ABSTRACT

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.

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