Calculation of complete seismograms for an explosive source in a layered medium

Geophysics ◽  
1980 ◽  
Vol 45 (2) ◽  
pp. 197-203 ◽  
Author(s):  
Michel Bouchon
Keyword(s):  
Elastic Wave ◽  
Layered Medium ◽  
Plane Waves ◽  
Three Dimensional ◽  
Synthetic Seismograms ◽  
Two Dimensional ◽  
Wave Fields ◽  
Source Radiation ◽  
Explosive Source ◽  
Periodic Arrangement

We apply the method of discrete wavenumber representation of elastic wave fields of Bouchon and Aki (1977) to the computation of synthetic seismograms for an explosive source in a layered medium. The method is based on the representation of the source radiation by a superposition of plane waves propagating in discrete directions. This discretization is exact and results from a periodic arrangement of sources. The two‐dimensional (2-D) and three‐dimensional (3-D) problems are described, and some examples of calculation are presented. They show that very complex seismograms can be obtained for rather simple geologic structures.

On the subharmonic instabilities of steady three-dimensional deep water waves

1994 ◽  
Vol 262 ◽  
pp. 265-291 ◽  
Author(s):  
Mansour Ioualalen ◽  
Christian Kharif
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Water Waves ◽  
Transverse Direction ◽  
Plane Waves ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Two Dimensional ◽  
Wave Steepness ◽  
Oblique Angle

A numerical procedure has been developed to study the linear stability of nonlinear three-dimensional progressive gravity waves on deep water. The three-dimensional patterns considered herein are short-crested waves which may be produced by two progressive plane waves propagating at an oblique angle, γ, to each other. It is shown that for moderate wave steepness the dominant resonances are sideband-type instabilities in the direction of propagation and, depending on the value of γ, also in the transverse direction. It is also shown that three-dimensional progressive gravity waves are less unstable than two-dimensional progressive gravity waves.

The relationship between two- and three-dimensional elastic-wave propagation

1971 ◽  
Vol 61 (6) ◽  
pp. 1583-1588 ◽  
Author(s):  
C. N. G. Dampney
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Three Dimensional ◽  
Elastic Wave Propagation ◽  
Simple Relationship ◽  
Two Dimensional ◽  
Intrinsic Interest ◽  
Cylindrically Symmetric ◽  
The Relationship ◽  
Dimensional Wave

abstract A technique similar to inverting Abel's equation is used to invert the descent of dimensions method between three-dimensional, cylindrically-symmetric and two-dimensional wave propagation. The end result is a very simple relationship between the two types of wave propagation. Apart from its intrinsic interest, the large number of two-dimensional studies reported in the literature could now be related to their three-dimensional counterparts.

ULTRASOUND AS A PROBE OF PLASTICITY? THE INTERACTION OF ELASTIC WAVES WITH DISLOCATIONS

2009 ◽  
Vol 19 (08) ◽  
pp. 2765-2781 ◽  
Author(s):  
AGNES MAUREL ◽  
VINCENT PAGNEUX ◽  
FELIPE BARRA ◽  
FERNANDO LUND
Keyword(s):  
Elastic Wave ◽  
Elastic Waves ◽  
Plane Waves ◽  
Dislocation Line ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Dislocation Segment ◽  
Plastic Behavior ◽  
Line Segments

An overview of recent work on the interaction of elastic waves with dislocations is given. The perspective is provided by the wish to develop nonintrusive tools to probe plastic behavior in materials. For simplicity, ideas and methods are first worked out in two dimensions, and the results in three dimensions are then described. These results explain a number of recent, hitherto unexplained, experimental findings. The latter include the frequency dependence of ultrasound attenuation in copper, the visualization of the scattering of surface elastic waves by isolated dislocations in LiNbO 3, and the ratio of longitudinal to transverse wave attenuation in a number of materials. Specific results reviewed include the scattering amplitude for the scattering of an elastic wave by a screw, as well as an edge, dislocation in two dimensions, the scattering amplitudes for an elastic wave by a pinned dislocation segment in an infinite elastic medium, and the wave scattering by a sub-surface dislocation in a semi-infinite medium. Also, using a multiple scattering formalism, expressions are given for the attenuation coefficient and the effective speed for coherent wave propagation in the cases of anti-plane waves propagating in a medium filled with many, randomly placed screw dislocations; in-plane waves in a medium similarly filled with randomly placed edge dislocations with randomly oriented Burgers vectors; elastic waves in a three-dimensional medium filled with randomly placed and oriented dislocation line segments, also with randomly oriented Burgers vectors; and elastic waves in a model three-dimensional polycrystal, with only low angle grain boundaries modeled as arrays of dislocation line segments.

