Attenuation of seismograms obtained by the Cagniard‐Pekeris method

Geophysics ◽  
1983 ◽  
Vol 48 (9) ◽  
pp. 1204-1211 ◽  
Author(s):  
P. G. Kelamis ◽  
E. R. Kanasewich ◽  
F. Abramovici
Keyword(s):  
Reflection Coefficient ◽  
Point Source ◽  
Frequency Domain ◽  
Elastic Medium ◽  
Half Space ◽  
Ad Hoc ◽  
Synthetic Seismograms ◽  
Weathered Layer ◽  
Attenuation And Dispersion

Attenuation and dispersion are included in synthetic seismograms obtained by a Cagniard‐Pekeris formulation for the problem of a point source in a layer over a half‐space. The solution is decompose into generalized rays, and the effects of attenuation and dispersion are incorporated in an ad hoc manner in the frequency domain. The effects of the viscoelastic interfaces are taken into account by corrections to the reflection coefficient for an elastic medium. The results are illustrated with synthetics for a model simulating a weathered layer over a halt‐space. Both the SH and P‐SV cases are treated.

Attenuation and dispersion phenomena of shear waves in anelastic and elastic porous strips

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Parvez Alam ◽  
Suprava Jena ◽  
Irfan Anjum Badruddin ◽  
Tatagar Mohammad Yunus Khan ◽  
Sarfaraz Kamangar
Keyword(s):  
Shear Wave ◽  
Half Space ◽  
Special Functions ◽  
Shear Waves ◽  
Finite Thickness ◽  
Dissipation Factor ◽  
Initial Stresses ◽  
Whittaker Functions ◽  
Content Type ◽  
Attenuation And Dispersion

Purpose This paper aims to study the attenuation and dispersion phenomena of shear waves in anelastic and elastic porous strips. Numerical investigations are performed for the phase and damped velocity profiles of the wave. For numerical computation purposes, water-saturated limestone and kerosene oil saturated sandstone for the first and second porous strips, respectively. Some other peculiarities have been observed and discussed. Design/methodology/approach Dispersion and attenuation characteristic of the shear wave propagations have been studied in an inhomogeneous poro-anelastic strip of finite thickness, which is clamped between an inhomogeneous poroelastic strip of finite thickness and an elastic half-space. Both the strips are initially stressed and the half-space is self-weighted. Analytical methods are used to calculate the interior deformations of the model with the involvement of special functions. The determination of the frequency equation, which includes the Bessel’s and Whittaker functions, has been obtained using the prescribed boundary conditions. Findings Impacts of attenuation coefficient, dissipation factor, inhomogeneities, initial stresses, Biot’s gravity, porosity and thickness ratio parameters on the velocity profile of the wave have been demonstrated through the graphical visuals. These parameters are playing an important role and working as a catalyst in affecting the propagation behaviour of the wave. Originality/value Inclusion of the concept of doubly layered initially stressed inhomogeneous porous structure of elastic and anelastic medium bedded over a self-weighted half-space medium brings a novelty to the existing literature related to the study of shear wave. It may be helpful to geologists, seismologists and structural engineers in the development of theoretical and practical studies.

Boundary conditions for the numerical solution of wave propagation problems

Geophysics ◽  
1978 ◽  
Vol 43 (6) ◽  
pp. 1099-1110 ◽  
Author(s):  
Albert C. Reynolds
Keyword(s):  
Wave Propagation ◽  
Reflection Coefficient ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Synthetic Seismograms ◽  
Neumann Boundary Conditions ◽  
Numerical Calculations ◽  
Reflection Coefficients

Many finite difference models in use for generating synthetic seismograms produce unwanted reflections from the edges of the model due to the use of Dirichlet or Neumann boundary conditions. In this paper we develop boundary conditions which greatly reduce this edge reflection. A reflection coefficient analysis is given which indicates that, for the specified boundary conditions, smaller reflection coefficients than those obtained for Dirichlet or Neumann boundary conditions are obtained. Numerical calculations support this conclusion.

scholarly journals Surface waves in multilayered elastic media I. Rayleigh and Love waves from buried sources in a multilayered elastic half-space

