A Fourth-Order Compact Numerical Scheme for Three-Dimensional Acoustic Wave Equation with Variable Velocity

2018 ◽  
pp. 279-289
Author(s):  
Wenyuan Liao ◽  
Ou Wei
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Fourth Order ◽  
Numerical Scheme ◽  
Three Dimensional ◽  
Variable Velocity ◽  
Acoustic Wave Equation

Obtaining three‐dimensional velocity information directly from reflection seismic data: An inverse scattering formalism

Geophysics ◽  
1981 ◽  
Vol 46 (8) ◽  
pp. 1116-1120 ◽  
Author(s):  
A. B. Weglein ◽  
W. E. Boyse ◽  
J. E. Anderson
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Inverse Scattering ◽  
Seismic Data ◽  
A Priori ◽  
Three Dimensional ◽  
Quantum Scattering ◽  
Acoustic Wave Equation ◽  
Reflection Seismic ◽  
The One

We present a formalism for obtaining the subsurface velocity configuration directly from reflection seismic data. Our approach is to apply the results obtained for inverse problems in quantum scattering theory to the reflection seismic problem. In particular, we extend the results of Moses (1956) for inverse quantum scattering and Razavy (1975) for the one‐dimensional (1-D) identification of the acoustic wave equation to the problem of identifying the velocity in the three‐dimensional (3-D) acoustic wave equation from boundary value measurements. No a priori knowledge of the subsurface velocity is assumed and all refraction, diffraction, and multiple reflection phenomena are taken into account. In addition, we explain how the idea of slant stack in processing seismic data is an important part of the proposed 3-D inverse scattering formalism.

NUMERICAL SOLUTION OF THE ACOUSTIC WAVE EQUATION AT THE LIMIT BETWEEN NEAR AND FAR FIELD PROPAGATION

2001 ◽  
Vol 12 (10) ◽  
pp. 1497-1507 ◽  
Author(s):  
ERICH STOLL ◽  
STEFAN DANGEL
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Seismic Waves ◽  
Near Field ◽  
Three Dimensional ◽  
Low Frequency ◽  
Far Field ◽  
Acoustic Wave Equation ◽  
Sound Sources ◽  
Continuous Waves

The acoustic wave equation is solved numerically for two and three-dimensional systems at the limit between near and far field propagation. Our results show that for large sound velocities, corresponding to wavelengths larger than the system, near field properties are dominant. When the near field conditions are no longer satisfied, standing waves close to the sound emitters and interference patterns between the near field and far field solutions appear. Our procedure is applied to sound sources, which broadcast coherent and continuous waves as well as to sources emitting bursts of incoherent and uncorrelated waves. Both cases can be used to simulate the spreading of low frequency seismic waves observed close to volcanoes and hydrocarbon reservoirs.

Three-dimensional acoustic wave equation modeling based on the optimal finite-difference scheme

2015 ◽  
Vol 12 (3) ◽  
pp. 409-420 ◽  
Author(s):  
Xiao-Hui Cai ◽  
Yang Liu ◽  
Zhi-Ming Ren ◽  
Jian-Min Wang ◽  
Zhi-De Chen ◽  
...  
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Three Dimensional ◽  
Equation Modeling ◽  
Acoustic Wave Equation
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