Comparison of the FORT approximation of the coupling ray theory with the Fourier pseudospectral method

Ivan Psencik Veronique Farra and Ekkehart Tessmer


The standard ray theory (RT) for inhomogeneous anisotropic media does not work properly or even fails when applied to S-wave propagation in inhomogeneous weakly aniso-tropic media or in the vicinity of shear-wave singularities. In both cases, the two shear waves propagate with similar phase velocities. The coupling ray theory was proposed to avoid this problem. In it, amplitudes of the two S waves are computed by solving two coupled, frequency-dependent differential equations along a common S-wave ray. In this paper, we test the recently developed approximation of coupling ray theory (CRT) based on the common S-wave rays obtained by first-order ray tracing (FORT). As a reference, we use the Fourier pseudospectral method (FM), which does not suffer from the limitations of the ray method and yields very accurate results. We study the behaviour of shear waves in weakly anisotropic media as well as in the vicinity of an intersection, kiss or conical singularities. By comparing CRT and RT results with results of the FM, we demonstrate the clear superiority of CRT over RT in the mentioned regions as well as the dangers of using RT there.

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In: Seismic Waves in Complex 3-D Structures, Report 21, pp. 129-165, Dep. Geophys., Charles Univ., Prague, 2011.