HEAD WAVES FROM A BED OF FINITE THICKNESS

Geophysics ◽  
1962 ◽  
Vol 27 (6) ◽  
pp. 753-765 ◽  
Author(s):  
Franklyn K. Levin ◽  
John D. Ingram
Keyword(s):  
Layer Thickness ◽  
High Speed ◽  
Finite Thickness ◽  
Thin Layers ◽  
Head Wave ◽  
Amplitude Dependence ◽  
Head Waves ◽  
Zero Layer ◽  
Bar Velocity ◽  
Seismic Models

The behavior of the head wave from a high‐speed layer embedded in a low‐speed half‐space has been investigated with two‐dimensional seismic models. Twelve layer thicknesses ranging from four wavelengths to one‐tenth wavelength were used. A simple theory based on interference between the head wave and the reflections from the bottom of the layer gave amplitude‐distance values which agreed with the observations for layer thicknesses down to about one‐third of a wavelength. For thick layers, the experimental amplitude dependence on distance was different from the theoretical law (−3/2 power of the distance). The velocity minimum for thin layers discovered by Lavergne was confirmed and a possible slight velocity maximum at intermediate layer thicknesses noted. The velocity for zero layer thickness appeared to be greater than the free bar velocity. Systematic variations of head‐wave spectra with layer thickness occurred.

MULTI‐REFLECTED HEAD WAVES IN A SINGLE‐LAYERED MEDIUM

Geophysics ◽  
1966 ◽  
Vol 31 (5) ◽  
pp. 927-939 ◽  
Author(s):  
Yosio Nakamura
Keyword(s):  
Layered Medium ◽  
Fourier Transforms ◽  
Finite Thickness ◽  
Single Layer ◽  
Head Wave ◽  
Two Dimensional ◽  
Propagation Characteristics ◽  
Dimensional Model ◽  
Dispersive Effect ◽  
Head Waves

The propagation characteristics of surface‐reflected head waves have been studied experimentally using two‐ dimensional, Plexiglas‐aluminum and polystyrene‐aluminum, single‐layer models. In addition to the contributions from the reflected refractions (with reflections near the source) and the refracted reflections (with reflections near the receiver) those from the refraction‐reflection intermixtures (with reflections midway in the refraction path) have been found to be significant, resulting in a slight reinforcement of the surface‐reflected head waves with increasing distance. The phase relations of the arrivals have been examined by computing the Fourier transforms of the observed waveforms. It has been found that, relative to the principal head‐wave arrival, the surface‐reflected head waves exhibit an anomalous phase shift, which is due probably to the finite thickness of the model materials. For the dispersive effect to be negligible, the thickness of the two‐dimensional model must be less than approximately one‐fifteenth of the wavelength of interest.

A STUDY OF TWO‐DIMENSIONAL HEAD WAVES IN FLUID AND SOLID SYSTEMS

Geophysics ◽  
1963 ◽  
Vol 28 (4) ◽  
pp. 563-581 ◽  
Author(s):  
John W. Dunkin
Keyword(s):  
Half Space ◽  
Vertical Displacement ◽  
Point Of View ◽  
Head Wave ◽  
Apparent Velocity ◽  
Two Dimensional ◽  
Multiple Reflections ◽  
Transient Wave ◽  
Line Load ◽  
Head Waves

The problem of transient wave propagation in a three‐layered, fluid or solid half‐plane is investigated with the point of view of determining the effect of refracting bed thickness on the character of the two‐dimensional head wave. The “ray‐theory” technique is used to obtain exact expressions for the vertical displacement at the surface caused by an impulsive line load. The impulsive solutions are convolved with a time function having the shape of one cycle of a sinusoid. The multiple reflections in the refracting bed are found to affect the head wave significantly. For thin refracting beds in the fluid half‐space the character of the head wave can be completely altered by the strong multiple reflections. In the solid half‐space the weaker multiple reflections affect both the rate of decay of the amplitude of the head wave with distance and the apparent velocity of the head wave by changing its shape. A comparison is made of the results for the solid half‐space with previously published results of model experiments.

