A novel spherical polar finite element for the solution of the steady-state scalar wave equation in three-dimensions

1981 ◽  
Vol 9 (1) ◽  
pp. 33-51 ◽  
Author(s):  
B. Nath
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Steady State ◽  
Three Dimensions ◽  
Scalar Wave ◽  
Scalar Wave Equation

INTEGRAL FORMULATION FOR MIGRATION IN TWO AND THREE DIMENSIONS

Geophysics ◽  
1978 ◽  
Vol 43 (1) ◽  
pp. 49-76 ◽  
Author(s):  
William A. Schneider
Keyword(s):  
Wave Equation ◽  
Transfer Functions ◽  
Mathematical Formulation ◽  
Three Dimensions ◽  
Scalar Wave ◽  
Surface Integral ◽  
Seismic Section ◽  
Scalar Wave Equation ◽  
Seismic Image ◽  
Recorded Data

Computer migration of seismic data emerged in the late 1960s as a natural outgrowth of manual migration techniques based on wavefront charts and diffraction curves. Summation (integration) along a diffraction hyperbola was recognized as a way to automate the familiar point‐to‐point coordinate transformation performed by interpreters in mapping reflections from the x, t (traveltime) domain into the x, z (depth domain). We will discuss the mathematical formulation of migration as a solution to the scalar wave equation in which surface seismic observations are the known boundary values. Solution of this boundary value problem follows standard techniques, and the migrated image is expressed as a surface integral over the known seismic observations when areal or 3-D overage exists. If only 2-D seismic coverage is available, wave equation migration is still possible by assuming the subsurface and hence surface recorded data do not vary perpendicular to the seismic profile. With this assumption, the surface integral reduces to a line integral over the seismic section, suitably modified to account for the implicit broadside integral. Neither the 2-D or 3-D integral migration algorithms require any approximation to the scalar wave equation. The only limitations imposed are those of space and time sampling, and accurate knowledge of the velocity field. Migration can also be viewed as a downward continuation operation which transforms surface recorded data to a deeper hypothetical recording surface. This transformation is convolutional in nature and the transfer functions in both two and three dimensions are developed and discussed in terms of their characteristic properties. Simple analytic and computer model data are migrated to illustrate the basic properties of migration and the fidelity of the integral method. Finally, applications of these algorithms to field data in both two and three dimensions are presented and discussed in terms of their impact on the seismic image.

Consistent Infinitesimal Finite Element Cell Method: Three-Dimensional Scalar Wave Equation

1996 ◽  
Vol 63 (3) ◽  
pp. 650-654 ◽  
Author(s):  
J. P. Wolf ◽  
Chongmin Song
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Three Dimensional ◽  
Time Domain Analysis ◽  
Spatial Dimension ◽  
Element Formulation ◽  
Scalar Wave ◽  
Scalar Wave Equation ◽  
Cell Method ◽  
Unbounded Medium

To calculate the unit-impulse response matrix of an unbounded medium governed by the scalar wave equation for use in a time-domain analysis of unbounded medium-structure interaction, the consistent infinitesimal finite element cell method is developed for the three-dimensional case. Its derivation is based on the finite element formulation and on similarity. The discretization is only performed on the structure-medium interface, yielding a reduction of the spatial dimension by 1. The procedure is exact in the radial direction and converges to the exact solution in the finite element sense in the circumferential directions.

Seismic scalar wave equation with variable coefficients modeling by a new convolutional differentiator

2010 ◽  
Vol 181 (11) ◽  
pp. 1850-1858 ◽  
Author(s):  
Xiaofan Li ◽  
Tong Zhu ◽  
Meigen Zhang ◽  
Guihua Long
Keyword(s):  
Wave Equation ◽  
Variable Coefficients ◽  
Scalar Wave ◽  
Scalar Wave Equation

scholarly journals MOTION OF MASSIVE AND MASSLESS TEST PARTICLES IN DYADOSPHERE GEOMETRY

2009 ◽  
Vol 24 (16) ◽  
pp. 1277-1287 ◽  
Author(s):  
B. RAYCHAUDHURI ◽  
F. RAHAMAN ◽  
M. KALAM ◽  
A. GHOSH
Keyword(s):  
Wave Equation ◽  
Test Particle ◽  
Massless Particle ◽  
Jacobi Method ◽  
Scalar Wave ◽  
Scalar Wave Equation ◽  
Test Particles

Motion of massive and massless test particle in equilibrium and nonequilibrium case is discussed in a dyadosphere geometry through Hamilton–Jacobi method. Scalar wave equation for massless particle is analyzed to show the absence of superradiance in the case of dyadosphere geometry.

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