Computation of multi-attribute seismic wavefields by solution of the elastodynamic equations

1992 ◽  
Vol 82 (2) ◽  
pp. 1134-1143
Author(s):  
How-Wei Chen ◽  
George A. McMechan
Keyword(s):  
Shear Stress ◽  
Particle Acceleration ◽  
Wave Equations ◽  
Layered Medium ◽  
Normal Strain ◽  
Particle Displacement ◽  
Seismic Modeling ◽  
Wave Fields ◽  
Single Piece ◽  
Explosive Source

Abstract By using the elastodynamic equations rather than wave equations for seismogram synthesis, multi-attribute wave fields can be computed in a single execution of one program. In the present implementation, for 2-D models, the wave fields and seismograms produced include any or all of the following: two components of each of particle acceleration, particle velocity, and particle displacement; two components of normal strain; shear strain; two components of normal stress; shear stress; and the dilatation and curl of the particle displacement. If flexible source and receiver configurations are also included, a single piece of software can be used for most seismic modeling applications. This significantly reduces the need for development and maintenance of separate programs. The algorithm is illustrated using waves synthesized for an explosive source in a layered medium. Snapshots and seismograms at both surface and borehole arrays are presented.

Modulational Instability in Directional Wave Fields, and Extreme Wave Events

2011 ◽  
Author(s):  
Alexander V. Babanin ◽  
Takuji Waseda ◽  
Igor Shugan ◽  
Hwung-Hweng Hwung
Keyword(s):  
Modulational Instability ◽  
Wave Train ◽  
Three Dimensional ◽  
Breaking Waves ◽  
Two Dimensional ◽  
Wave Fields ◽  
Linear Evolution ◽  
Individual Wave ◽  
Wave Trains ◽  
Directional Wave

The paper is based on review of research articles by the authors, with the purpose to demonstrate that the modulational-instability mechanism is active in typical directional wave fields. If so, possible limits for the wave height due to such mechanism can be outlined. The modulational instability can lead to occurrence of very high waves, which either proceed to the breaking or appear as rogue events, but it was derived for and is usually associated with two-dimensional wave trains. There exists argument, both analytical and experimental, that this kind of instability is impaired or even suppressed in three-dimensional (directional) wave systems. The first part of the paper demonstrates indirect experimental evidences which relate the wave breaking in oceanic conditions to features of two-dimensional breaking waves due to modulational instability. The second section is dedicated to direct measurements of such instability-caused breaking in a directional wave tank with directional spread and mean steepness typical of those in the field. The last section provides conclusions on what is maximal height of an individual wave, depending on the mean wave steepness in a wave train/field, that can be achieved due to such non-linear evolution of wave trains.

DEPENDENCE OF THE AXIAL WAVE ON RANGE AND SOUND-SPEED PROFILE PROPERTIES IN A RANGE-INDEPENDENT OCEAN

2005 ◽  
Vol 13 (02) ◽  
pp. 259-278 ◽  
Author(s):  
NATALIE S. GRIGORIEVA ◽  
GREGORY M. FRIDMAN
Keyword(s):  
Numerical Simulation ◽  
Sound Speed ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Speed Profile ◽  
Wave Fields ◽  
Sound Speed Profile ◽  
Average Profile ◽  
Ducted Propagation ◽  
Dimensional Range

For ducted propagation in a waveguide when the source and receiver are placed closely to the depth of the waveguide axis, there exist cusped caustics repeatedly along the axis. In neighborhoods of these cusped caustics, the interference of the wave fields that correspond to near-axial rays occurs. This results in the formation of a coherent structure (the axial wave) that propagates along the waveguide axis like a wave. In this paper the integral representation of the axial wave obtained before for an arbitrary waveguide in a two-dimensional range-independent medium is generalized to a three-dimensional range-independent medium. Through numerical simulation, the dependencies of the axial wave on range, sound-speed profile properties, and geometry of the experiment are studied for two sound-speed profiles: the average profile from the AET experiment and the Munk canonical profile. The sound source frequency is taken equal to 75 Hz; the propagation range is up to 3250 km. The strong difference between shapes of the axial wave for the average profile from the AET experiment and the Munk canonical profile is shown for all the examined models.

