The dynamically correct Poynting vector for acoustic media with application in calculating multidirectional-propagation vectors to produce angle gathers from reverse time migration

Author(s):  
Chen Tang ◽  
George A. McMechan
Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. S365-S374 ◽  
Author(s):  
Chen Tang ◽  
George A. McMechan

The Poynting vector (PV) has been widely used to calculate propagation vectors of a pressure field (PF) in acoustic media. The most widely used acoustic PV formula is the negative of a product of the time and space derivatives. These two derivatives result in a phase shift between the PF and its PV; particularly, for a PF at a local magnitude peak, the PV modulus is zero and thus the propagation direction there is undefined. This “zero-modulus” issue is not consistent with the physical definition of the PV, which is the directional energy flux density of a PF because this definition indicates that the variation of the PV modulus should be consistent with the PF magnitude. This PV is only considered as kinematically correct and defined as K-PV. We derive the dynamically correct PV (D-PV) formula for acoustic media, which is the negative of the product of the reciprocal of the density, the PF itself, and a factor that is obtained by applying a time integration and a space derivative to the PF. There are two derivations. One uses the slowness vector, and the other is by simplifying the elastic PV. This D-PV does not suffer from the zero-modulus problem, and we also use it to update the multidirectional PV (MPV), which produces a D-MPV. Two strategies are provided to reduce the computational complexity of the time integration in the D-PV formula. Because the MPV already involves Fourier transforms between the time and frequency domains (which facilitates implementation of the time integration), its updated version causes only a very minor increase in the computational complexity of the original one. Numerical examples indicate that the D-PV provides more reliable propagation vectors than the K-PV, and the D-MPV provides more accurate angle-domain common-image gathers from reverse time migration of acoustic media than the K-MPV.


2013 ◽  
Author(s):  
Edvaldo S. Araujo ◽  
Reynam C. Pestana ◽  
Adriano W. G. dos Santos

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. S359-S376 ◽  
Author(s):  
Chen Tang ◽  
George A. McMechan

Because receiver wavefields reconstructed from observed data are not as stable as synthetic source wavefields, the source-propagation vector and the reflector normal have often been used to calculate angle-domain common-image gathers (ADCIGs) from reverse time migration. However, the existing data flows have three main limitations: (1) Calculating the propagation direction only at the wavefields with maximum amplitudes ignores multiarrivals; using the crosscorrelation imaging condition at each time step can include the multiarrivals but will result in backscattering artifacts. (2) Neither amplitude picking nor Poynting-vector calculations are accurate for overlapping wavefields. (3) Calculating the reflector normal in space is not accurate for a structurally complicated reflection image, and calculating it in the wavenumber ([Formula: see text]) domain may give Fourier truncation artifacts. We address these three limitations in an improved data flow with two steps: During imaging, we use a multidirectional Poynting vector (MPV) to calculate the propagation vectors of the source wavefield at each time step and output intermediate source-angle-domain CIGs (SACIGs). After imaging, we use an antitruncation-artifact Fourier transform (ATFT) to convert SACIGs to ADCIGs in the [Formula: see text]-domain. To achieve the new flow, another three innovative aspects are included. In the first step, we develop an angle-tapering scheme to remove the Fourier truncation artifacts during the wave decomposition (of MPV) while preserving the amplitudes, and we use a wavefield decomposition plus angle-filter imaging condition to remove the backscattering artifacts in the SACIGs. In the second step, we compare two algorithms to remove the Fourier truncation artifacts that are caused by the plane-wave assumption. One uses an antileakage FT (ALFT) in local windows; the other uses an antitruncation-artifact FT, which relaxes the plane-wave assumption and thus can be done for the global space. The second algorithm is preferred. Numerical tests indicate that this new flow (source-side MPV plus ATFT) gives high-quality ADCIGs.


Geophysics ◽  
2009 ◽  
Vol 74 (3) ◽  
pp. S57-S66 ◽  
Author(s):  
J. C. Costa ◽  
F. A. Silva Neto ◽  
M. R. Alcântara ◽  
J. Schleicher ◽  
A. Novais

The quality of seismic images obtained by reverse time migration (RTM) strongly depends on the imaging condition. We propose a new imaging condition that is motivated by stationary phase analysis of the classical crosscorrelation imaging condition. Its implementation requires the Poynting vector of the source and receiver wavefields at the imaging point. An obliquity correction is added to compensate for the reflector dip effect on amplitudes of RTM. Numerical experiments show that using an imaging condition with obliquity compensation improves reverse time migration by reducing backscattering artifacts and improving illumination compensation.


2013 ◽  
Author(s):  
Edvaldo S. Araujo ◽  
Reynam C. Pestana ◽  
Adriano W. G. dos Santos

Geophysics ◽  
2014 ◽  
Vol 79 (5) ◽  
pp. S163-S172 ◽  
Author(s):  
Edvaldo S. Araujo ◽  
Reynam C. Pestana ◽  
Adriano W. G. dos Santos

2006 ◽  
Vol 37 (1) ◽  
pp. 102-107 ◽  
Author(s):  
Kwangjin Yoon ◽  
Kurt J. Marfurt

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