Green’s Function of an Integrated Optical Directional Coupler by Plane-Wave-Spectrum Approach

1987 ◽  
Vol 16 (4) ◽  
pp. 98-101
Author(s):  
T. K. Sen ◽  
A. Basuray ◽  
A. K. Datta
Keyword(s):  
Plane Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Directional Coupler ◽  
Wave Spectrum ◽  
Integrated Optical

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.

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 Tutorial on seismic interferometry: Part 1 — Basic principles and applications

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. 75A195-75A209 ◽  
Author(s):  
Kees Wapenaar ◽  
Deyan Draganov ◽  
Roel Snieder ◽  
Xander Campman ◽  
Arie Verdel
Keyword(s):  
Surface Wave ◽  
Plane Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Ambient Noise ◽  
Source Function ◽  
Stationary Points ◽  
Seismic Interferometry ◽  
Direct Wave ◽  
Reflected Wave

Seismic interferometry involves the crosscorrelation of responses at different receivers to obtain the Green’s function between these receivers. For the simple situation of an impulsive plane wave propagating along the [Formula: see text]-axis, the crosscorrelation of the responses at two receivers along the [Formula: see text]-axis gives the Green’s function of the direct wave between these receivers. When the source function of the plane wave is a transient (as in exploration seismology) or a noise signal (as in passive seismology), then the crosscorrelation gives the Green’s function, convolved with the autocorrelation of the source function. Direct-wave interferometry also holds for 2D and 3D situations, assuming the receivers are surrounded by a uniform distribution of sources. In this case, the main contributions to the retrieved direct wave between the receivers come from sources in Fresnel zones around stationary points. The main application of direct-wave interferometry is theretrieval of seismic surface-wave responses from ambient noise and the subsequent tomographic determination of the surface-wave velocity distribution of the subsurface. Seismic interferometry is not restricted to retrieving direct waves between receivers. In a classic paper, Claerbout shows that the autocorrelation of the transmission response of a layered medium gives the plane-wave reflection response of that medium. This is essentially 1D reflected-wave interferometry. Similarly, the crosscorrelation of the transmission responses, observed at two receivers, of an arbitrary inhomogeneous medium gives the 3D reflection response of that medium. One of the main applications of reflected-wave interferometry is retrieving the seismic reflection response from ambient noise and imaging of the reflectors in the subsurface. A common aspect of direct- and reflected-wave interferometry is that virtual sources are created at positions where there are only receivers without requiring knowledge of the subsurface medium parameters or of the positions of the actual sources.

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