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

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 anisotropic 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 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.     

P-wave traveltime and polarization tomography of VSP data

The presence of anisotropy requires that tomographic methods be generalized to account for anisotropy. This generalization allows geological structure to be correctly imaged and allows the anisotropic parameters to be estimated. Use of isotropic inversion for imaging anisotropic structures gives systematic trends in the traveltime and polarization residuals. However, due to the limited directional coverage, the traveltimes along may not be sufficient to study the anisotropic properties of the structure. Polarizations can provide independent information on the structure. Traveltime and polarization inversion are applied to synthetic examples simulating VSP experiments. Transverse isotropy and 1-D structure are assumed. Plots of traveltime and polarization residuals are an important tool to detect the anomalies due to the presence of anisotropy. For receivers located in anisotropic layers, polarization residuals display consistent anomalies of several degrees. The synthetic examples show that even the simple 1-D problem is difficult, when using direct arrivals only. Large a posteriori errors in anisotropic parameters are obtained by traveltime inversion in layers where available incidence angles are less than 45°. Resolution of the tomographic image of VSP data is greatly improved by a combination of traveltime and polarization information. In order to obtain accurate inversion results, the measurement error of polarization data should be kept to within a few degrees.     

Improved First-Order Approximation of Group Velocities in Weakly Anisotropic Media

A first-order approximation of the group velocity is derived for qP and qS waves in weakly anisotropic media. The formula gives an explicit expression of the group velocity in terms of elastic parameters and wave normal and is independent of any reference isotropic media. The approximated group velocity differs from the first order phase velocity in direction and in magnitude, the difference being of the first order in direction and the second order in magnitude. The accuracy of the approximate formula is tested on two examples of TI media. The formula well approximates the qS-waves group velocity surface even in the presence of triplications.     

Off‐great‐circle propagation of intermediate‐period surface waves observed on a dense array in the French Alps

Array analysis is performed on surface waves recorded in the French Alps using a small‐aperture (25 km) temporary array of six broad‐band stations. The analysis shows that both Rayleigh and Love waves deviate relative to the great‐circle path. The deviations are particularly strong, up to 30°, between 20 and 40 s period. To interpret these observations, we first study the effect of large‐scale structures using ray tracing in a smooth, laterally heterogeneous model of the Earth. Second, we evaluate the local effect by considering a model for the French Alps including strong lateral heterogeneities around the array that were not taken into account in the ray tracing. By combining these two possible causes of the observed deviations, we propose an explanation for the general trend in the observed deviations. Finally, we show that by taking into account azimuthal deviations, phase velocities measured at a regional scale can be significantly improved.