not more difficult than the corresponding one in the case of a point-like source at the plane boundary of an elastic solid. Numerical computations were carried out for the case of perfect lubrication with the help of the Elecom digital computer in order to determine the first two modes and their contributions to the motion of the disk. As long as Poisson’s ratio for the elastic solid exceeds 1/4, the results do not depend strongly on the value of Poisson’s ratio. The ratio of the areal mass densities of the disk to the elastic solid is the main parameter of the theory. The shear wave velocity of the elastic solid determines the time scale of the motion.

scholarly journals Characterization of hydrocarbon reservoir by pore fluid and lithology using elastic parameters in an x field, Niger delta, Nigeria

2018 ◽  
Vol 6 (2) ◽  
pp. 173
Author(s):  
Akpabio . ◽  
Idara O ◽  
Ojo . ◽  
Odunayo T
Keyword(s):  
Wave Velocity ◽  
Niger Delta ◽  
Poisson’S Ratio ◽  
Velocity Ratio ◽  
Rock Physics ◽  
Pore Fluid ◽  
Poisson's Ratio ◽  
Oil Sand ◽  
Elastic Parameters ◽  
Hydrocarbon Reservoir

Quantitative rock physics analysis was carried out to determine the lithology and pore fluid of a reservoir in the Niger Delta. Density, compressional wave velocity and shear wave velocity logs were used as input to calculate elastic parameters such as velocity ratio, Poisson’s ratio, and Bulk Modulus, after estimating the hydrocarbon reservoir in the X field. The calculated velocity ratio log was used to differentiate between sand, sandstone and shale. Poisson’s ratio and velocity ratio were used delineate pore fluid content; gas sand, oil sand and sandstone formation from cross plot analysis. The reservoir in the field lies ranges from 9050 - 9426.5ft, (2760.25 – 2874.93m), this confirm what is obtained in the Niger Delta Basin. The Net Pay zones show an economical viable reservoir, it Net pay depth is 39 – 73.5ft. The Porosity and Permeability of the reservoirs suggested a productivity hydrocarbon reservoir. The reservoir lies between Gas sands, Oil sands and Brine sands, reservoir 2 and reservoir 3 are oil sand reservoirs while reservoir 1 lies between an oil sand and a brine sand.   

THE MECHANISM OF GENERATION OF LONG WAVES FROM EXPLOSIONS

Geophysics ◽  
1955 ◽  
Vol 20 (1) ◽  
pp. 87-103 ◽  
Author(s):  
C. Hewitt Dix
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Elastic Solid ◽  
Vertical Axis ◽  
Vertical Displacement ◽  
Transverse Waves ◽  
Displacement Potential ◽  
Long Period ◽  
Duhamel Integral ◽  
Ground Roll

Cagniard’s method is applied to the numerical calculation of the vertical displacement due to a point source in a semi‐infinite elastic solid medium at three points on a vertical line through the source. The source is a step in the scalar displacement potential. From these calculated responses the response for any physically possible spherically symmetric source can be computed by application of the Duhamel integral. Clear evidence of backward transmission of transverse wave energy is found along the vertical axis through the source. This, together with the energy of the longitudinal waves, also transmitted backwards, accounts for the mechanism by which energy is held near the source and near the free surface long enough to account for the generation of long period surface waves. This mechanism of generation of long period surface waves is not restricted to the free surface case. Any good reflector, which also generates secondary transverse waves from longitudinal primary waves, will serve the purpose. It is suggested that this gives a clue to the mechanism of the formation of “ground roll” in many practical cases.

Surface-wave dispersion in Byrd Land, Antarctica

1972 ◽  
Vol 62 (4) ◽  
pp. 955-959 ◽  
Author(s):  
H. K. Acharya
Keyword(s):  
Surface Wave ◽  
Ultrasonic Velocity ◽  
Poisson’S Ratio ◽  
Wave Dispersion ◽  
Poisson's Ratio ◽  
Constant Density ◽  
Velocity Measurements ◽  
Land Area ◽  
Surface Wave Dispersion ◽  
Ice Cap

Abstract Assuming constant density and Poisson's ratio of 0.25, theoretical surface-wave dispersion has been computed for the Byrd Land area in Antarctica, where the velocity increases monotonically with depth. Comparison with observed dispersion indicates 8 to 10 per cent anisotropy in the ice cap. Such anisotropy was also detected from ultrasonic velocity measurements on snow cores.

