The attentuation of compression waves in lossy media*

1956 ◽  
Vol 46 (1) ◽  
pp. 47-56
Author(s):  
L. Knopoff
Keyword(s):  
Spherical Wave ◽  
Multiple Reflection ◽  
Reflection Coefficients ◽  
Lithium Sulfate ◽  
Seismic Modeling ◽  
Wave Fronts ◽  
Loss Mechanism ◽  
Compression Waves ◽  
Lossy Media ◽  
Internal Viscosity

ABSTRACT By means of modeling experiments on a wax slab, oil-coupled lithium sulfate transducers are found to have excellent directional properties as seismic modeling transducers. Investigation of the several orders of multiple reflection amplitudes shows that consistency in the measured reflection coefficients for the spherical wave fronts is easily achieved if a loss mechanism of the internal viscosity type is attributed to the wax.

scholarly journals Natural Qubit Matrix of Primary Elements of Matter

2018 ◽  
Vol 186 ◽  
pp. 01005
Author(s):  
Eugene Machusky
Keyword(s):  
Quantum Physics ◽  
Spherical Wave ◽  
Accurate Estimation ◽  
Fundamental Constants ◽  
Absolute Accuracy ◽  
Wave Fronts ◽  
Functional Relationships ◽  
Transcendental Numbers ◽  
Necessary And Sufficient ◽  
First Time

The arithmetic limits of natural bit calculations are strictly established. The natural quantum metric system has been developed. Only seven scaling units that generate thirteen invariant values are necessary and sufficient for an accurate estimation and a mutual coordination of the fundamental constants of quantum physics. For the first time, the calibration constants of quantum physics were obtained, calculated and identified analytically with almost an absolute accuracy, which is limited only by a bit capacity of a computer. The basic constants of quantum physics are, in fact, the dynamic parameters of the functional relationships of the transcendental numbers PI and E with natural numbers, which draw a holographic picture of the motion of spherical wave fronts.

Fast computation of seabed spherical-wave reflection coefficients in geoacoustic inversion

2015 ◽  
Vol 138 (4) ◽  
pp. 2106-2117 ◽  
Author(s):  
Jorge E. Quijano ◽  
Stan E. Dosso ◽  
Jan Dettmer ◽  
Charles W. Holland
Keyword(s):  
Wave Reflection ◽  
Spherical Wave ◽  
Reflection Coefficients ◽  
Fast Computation ◽  
Geoacoustic Inversion

On diffracted wave fronts

1979 ◽  
Vol 84 (1-2) ◽  
pp. 35-54
Author(s):  
Peter Wolfe
Keyword(s):  
Wave Equation ◽  
Wave Front ◽  
Incident Wave ◽  
Spherical Wave ◽  
Small Time ◽  
Time Interval ◽  
Wave Fronts ◽  
Incident Plane ◽  
Small Time Interval ◽  
Propagation Of Singularities

SynopsisIn this paper we study the wave equation, in particular the propagation of discontinuities. Two problems are considered: diffraction of a normally incident plane pulse by a plane screen and diffraction of a spherical wave by the same screen. It is shown that when an incident wave front strikes the edge of the screen a diffracted wave front is produced. The discontinuities are precisely computed in a neighbourhood of the edge for a small time interval after the arrival of the incident wave front and a theorem of Hörmander on the propagation of singularities is used to obtain a globalresult.

Reflection and Transmission of Elastic-Plastic Spherical Waves at a Spherical Interface

1975 ◽  
Vol 42 (4) ◽  
pp. 837-841 ◽  
Author(s):  
M. G. Srinivasan
Keyword(s):  
Shock Wave ◽  
Spherical Wave ◽  
Acceleration Wave ◽  
Wave Fronts ◽  
Reflection And Transmission ◽  
Elastic Plastic ◽  
Spherical Waves ◽  
The Many ◽  
Discontinuity Conditions ◽  
Spherical Interface

When a spherical wave is incident on a spherical interface of two different elastic-plastic, rate-independent materials, which of the many different admissible cases of reflection and transmission will actually occur must be determined in order to extend any numerical solution for subsequent times. An analytical method for this determination in terms of the known solution for times just prior to the incidence of the wave is outlined. The wave considered may be either an acceleration wave or a shock wave. The discontinuity conditions across the wave fronts and the continuity of displacement at the interface form the basis of this method and examples are given for illustration.

