A New Representation for the Green's Function of Multilayer Media Based on Plane Wave Expansion

2004 ◽  
Vol 52 (6) ◽  
pp. 1548-1557 ◽  
Author(s):  
M. Ayatollahi ◽  
S. Safavi-Naeini
Keyword(s):  
Plane Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Plane Wave Expansion ◽  
Wave Expansion ◽  
Multilayer Media

Fast plane-wave reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. S549-S556 ◽  
Author(s):  
Xiongwen Wang ◽  
Xu Ji ◽  
Hongwei Liu ◽  
Yi Luo
Keyword(s):  
Time Delay ◽  
Plane Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Time Domain ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Wave Source ◽  
Computation Cost ◽  
Time Migration

Plane-wave reverse time migration (RTM) could potentially provide quick subsurface images by migrating fewer plane-wave gathers than shot gathers. However, the time delay between the first and the last excitation sources in the plane-wave source largely increases the computation cost and decreases the practical value of this method. Although the time delay problem is easily overcome by periodical phase shifting in the frequency domain for one-way wave-equation migration, it remains a challenge for time-domain RTM. We have developed a novel method, referred as to fast plane-wave RTM (FP-RTM), to eliminate unnecessary computation burden and significantly reduce the computational cost. In the proposed FP-RTM, we assume that the Green’s function has finite-length support; thus, the plane-wave source function and its responding data can be wrapped periodically in the time domain. The wrapping length is the assumed total duration length of Green’s function. We also determine that only two period plane-wave source and data after the wrapping process are required for generating the outcome with adequate accuracy. Although the computation time for one plane-wave gather is twice as long as a normal shot gather migration, a large amount of computation cost is saved because the total number of plane-wave gathers to be migrated is usually much less than the total number of shot gathers. Our FP-RTM can be used to rapidly generate RTM images and plane-wave domain common-image gathers for velocity model building. The synthetic and field data examples are evaluated to validate the efficiency and accuracy of our method.

scholarly journals Harmonic analysis of lossy, piezoelectric composite transducers using the plane wave expansion method

Ultrasonics ◽  
2008 ◽  
Vol 48 (8) ◽  
pp. 652-663 ◽  
Author(s):  
Leigh-Ann Orr ◽  
Anthony J. Mulholland ◽  
Richard L. O’Leary ◽  
Gordon Hayward
Keyword(s):  
Plane Wave ◽  
Harmonic Analysis ◽  
Expansion Method ◽  
Piezoelectric Composite ◽  
Plane Wave Expansion ◽  
Plane Wave Expansion Method ◽  
Wave Expansion

Green's function of the Lord–Shulman thermo-poroelasticity theory

2020 ◽  
Vol 221 (3) ◽  
pp. 1765-1776 ◽  
Author(s):  
Jia Wei ◽  
Li-Yun Fu ◽  
Zhi-Wei Wang ◽  
Jing Ba ◽  
José M Carcione
Keyword(s):  
Plane Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Heterogeneous Media ◽  
Numerical Algorithms ◽  
Heat Diffusion ◽  
P Wave ◽  
Wave Analysis ◽  
S Wave ◽  
S Waves

SUMMARY The Lord–Shulman thermoelasticity theory combined with Biot equations of poroelasticity, describes wave dissipation due to fluid and heat flow. This theory avoids an unphysical behaviour of the thermoelastic waves present in the classical theory based on a parabolic heat equation, that is infinite velocity. A plane-wave analysis predicts four propagation modes: the classical P and S waves and two slow waves, namely, the Biot and thermal modes. We obtain the frequency-domain Green's function in homogeneous media as the displacements-temperature solution of the thermo-poroelasticity equations. The numerical examples validate the presence of the wave modes predicted by the plane-wave analysis. The S wave is not affected by heat diffusion, whereas the P wave shows an anelastic behaviour, and the slow modes present a diffusive behaviour depending on the viscosity, frequency and thermoelasticity properties. In heterogeneous media, the P wave undergoes mesoscopic attenuation through energy conversion to the slow modes. The Green's function is useful to study the physics in thermoelastic media and test numerical algorithms.

scholarly journals A q-linear analogue of the plane wave expansion

2013 ◽  
Vol 50 (3) ◽  
pp. 415-428 ◽  
Author(s):  
Luís Daniel Abreu ◽  
Óscar Ciaurri ◽  
Juan Luis Varona
Keyword(s):  
Plane Wave ◽  
Plane Wave Expansion ◽  
Wave Expansion
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