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.

True amplitude recovery in reverse time extrapolation of plane and spherical waves

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. T103-T122 ◽  
Author(s):  
Yulang Wu ◽  
George A. McMechan
Keyword(s):  
Incident Wave ◽  
Horizontal Well ◽  
Spherical Wave ◽  
Reverse Time ◽  
Multiple Reflections ◽  
Reflection And Transmission ◽  
Spherical Waves ◽  
Reflection Data ◽  
Time Propagation ◽  
Time Extrapolation

A challenging outstanding problem in reverse time extrapolation is recovering accurate amplitudes at reflectors from the receiver wavefield. Various migrations have been developed to produce accurate image locations rather than correct amplitude information because of inadequate compensation of attenuation, dispersion, and transmission losses. We have evaluated the requirements, and determined the theoretical feasibility, of true amplitude recovery of 2D acoustic and elastic seismic data by using the analytic Zoeppritz equations for plane-wave reflection and transmission coefficients. Then, we used synthetic acoustic and elastic wavefield data generated by elastodynamic finite differences to verify the recovery, in the reverse time propagation, of spherical waves and illustrated the salient differences between the incident wavefields reconstructed from reflection data only and from the combination of reflection and transmission data. These examples quantitatively verify that recovering an incident plane or a spherical wave requires the reverse time propagation of all reflections and transmissions in a model with the correct velocity and density. Accurate reconstruction of an incident wave is not possible by backward propagation of only reflections. As an application, we removed downgoing internal multiple reflections generated by upgoing waves incident at reflectors shallower than a horizontal well, in which geophones are deployed. The subtraction of the downgoing reflection involves wavefield reconstruction at depths shallower than the horizontal well and separation of upgoing and downgoing wavefields. This approach assumes that the correct acoustic (or elastic) velocity and density models are available in, and shallower than, the layer where the horizontal well is located. Incident-wave reconstruction works equally well for smooth models, as for models with sharp boundaries. Uncertainties in the model used for reconstruction, and incompleteness of the data aperture are propagated into the equivalent uncertainties, and incompleteness of the reconstruction.

Spherical waves in a simple locking medium

1964 ◽  
Vol 54 (2) ◽  
pp. 737-754
Author(s):  
Sathyanarayana Hanagud
Keyword(s):  
Shock Wave ◽  
Stress Distribution ◽  
Mechanical Behavior ◽  
Spherical Cavity ◽  
Shear Resistance ◽  
Finite Deformations ◽  
Spherical Shock Wave ◽  
Spherical Waves ◽  
Spherical Shock ◽  
Elastic Shear

ABSTRACT The mechanical behavior of some types of soils can be idealized by that of a “Locking Solid.” This paper investigates the spherical shock wave and the stress distribution behind the wave in a simple locking solid due to a sudden explosion at the surface of a small spherical cavity. The cases of infinitesimal and finite deformations are considered. The effect of an elastic shear resistance and the consequent phenomenon of “unlocking” are also studied.

Experiment on the Attenuation Characteristics of Shock Wave Interacting with Open and Closed Foam

2014 ◽  
Vol 1035 ◽  
pp. 445-452
Author(s):  
Jian Wang ◽  
Bao Gui Wang ◽  
Gang Tao
Keyword(s):  
Shock Wave ◽  
Internal Friction ◽  
Dynamic Behavior ◽  
Solid Phase ◽  
Experimental Results ◽  
Reflection And Transmission ◽  
Attenuation Characteristics

For understanding the dynamic behavior of open and closed foam subject to a shock wave, this paper through experiments, to gain a deeper understanding of the incidence, reflection and transmission of a shock wave when it interacted with cellular foam. Moreover, by analyzing the loss of the peak overpressure and positive impulse, we were able to respectively know the positive impulse of the incidence, reflection and transmission shock wave. The experimental results indicated that the attenuation capability for foam to the shock wave was caused by the internal friction and deformation of solid phase, which would absorb the energy of the shock wave. From the results we gain an understanding that the mechanical phenomenon of open foam to shock wave are not fully consistent with those of closed foam , while the attenuation of open foam to shock wave is more effective than that of closed foam.

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 3D Display System Based on Spherical Wave Field Synthesis

2019 ◽  
Vol 9 (18) ◽  
pp. 3862
Author(s):  
Claas Falldorf ◽  
Ping-Yen Chou ◽  
Daniel Prigge ◽  
Ralf Bergmann
Keyword(s):  
Liquid Crystal Display ◽  
Spherical Wave ◽  
Depth Information ◽  
Natural Scene ◽  
Display System ◽  
3D Display ◽  
Spherical Waves ◽  
New Type ◽  
Wave Field Synthesis ◽  
Novel Concept

We present a novel concept and first experimental results of a new type of 3D display, which is based on the synthesis of spherical waves. The setup comprises a lens array (LA) with apertures in the millimeter range and a liquid crystal display (LCD) panel. Each pixel of the LCD creates a spherical wave cutout that propagates towards the observer. During the displaying process, the curvature of the spherical waves is dynamically changed by either changing the distance between LA and LCD or by adapting the focal lengths of the lenses. Since the system, similar to holography, seeks to approximate the wavefront of a natural scene, it provides true depth information to the observer and therefore avoids any vergence–accommodation conflict (VAC).

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