Dynamic rupture in a layered medium: The 1966 Parkfield earthquake

1980 ◽  
Vol 70 (3) ◽  
pp. 671-689
Author(s):  
Ralph J. Archuleta ◽  
Steven M. Day
Keyword(s):  
Wave Propagation ◽  
Stress Relaxation ◽  
Ground Motion ◽  
Layered Medium ◽  
Heterogeneous Medium ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dynamic Rupture ◽  
Time Histories ◽  
Parkfield Earthquake

abstract A method for computing ground motion from a propagating stress relaxation in a vertically heterogeneous medium was developed wherein computational efficiency is enhanced by separating the source, a three-dimensional calculation, from the wave propagation, a two-dimensional calculation. As an application of this technique, displacement-time histories were computed corresponding to those determined from accelerograms recorded during the 1966 Parkfield, California earthquake. On the basis of these comparisons, an effective stress of 25 bars, an average slip of 43 cm, and a moment of 2.32 × 1025 dyne-cm were determined for the Parkfield earthquake.

High Resolution Microscopy of Multi-Layered Biological Crystals

1982 ◽  
Vol 40 ◽  
pp. 80-83
Author(s):  
H.A. Cohen ◽  
T.W. Jeng ◽  
W. Chiu
Keyword(s):  
High Resolution ◽  
Low Dose ◽  
Three Dimensional ◽  
Data Interpretation ◽  
Two Dimensional ◽  
Biological Objects ◽  
Density Maps ◽  
Density Map ◽  
Complex Crystal ◽  
High Resolution Microscopy

This tutorial will discuss the methodology of low dose electron diffraction and imaging of crystalline biological objects, the problems of data interpretation for two-dimensional projected density maps of glucose embedded protein crystals, the factors to be considered in combining tilt data from three-dimensional crystals, and finally, the prospects of achieving a high resolution three-dimensional density map of a biological crystal. This methodology will be illustrated using two proteins under investigation in our laboratory, the T4 DNA helix destabilizing protein gp32*I and the crotoxin complex crystal.

Instrumentation For Quantitative Microscopy

1977 ◽  
Vol 35 ◽  
pp. 206-209
Author(s):  
B. Ralph ◽  
A.R. Jones
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Automatic Data ◽  
Phase Volume Fraction ◽  
Statistical Confidence ◽  
Resultant Data ◽  
Automatic Data Collection ◽  
Third Dimension ◽  
Evolution Of Microstructure

In all fields of microscopy there is an increasing interest in the quantification of microstructure. This interest may stem from a desire to establish quality control parameters or may have a more fundamental requirement involving the derivation of parameters which partially or completely define the three dimensional nature of the microstructure. This latter categorey of study may arise from an interest in the evolution of microstructure or from a desire to generate detailed property/microstructure relationships. In the more fundamental studies some convolution of two-dimensional data into the third dimension (stereological analysis) will be necessary.In some cases the two-dimensional data may be acquired relatively easily without recourse to automatic data collection and further, it may prove possible to perform the data reduction and analysis relatively easily. In such cases the only recourse to machines may well be in establishing the statistical confidence of the resultant data. Such relatively straightforward studies tend to result from acquiring data on the whole assemblage of features making up the microstructure. In this field data mode, when parameters such as phase volume fraction, mean size etc. are sought, the main case for resorting to automation is in order to perform repetitive analyses since each analysis is relatively easily performed.

A linearity test for thick specimens imaged by HVEM over a 180° angular range

1991 ◽  
Vol 49 ◽  
pp. 552-553
Author(s):  
Yu Liu
Keyword(s):  
Phase Contrast ◽  
Three Dimensional ◽  
Angular Range ◽  
Two Dimensional ◽  
Back Projection ◽  
Line Integral ◽  
Exponential Law ◽  
Transmission Electron ◽  
Absorption Law ◽  
Linearity Test

The image obtained in a transmission electron microscope is the two-dimensional projection of a three-dimensional (3D) object. The 3D reconstruction of the object can be calculated from a series of projections by back-projection, but this algorithm assumes that the image is linearly related to a line integral of the object function. However, there are two kinds of contrast in electron microscopy, scattering and phase contrast, of which only the latter is linear with the optical density (OD) in the micrograph. Therefore the OD can be used as a measure of the projection only for thin specimens where phase contrast dominates the image. For thick specimens, where scattering contrast predominates, an exponential absorption law holds, and a logarithm of OD must be used. However, for large thicknesses, the simple exponential law might break down due to multiple and inelastic scattering.

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