A two‐way nonreflecting wave equation

Geophysics ◽  
1984 ◽  
Vol 49 (2) ◽  
pp. 132-141 ◽  
Author(s):  
Edip Baysal ◽  
Dan D. Kosloff ◽  
J. W. C. Sherwood
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Forward Modeling ◽  
Conventional Approach ◽  
Reflection Coefficients ◽  
Constant Density ◽  
Acoustic Wave Equation ◽  
Seismic Modeling ◽  
Homogeneous Regions ◽  
Dominant Direction

In seismic modeling and in migration it is often desirable to use a wave equation (with varying velocity but constant density) which does not produce interlayer reverberations. The conventional approach has been to use a one‐way wave equation which allows energy to propagate in one dominant direction only, typically this direction being either upward or downward (Claerbout, 1972). We introduce a two‐way wave equation which gives highly reduced reflection coefficients for transmission across material boundaries. For homogeneous regions of space, however, this wave equation becomes identical to the full acoustic wave equation. Possible applications of this wave equation for forward modeling and for migration are illustrated with simple models.

Computational poroelasticity — A review

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. 75A229-75A243 ◽  
Author(s):  
José M. Carcione ◽  
Christina Morency ◽  
Juan E. Santos
Keyword(s):  
Porous Media ◽  
Wave Propagation ◽  
Rock Physics ◽  
Spectral Element ◽  
Seismic Modeling ◽  
Loss Mechanism ◽  
Diffusion Wave ◽  
Interface Waves ◽  
Element Technique

Computational physics has become an essential research and interpretation tool in many fields. Particularly in reservoir geophysics, ultrasonic and seismic modeling in porous media is used to study the properties of rocks and to characterize the seismic response of geologic formations. We provide a review of the most common numerical methods used to solve the partial differential equations describing wave propagation in fluid-saturated rocks, i.e., finite-difference, pseudospectral, and finite-element methods, including the spectral-element technique. The modeling is based on Biot-type theories of dynamic poroelasticity, which constitute a general framework to describe the physics of wave propagation. We explain the various techniques and discuss numerical implementation aspects for application to seismic modeling and rock physics, as, for instance, the role of the Biot diffusion wave as a loss mechanism and interface waves in porous media.

scholarly journals Reverberation time and audibility in phased geometrical acoustics using plane or spherical wave reflection coefficients

2019 ◽  
Vol 145 (3) ◽  
pp. 1888-1888
Author(s):  
Matthew Boucher ◽  
Monika Rychtarikova ◽  
Lukas Zelem ◽  
Bert Pluymers ◽  
Wim Desmet
Keyword(s):  
Wave Reflection ◽  
Spherical Wave ◽  
Reflection Coefficients ◽  
Reverberation Time ◽  
Geometrical Acoustics

Amplitude and phase versus angle for elastic wide-angle reflections in the τ‐p domain

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. N1-N9 ◽  
Author(s):  
Xinfa Zhu ◽  
George A. McMechan
Keyword(s):  
Plane Wave ◽  
Incident Angle ◽  
Plane Waves ◽  
Spherical Wave ◽  
Reflection Coefficients ◽  
Phase Versus ◽  
Angle Data ◽  
Wave Effects ◽  
Phase Variations ◽  
Time Offset

Near- and postcritical spherical-wave reflections contain amplitude and phase variations with incident angle that are not predicted by plane-wave solutions. However, if a spherical wavefield is decomposed into plane waves by a time-intercept-slowness ([Formula: see text]) transform, then plane-wave reflection coefficients (the Zoeppritz) can be used as the basis of amplitude/phase versus angle analysis. The spherical-wave effects on reflection coefficients near the critical angle (in the time-offset domain) were decomposed by [Formula: see text] transformation into plane waves. Kinematic ray tracing linked the reflection angle at the target reflector and the apparent slowness at the surface receiver, which enabled extracting the amplitude/phase versus angle data at the reflector from the surface [Formula: see text] data. The most reliable inversion results were obtained by combining the extracted amplitudes and phases in a composite inversion for the elastic parameters below the target reflector.

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