The azimuthal and polar radiation patterns obtained from a horizontal stress applied at the surface of an elastic half space

1962 ◽  
Vol 52 (1) ◽  
pp. 27-36
Author(s):  
J. T. Cherry
Keyword(s):  
Surface Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Poisson’S Ratio ◽  
Horizontal Stress ◽  
Elastic Half Space ◽  
The Body ◽  
Body Waves ◽  
Poisson's Ratio ◽  
A Value

Abstract The body waves and surface waves radiating from a horizontal stress applied at the free surface of an elastic half space are obtained. The SV wave suffers a phase shift of π at 45 degrees from the vertical. Also, a surface wave that is SH in character but travels with the Rayleigh velocity is shown to exist. This surface wave attenuates as r−3/2. For a value of Poisson's ratio of 0.25 or 0.33, the amplitude of the Rayleigh waves from a horizontal source should be smaller than the amplitude of the Rayleigh waves from a vertical source. The ratio of vertical to horizontal amplitude for the Rayleigh waves from the horizontal source is the same as the corresponding ratio for the vertical source for all values of Poisson's ratio.

scholarly journals Experimental Study on Petrophysical Properties as a Tool to Identify Pore Fluids in Tight-Rock Reservoirs

2021 ◽  
Vol 9 ◽  
Author(s):  
Rupeng Ma ◽  
Jing Ba ◽  
José Carcione ◽  
Maxim Lebedev ◽  
Changsheng Wang
Keyword(s):  
Wave Velocity ◽  
Poisson’S Ratio ◽  
Velocity Ratio ◽  
Data Distribution ◽  
Poisson's Ratio ◽  
Petrophysical Properties ◽  
Pore Fluids ◽  
S Wave ◽  
Wave Velocities ◽  
Lame Constant

The petrophysical properties can be proper indicators to identify oil and gas reservoirs, since the pore fluids have significant effects on the wave response. We have performed ultrasonic measurements on two sets of tight siltstones and dolomites at partial saturation. P- and S-wave velocities are obtained by the pulse transmission technique, while attenuation is calculated using the centroid-frequency shift and spectral-ratio methods. The fluid sensitivities of different properties (i.e., P- and S-wave velocities, impedances and attenuation, Poisson's ratio, density, and their combinations) are quantitatively analyzed by considering the data distribution, based on the crossplot technique. The result shows that the properties (P- to S-wave velocity and attenuation ratios, Poisson's ratio, and first to second Lamé constant ratio) with high fluid-sensitivity indicators successfully distinguish gas from oil and water, unlike oil from water. Moreover, siltstones and dolomites can be identified on the basis of data distribution areas. Ultrasonic rock-physics templates of the P- to S-wave velocity ratio vs. the product of first Lamé constant with density obtained with a poroelastic model, considering the structural heterogeneity and patchy saturation, are used to predict the saturation and porosity, which are in good agreement with the experimental data at different porosity ranges.

THE REFLECTION OF RAYLEIGH WAVES BY A HIGH IMPEDANCE OBSTACLE ON A HALF‐SPACE

Geophysics ◽  
1960 ◽  
Vol 25 (6) ◽  
pp. 1195-1202 ◽  
Author(s):  
R. W. Fredricks ◽  
L. Knopoff
Keyword(s):  
Reflection Coefficient ◽  
Rayleigh Wave ◽  
Half Space ◽  
Poisson’S Ratio ◽  
Vertical Displacement ◽  
Elastic Half Space ◽  
Poisson's Ratio ◽  
Dual Integral Equations ◽  
High Impedance ◽  
Theoretic Solution

The reflection of a time‐harmonic Rayleigh wave by a high impedance obstacle in shearless contact with an elastic half‐space of lower impedance is examined theoretically. The potentials are found by a function—theoretic solution to dual integral equations. From these potentials, a “reflection coefficient” is defined for the surface vertical displacement in the Rayleigh wave. Results show that the reflected wave is π/2 radians out of phase with the incident wave for arbitrary Poisson’s ratio. The modulus of the “reflection coefficient” depends upon Poisson’s ratio, and is evaluated as [Formula: see text] for σ=0.25.

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