Ray-synthetic seismograms for SH waves in anelastic media

1980 ◽  
Vol 70 (1) ◽  
pp. 29-46
Author(s):  
E. S. Krebes ◽  
F. Hron
Keyword(s):  
Plane Waves ◽  
Synthetic Seismograms ◽  
Body Waves ◽  
Plane Boundary ◽  
Theory Approach ◽  
Reflection And Transmission ◽  
Sh Waves ◽  
Transmission Coefficients ◽  
Mathematical Properties ◽  
Crustal Model

abstract The linear theory of viscoelasticity is used to study the effects of anelasticity on SH body waves propagating through a layered medium. The mathematical properties of SH waves in a viscoelastic medium are outlined. Reflection and transmission coefficients for SH plane waves impinging upon a plane boundary separating two anelastic media are calculated and compared with the coefficients for the perfectly elastic case. Synthetic seismograms for teleseismic SH body waves are computed for a plane-layered crustal model in both the elastic and anelastic cases, using a ray theory approach.

A method for calculating synthetic seismograms which include the effects of absorption and dispersion

Geophysics ◽  
1981 ◽  
Vol 46 (8) ◽  
pp. 1100-1107 ◽  
Author(s):  
D. C. Ganley
Keyword(s):  
Communication Theory ◽  
Plane Waves ◽  
Complex Function ◽  
Synthetic Seismograms ◽  
Theory Approach ◽  
Reflection And Transmission ◽  
Usual Model ◽  
Transmission Coefficients ◽  
Complex Functions ◽  
Absorption And Dispersion

A method is outlined for the calculation of synthetic seismograms which include the effects of absorption and dispersion. The absorption model used is the usual model of exponential decay of amplitude with distance given by [Formula: see text], where α is a linear function of frequency. This attenuation is accounted for mathematically by allowing the elastic modulus to be a complex function of frequency. This results in a complex velocity and wavenumber, and the reflection and transmission coefficients also become complex functions of frequency. The method is based upon the communication theory approach and is applicable to plane waves in a flat layered model. The source can be placed at an arbitrary depth. The equations are outlined in detail for a particular absorption‐dispersion pair taken from Futterman (1962). An example with a surface synthetic seismogram and synthetic traces at several depths is presented.

Determination of crustal thickness from spectral behavior of SH waves

1969 ◽  
Vol 59 (3) ◽  
pp. 1247-1258
Author(s):  
Abou-Bakr K. Ibrahim
Keyword(s):  
Amplitude Spectrum ◽  
Body Waves ◽  
Multiple Reflections ◽  
Matrix Formulation ◽  
Sh Waves ◽  
Crustal Model ◽  
Amplitude Spectra ◽  
Phase Spectra ◽  
Zero Phase

abstract The amplitude spectrum obtained from Haskell's matrix formulation for body waves travelling through a horizontally layered crustal model shows a sequence of minima and maxima. It is known that multiple reflections within the crustal layers produce constructive and destructive interferences, which are shown as maxima and minima in the amplitude spectrum. Analysis of the minima in the amplitude spectra, which correspond to zero phase in the phase spectra, enables us to determine the thickness of the crust, provided the ratio of wave velocity in the crust to velocity under the Moho is known.

Reflection and Transmission Coefficients of Plane Waves in Magnetoelectroelastic Layered Structures

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
J. Y. Chen ◽  
H. L. Chen ◽  
E. Pan
Keyword(s):  
Piezoelectric Materials ◽  
Plane Waves ◽  
Layered Structures ◽  
Organic Glass ◽  
Reflection And Transmission Coefficients ◽  
Material Structure ◽  
Layered System ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Novel Material

Reflection and transmission coefficients of plane waves with oblique incidence to a multilayered system of piezomagnetic and/or piezoelectric materials are investigated in this paper. The general Christoffel equation is derived from the coupled constitutive and balance equations, which is further employed to solve the elastic displacements and electric and magnetic potentials. Based on these solutions, the reflection and transmission coefficients in the corresponding layered structures are subsequently obtained by virtue of the propagator matrix method. Two layered examples are selected to verify and illustrate our solutions. One is the purely elastic layered system composed of aluminum and organic glass materials. The other layered system is composed of the novel magnetoelectroelastic material and the organic glass. Numerical results are presented to demonstrate the variation of the reflection and transmission coefficients with different incident angles, frequencies, and boundary conditions, which could be useful to nondestructive evaluation of this novel material structure based on wave propagations.

Body waves in a “real Earth”. Part I

1973 ◽  
Vol 63 (1) ◽  
pp. 145-156 ◽  
Author(s):  
A. Cisternas ◽  
O. Betancourt ◽  
A. Leiva
Keyword(s):  
Exact Solution ◽  
Theoretical Analysis ◽  
Power Series ◽  
Arbitrary Number ◽  
Body Waves ◽  
Reflection And Transmission Coefficients ◽  
Earth Model ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Earth

abstract A theoretical analysis of body waves in a “real Earth” is presented. The earth model consists of an arbitrary number of spherical liquid and solid layers. The algebraic part of the analysis deals with the way to obtain generalized rays out of the exact solution. It is shown that the Rayleigh matrix, and not the Rayleigh determinant, should be used to expand the solution into a power series of modified reflection and transmission coefficients in order to obtain rays.