scholarly journals Spreadability Testing of Powder for Additive Manufacturing

2021 ◽  
Vol 166 (1) ◽  
pp. 9-13
Author(s):  
Christopher Neil Hulme-Smith ◽  
Vignesh Hari ◽  
Pelle Mellin
Keyword(s):  
Additive Manufacturing ◽  
Layer Thickness ◽  
Measurement Procedure ◽  
Quantitative Information ◽  
Thin Layers ◽  
Spreading Speed ◽  
Powder Bed ◽  
Critical Step ◽  
Robust Image

AbstractThe spreading of powders into thin layers is a critical step in powder bed additive manufacturing, but there is no accepted technique to test it. There is not even a metric that can be used to describe spreading behaviour. A robust, image-based measurement procedure has been developed and can be implemented at modest cost and with minimal training. The analysis is automated to derive quantitative information about the characteristics of the spread layer. The technique has been demonstrated for three powders to quantify their spreading behaviour as a function of layer thickness and spreading speed.

Dynamic properties of reflected and head waves near the critical point

1979 ◽  
Vol 16 (7) ◽  
pp. 1388-1401 ◽  
Author(s):  
Larry W. Marks ◽  
F. Hron
Keyword(s):  
Exact Solution ◽  
High Frequency ◽  
Classical Problem ◽  
Plane Boundary ◽  
Head Wave ◽  
Disk File ◽  
Ray Theory ◽  
Computational Point ◽  
Spherical Waves ◽  
Head Waves

The classical problem of the incidence of spherical waves on a plane boundary has been reformulated from the computational point of view by providing a high frequency approximation to the exact solution applicable to any seismic body wave, regardless of the number of conversions or reflections from the bottoming interface. In our final expressions the ray amplitude of the interference reflected-head wave is cast in terms of a Weber function, the numerical values of which can be conveniently stored on a computer disk file and retrieved via direct access during an actual run. Our formulation also accounts for the increase of energy carried by multiple head waves arising during multiple reflections of the reflected wave from the bottoming interface. In this form our high frequency expression for the ray amplitude of the interference reflected-head wave can represent a complementary technique to asymptotic ray theory in the vicinity of critical regions where the latter cannot be used. Since numerical tests indicate that our method produces results very close to those obtained by the numerical integration of the exact solution, its combination with asymptotic ray theory yields a powerful technique for the speedy computation of synthetic seismograms for plane homogeneous layers.

Exact seismograms for a point force using generalized ray theory

Geophysics ◽  
1983 ◽  
Vol 48 (11) ◽  
pp. 1421-1427 ◽  
Author(s):  
E. R. Kanasewich ◽  
P. G. Kelamis ◽  
F. Abramovici
Keyword(s):  
Half Space ◽  
Near Field ◽  
Sedimentary Basins ◽  
Transverse Component ◽  
Point Force ◽  
Seismic Exploration ◽  
Head Wave ◽  
Vertical Force ◽  
Low Velocity ◽  
Head Waves

Exact synthetic seismograms are obtained for a simple layered elastic half‐space due to a buried point force and a point torque. Two models, similar to those encountered in seismic exploration of sedimentary basins, are examined in detail. The seismograms are complete to any specified time and make use of a Cagniard‐Pekeris method and a decomposition into generalized rays. The weathered layer is modeled as a thin low‐velocity layer over a half‐space. For a horizontal force in an arbitrary direction, the transverse component, in the near‐field, shows detectable first arrivals traveling with a compressional wave velocity. The radial and vertical components, at all distances, show a surface head wave (sP*) which is not generated when the source is compressive. A buried vertical force produces the same surface head wave prominently on the radial component. An example is given for a simple “Alberta” model as an aid to the interpretation of wide angle seismic reflections and head waves.

scholarly journals High-Velocity Shear and Soft Friction at the Nanometer Scale

2021 ◽  
Vol 7 ◽  
Author(s):  
Per-Anders Thorén ◽  
Riccardo Borgani ◽  
Daniel Forchheimer ◽  
David B. Haviland
Keyword(s):  
High Speed ◽  
Surface Deformation ◽  
Soft Materials ◽  
Lateral Force ◽  
Velocity Shear ◽  
Polymer Materials ◽  
Amplitude Dependence ◽  
Dynamic Force ◽  
Stick Slip ◽  
Soft Polymer

