Seismic Waves in Laterally Inhomogeneous Media

Vlastislav Cerveny Ivan Psencik Academy of Sciences of the Czech Charles University Republic Faculty of Mathematics & Physics Geophysical Institute Dep. of Geophysics Bocni II, 1401 Ke Karlovu 3 14131 Praha 4 12116 Praha 2 Czech Republic Czech Republic e-mail: ip@ig. cas. cz e-mail: vcerveny@seis. karlov. mff. cuni. cz © Birkhauser Verlag, Basel, 2002 Pure appl. geophys. 159 (2002) 1403-1417 I Pure and Applied Geophysics 0033-4553/02/081403-15 $ 1. 50 + 0. 20/0 Coupled Anisotropic Shear-wave Ray Tracing in Situations where Associated Slowness Sheets Are Almost Tangent l P. M. BAKKER Summary- For shear waves in anisotropic media a frequency-dependent transport equation is derived, which involves coupling of both shear modes if the slowness vector points in adirection for which the associated slowness surfaces are (almost) tangent. This is achieved by averaging the Hamiltonians for both uncoupled shear modes. No assumption on weak anisotropy is made, and the shear polarisation is perpendicular to the P-wave polarisation for the actual slowness direction instead of an isotropically approximated P-wave polarisation. These are the main differences compared with the so-called zero-order quasi-isotropic approach. Key words: Anisotropy, ray tracing, shear wave. J. Introduction Reliable modelling of polarisations for shear waves in anisotropic media is relevant in the context of imaging mode-converted (OBCjOBS) data in cases where not only poSY, but also poSH conversions take place. In such situations it may be necessary to use the polarisation direction for consistent continuation of the different wave modes and for appropriate imaging.

Inhalt
Preface.- Coupled Anisotropic Shear-wave Ray Tracing in Situations where Associated Slowness Sheets Are Almost Tangent.- Numerical Algorithm of the Coupling Ray Theory in Weakly Anisotropic Media.- Perturbation of the Polarization Vectors in the Isotropic Ray Theory.- Synthetic Seismograms and Wide-angle Seismic Attributes from the Gaussian Beam and Reflectivity Methods for Models with Interfaces and Velocity Gradients.- Lyapunov Exponents for 2-D Ray Tracing Without Interfaces.- obolev Scalar Products in the Construction of Velocity Models: Application to Model Hess and to SEG/EAGE Salt Model.- Smoothing the Marmousi Model.- Converted PS-wave Reflection Coefficients in Weakly Anisotropic Media.- Three-dimensional Travel-time Calculation Based on Fermat's Principle.- True Amplitude Migration Weights from Travel Times.- Model-independent Travel-time Attributes for 2-D, Finite-offset Multi-coverage Reflections.- Statistical Travel-time Tomography in Terms of Stacking Velocity.- Applications of Directional Wavefield Decomposition, Phase Space, and Path Integral Methods to Seismic Wave Propagation and Inversion.- Parabolic Equation Techniques for Seismic Waves.- A Full Waveform Test of the Southern California Velocity Model by the Reciprocity Method.- Constant Q and a Fractal, Stratified Earth.- Time-domain Modeling of Constant-Q Seismic Waves Using Fractional Derivatives.- Numerical Computation of Nonlinear Inelastic Waves in Soil.- Propagation of Pulses in Viscoelastic Media.- Scattering of Seismic Waves by Cracks with the Boundary Integral Method.- Application of the Medium Covariance Functions to Travel-time Tomography.- Correlation Functions of Random Media.- Estimating the Correlation Function of a Self-affine Random Medium.- P-wave Tomography in InhomogeneousOrthorhombic Media.- Local Determination of Weak Anisotropy Parameters from qP-wave Slowness and Particle Motion Measurements.