The effect of boundaries on wave propagation in a liquid-filled porous solid: III. Reflection of plane waves at a free plane boundary (general case)

1962 ◽  
Vol 52 (3) ◽  
pp. 595-625 ◽  
Author(s):  
H. Deresiewicz ◽  
J. T. Rice
Keyword(s):  
Electromagnetic Waves ◽  
Plane Waves ◽  
Body Waves ◽  
Porous Solid ◽  
Plane Boundary ◽  
Field Equations ◽  
Attenuation Coefficients ◽  
Reflected Waves ◽  
Three Body ◽  
Analytical Expressions

abstract A general solution is derived of Biot's field equations governing small motions of a porous solid saturated with a viscous liquid. The solution is then employed to study some of the phenomena attendant upon the reflection from a plane, traction-free boundary of each of the three body waves predicted by the equations. The problem, though more complex, bears some similarity to that of electromagnetic waves in a conducting medium, in that some of the reflected waves are inhomogeneous, planes of constant amplitude not coinciding with planes of constant phase. Analytical expressions are displayed for the phase velocities, attenuation coefficients, angles of reflection and the amplitude ratios, and explicit formulas are given for the limiting cases of low and high frequencies, representing first-order corrections for porosity of the solid and viscosity of the liquid, respectively. The paper concludes with a presentation of results of numerical calculations pertinent to a kerosene-saturated sandstone.

REFLECTION AND TRANSMISSION COEFFICIENTS FOR PLANE WAVES IN ELASTIC MEDIA

Geophysics ◽  
1940 ◽  
Vol 5 (2) ◽  
pp. 115-148 ◽  
Author(s):  
M. Muskat ◽  
M. W. Meres
Keyword(s):  
Incident Energy ◽  
Plane Waves ◽  
Total Reflection ◽  
Interfacial Velocity ◽  
Reflection And Transmission ◽  
Transverse Waves ◽  
Longitudinal Waves ◽  
Transmission Coefficients ◽  
Elastic Interfaces ◽  
Density Ratios

The results are given of a systematic series of calculations on the coefficients of reflection and transmission for plane waves incident on elastic interfaces. Tables are given for the amplitudes of the reflected and transmitted longitudinal and transverse waves, for the intensities of these components, and for the fractions of the incident energy carried away by them. For incident longitudinal waves calculations were carried out for angles of incidence between 0 and 30 with 5° intervals. For incident transverse waves polarized in the plane of incidence results are given for four angles of incidence up to approximately 16°. For incident transverse waves polarized normal to the plane of incidence the calculations were carried through for all angles of incidence—in steps of 5°—up to total reflection. All the calculations were carried through for interfacial density ratios of 0.7 to 1.3 in steps of 0.1, and interfacial velocity ratios between 0.5 and 2.0 in steps of 0.25.

Body waves as normal and leaking modes. Part I: Introduction

1967 ◽  
Vol 57 (2) ◽  
pp. 191-198
Author(s):  
J. Cl. De Bremaecker
Keyword(s):  
Rayleigh Waves ◽  
Fourier Transformation ◽  
Normal Modes ◽  
Synthetic Seismograms ◽  
Body Waves ◽  
Apparent Velocity ◽  
S Wave ◽  
Sh Waves ◽  
P And Sv Waves ◽  
Method Of Residues

abstract Realistic artificial seismograms may be computed by considering body waves as sums of normal or leaking modes of surface waves: the S wave and those arriving after S may be considered as sums of higher normal modes of Rayleigh waves (RiN) and Love waves (LiN); in this case the apparent velocity c < βn. Earlier arrivals are generally due to the first kind of leaking modes of Rayleigh waves (RiL1) for which βn < c < αn. Deep reflections in seismic prospecting are RiL2 for which c > αn. Synthetic seismograms can be computed by double Fourier transformation in those two last cases. Alternately the method of residues followed by a single Fourier (or Laplace) transformation may be used in all cases. Earth-stretching approximations should give excellent results for SH waves and may give satisfactory results for P and SV waves.

scholarly journals A trace formula for schrödinger operators with step potentials

1982 ◽  
Vol 24 (2) ◽  
pp. 138-159 ◽  
Author(s):  
D. M. O'Brien
Keyword(s):  
Compact Support ◽  
Plane Waves ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Step Potential ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Simple Step ◽  
Infinitely Differentiable Function

AbstractThis paper shows how to compute the trace of G(T) – G(T0), where G is an infinitely differentiable function with compact support, and where T and T0 are one-dimensional Schrödinger operators on (−∞, ∞) with potentials q and q0. It is assumed that q0 is a simple step potential and that q decays exponentially to q0. The trace is expressed in terms of the reflection and transmission coefficients for the scattering of plane waves by the potential q.

Sign in / Sign up

Export Citation Format

Share Document