1964 ◽  
Vol 54 (2) ◽  
pp. 627-679
Author(s):  
David G. Harkrider
Keyword(s):  
Surface Waves ◽  
Frequency Domain ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Half Space ◽  
Love Waves ◽  
Displacement Fields ◽  
Matrix Formulation ◽  
Total Displacement ◽  
Rayleigh And Love Waves

ABSTRACT A matrix formulation is used to derive integral expressions for the time transformed displacement fields produced by simple sources at any depth in a multilayered elastic isotropic solid half-space. The integrals are evaluated for their residue contribution to obtain surface wave displacements in the frequency domain. The solutions are then generalized to include the effect of a surface liquid layer. The theory includes the effect of layering and source depth for the following: (1) Rayleigh waves from an explosive source, (2) Rayleigh waves from a vertical point force, (3) Rayleigh and Love waves from a vertical strike slip fault model. The latter source also includes the effect of fault dimensions and rupture velocity. From these results we are able to show certain reciprocity relations for surface waves which had been previously proved for the total displacement field. The theory presented here lays the ground work for later papers in which theoretical seismograms are compared with observations in both the time and frequency domain.

ELECTRIC POTENTIAL NEAR A SPHERICAL BODY IN A CONDUCTING HALF‐SPACE

Geophysics ◽  
1971 ◽  
Vol 36 (4) ◽  
pp. 763-767 ◽  
Author(s):  
David B. Large
Keyword(s):  
Point Source ◽  
Electric Current ◽  
Half Space ◽  
Electric Potential ◽  
Spherical Body ◽  
Classical Potential

An extensive summary of classical potential solutions has been given recently by Van Nostrand and Cook (1966). This note presents a solution for the potential due to a point source of electric current placed on the earth’s surface in the vicinity of a buried spherical body of arbitrary resistivity. The analysis follows the procedure suggested by Van Nostrand and Cook and is similar to that used recently by Merkel (1969, 1971).

On: “Correction of topographic distortions in potential‐field data: A fast and accurate approach” by Jianghai Xia, Donald R. Sprowl, and Dana Adkins‐Heljeson (April 1993 GEOPHYSICS, p. 515–523).

Geophysics ◽  
1993 ◽  
Vol 58 (12) ◽  
pp. 1874-1874
Author(s):  
David A. Chapin
Keyword(s):  
Point Source ◽  
Frequency Domain ◽  
Potential Field ◽  
Field Data ◽  
New Method ◽  
Potential Fields ◽  
Potential Field Data ◽  
Source Method ◽  
Equivalent Point ◽  
Breakthrough Technology

Xia et al. do an excellent job developing a new method for using the equivalent point source method in the frequency domain. The transformation from a varying datum to flat datum has always been a major problem in potential fields data. This is because the existing methods to perform this transformation have tended to be cumbersome, time‐consuming, and expensive. I congratulate the authors for this breakthrough technology.

Reflection Coefficient for Plane Waves in a Fluid Incident on a Layered Elastic Half-Space

1983 ◽  
Vol 50 (2) ◽  
pp. 405-414 ◽  
Author(s):  
D. B. Bogy ◽  
S. M. Gracewski
Keyword(s):  
Reflection Coefficient ◽  
Half Space ◽  
Plane Waves ◽  
Elastic Half Space ◽  
Wave Number ◽  
Solid Boundary ◽  
Inviscid Fluid ◽  
Interface Waves ◽  
Plate Models ◽  
Layered Solid

The reflection coefficient is derived for an isotropic, homogeneous elastic layer of arbitrary thickness that is perfectly bonded to such an elastic half-space of a different material for the case when plane waves are incident from an inviscid fluid onto the layered solid. The derived function is studied analytically by considering several limiting cases of geometry and materials to recover previously known results. Approximate reflection coefficents are then derived using various plate models for the layer to obtain simpler expressions that are useful for small values of σd, where σ is the wave number and d is the layer thickness. Numerical results based on all the models for the propagation of interface waves localized near the fluid-solid boundary are obtained and compared. These results are also compared with some previously published experimental measurements.

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