We study high-speed friction on soft polymer materials by measuring the amplitude dependence of cyclic lateral forces on the atomic force microscope (AFM) tip as it slides on the surface with fixed contact force. The resulting dynamic force quadrature curves separate the elastic and viscous contributions to the lateral force, revealing a transition from stick-slip to free-sliding motion as the velocity increases. We explain force quadratures and describe how they are measured, and we show results for a variety of soft materials. The results differ substantially from the measurements on hard materials, showing hysteresis in the force quadrature curves that we attribute to the finite relaxation time of viscoelastic surface deformation.

scholarly journals Microseismic hydraulic fracture imaging in the Marcellus Shale using head waves

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. KS1-KS10 ◽  
Author(s):  
Zhishuai Zhang ◽  
James W. Rector ◽  
Michael J. Nava
Keyword(s):  
Marcellus Shale ◽  
P Wave ◽  
Head Wave ◽  
Wave Polarization ◽  
Horizontal Section ◽  
Location Accuracy ◽  
Arrival Times ◽  
Microseismic Data ◽  
Head Waves ◽  
Event Location

We have studied microseismic data acquired from a geophone array deployed in the horizontal section of a well drilled in the Marcellus Shale near Susquehanna County, Pennsylvania. Head waves were used to improve event location accuracy as a substitution for the traditional P-wave polarization method. We identified that resonances due to poor geophone-to-borehole coupling hinder arrival-time picking and contaminate the microseismic data spectrum. The traditional method had substantially greater uncertainty in our data due to the large uncertainty in P-wave polarization direction estimation. We also identified the existence of prominent head waves in some of the data. These head waves are refractions from the interface between the Marcellus Shale and the underlying Onondaga Formation. The source location accuracy of the microseismic events can be significantly improved by using the P-, S-wave direct arrival times and the head wave arrival times. Based on the improvement, we have developed a new acquisition geometry and strategy that uses head waves to improve event location accuracy and reduce acquisition cost in situations such as the one encountered in our study.

scholarly journals Evaluating Mechanical Properties of Thin Layers using Nanoindentation and Finite-Element Modeling: Implanted Metals and Deposited Layers

1996 ◽  
Vol 438 ◽  
Author(s):  
J. A. Knapp ◽  
D. M. Follstaedt ◽  
J. C. Barbour ◽  
S. M. Myers ◽  
J. W. Ager ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Finite Element Modeling ◽  
Yield Stress ◽  
Young’S Modulus ◽  
Layer Thickness ◽  
Young's Modulus ◽  
Thin Layers ◽  
Element Modeling ◽  
Surface Modified

AbstractWe present a methodology based on finite-element modeling of nanoindentation data to extract reliable and accurate mechanical properties from thin, hard films and surface-modified layers on softer substrates. The method deduces the yield stress, Young's modulus, and hardness from indentations as deep as 50% of the layer thickness.

scholarly journals Characteristics of Large-Scale Structures in Supersonic Planar Mixing Layer with Finite Thickness

2014 ◽  
Vol 6 ◽  
pp. 878679
Author(s):  
Hailong Zhang ◽  
Jiping Wu ◽  
Jian Chen ◽  
Weidong Liu
Keyword(s):  
High Speed ◽  
Large Scale ◽  
Finite Thickness ◽  
Mixing Layer ◽  
Mixing Enhancement ◽  
Laser Scattering ◽  
Large Scale Structures ◽  
Eddy Simulation ◽  
Planar Laser ◽  
Scale Structures

Nanoparticle-based planar laser scattering (NPLS) experiments and large eddy simulation (LES) were launched to get the fine structure of the supersonic planar mixing layer with finite thickness in the present study. Different from the turbulent development of supersonic planar mixing layer with thin thickness, the development of supersonic planar mixing layer with finite thickness is rapidly. The large-scale structures of mixing layer that possess the characters of quick movement and slow changes transmit to downriver at invariable speed. The transverse results show that the mixing layer is strip of right and dim and possess 3D characteristics. Meanwhile the vortices roll up from two sides to the center. Results indicate that the higher the pressure of the high speed side is, the thicker the mixing layer is. The development of mixing layer is restrained when the pressure of lower speed side is higher. The momentum thickness goes higher with the increase of the clapboard thickness. Through increasing the temperature to change the compression can affect the development of the vortices. The present study can make a contribution to the mixing enhancement and provide initial data for the later investigations.

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