Prevailing-frequency approximation of the coupling ray theory for electromagnetic waves or elastic S waves

Abstract

The coupling-ray-theory tensor Green function for electromagnetic waves or elastic S waves is frequency dependent, and is usually calculated for many frequencies. This frequency dependence represents no problem in calculating the Green function, but may represent a great problem in storing the Green function at the nodes of dense grids, typical for applications such as the Born approximation. This paper is devoted to the approximation of the coupling-ray-theory tensor Green function, which practically eliminates this frequency dependence within a reasonably broad frequency band.In the vicinity of a given prevailing frequency, we approximate the frequencydependent frequency-domain coupling-ray-theory tensor Green function by two dyadic Green functions corresponding to two waves described by their travel times and amplitudes calculated for the prevailing frequency. We refer to these travel times and amplitudes as the coupling-ray-theory travel times and the coupling-ray-theory amplitudes. This "prevailing-frequency approximation" of the coupling ray theory for electromagnetic waves or elastic S waves allows us to process the coupling-raytheory wave field in the same way as the anisotropic-ray-theory wave field. This simplification may be decisive when storing the tensor Green function at the nodes of dense grids, which is typical for applications such as the Born approximation.We test the accuracy of the proposed prevailing-frequency approximation of the coupling ray theory numerically using elastic S waves in eight anisotropic velocity models. The additional inaccuracy introduced by the prevailing-frequency approximation is smaller than the inaccuracy of the standard frequency-domain coupling ray theory, and smaller than the additional inaccuracy introduced by many other approximations of the coupling ray theory.K e y wo r d s :

Interpolation of the coupling-ray-theory Green function within ray cells

“…The density is constant. For a sketch of the source-receiver configuration refer to Klimeš and Bulant (2016, Fig. 1).…”

“…We plot the relative coupling-ray-theory travel-time difference (half the relative coupling-ray-theory travel-time splitting) d = |D/τ | in the vertical rectangular section bounded by the point source from the left, and by the vertical well from the right (Klimeš and Bulant, 2012, Fig. 1 ; 2016, Fig.…”

“…Its slowness surface contains a split intersection singularity, whereas velocity models QIH, QI, QI2 and QI4 display no exact or split intersection singularity (Pšenčík et al 2012 ). Refer to Klimeš and Bulant (2016) for a more detailed discussion. The relative coupling-ray-theory travel-time difference d = |D/τ | in the vertical source-receiver section is displayed in Fig.…”

Transformation of spatial and perturbation derivatives of travel time at a curved interface between two arbitrary media

“…In smooth media, the third-order and higher-order spatial derivatives of travel time and all perturbation derivatives of travel time can be calculated along the unperturbed rays by simple numerical quadratures using the equations derived by Klimeš (2002a). These equations have already found various applications (Duchkov and Goldin, 2001 ;Klimeš, 2002bKlimeš, , 2006Klimeš, , 2013Klimeš, 2002, 2008 ;Goldin and Duchkov, 2003 ;Klimeš and Bulant, 2004, 2006, 2012, 2015Červený et al, 2008 ;Červený and Pšenčík, 2009 ;Klimeš and Klimeš, 2011 ;Shekar and Tsvankin, 2014 ;Zheng, 2010 ), and it is desirable to extend the equations and their applications to media composed of layers and blocks separated by smooth curved interfaces. The perturbation derivatives are especially important for the coupling ray theory and for travel-time inversion.…”

Determination of the reference symmetry axis of a generally anisotropic medium which is approximately transversely isotropic

“…The coupling ray theory (Coates and Chapman, 1990 ;Bulant and Klimeš, 2002 ;Klimeš and Bulant, 2012 ) is usually applied to common anisotropic rays (Bakker, 2002 ;Bulant, 2004, 2006 ;Klimeš, 2006 ;Bulant and Klimeš, 2008 ). However, the coupling ray theory is more accurate if it is applied to reference rays which are closer to the actual S-wave paths Bulant, 2014a, 2015 ).…”