Real ray tracing in isotropic viscoelastic media: a numerical modelling (original) (raw)

An accurate and efficient scheme for wave propagation in linear viscoelastic media

GEOPHYSICS, 1990

The problem of wave propagation in a linear viscoelastic medium can be described mathematically as an exponential evolution operator of the form [Formula: see text] acting on a vector representing the initial conditions, where [Formula: see text] is a spatial operator matrix and t is the time variable. Techniques like finite difference, for instance, are based on a Taylor expansion of this evolution operator. We propose an optimal polynomial approximation of [Formula: see text] based on the powerful method of interpolation in the complex plane, in a domain which includes the eigenvalues of the matrix [Formula: see text]. The new time‐integration technique is implemented to solve the isotropic viscoacoustic equation of motion. The algorithm is tested for the problem of wave propagation in a homogeneous medium and compared with second‐order temporal differencing and the spectral Chebychev method. The algorithm solves efficiently, and with machine accuracy, the problem of seismic wave ...

VISCOELASTIC R/T PROBLEM FOR ARBITRARY ORIENTATION OF PROPAGATION AND ATTENUATION VECTORS

We consider the reeection/transmission problem of inhomogeneous plane waves at a plane interface be-tween two homogeneous isotropic viscoelastic halfspaces. An arbitrary orientation of the attenuation vector of the incident wave i s allowed, even the orientation away f r o m the plane of incidence. The procedure of determining the complex-valued normal components of the slowness vectors of generated R/T waves from the tangential components of the slowness vector, known along the interface from the Snell's law, is pro-posed. Particular attention is devoted to the determination of the signs of complex-valued square roots, involved in the problem. Continuity criterion is proposed, which is based on the requirement that the ver-tical components of the slowness vectors of generated waves must be continuous along a parametric line in the complex-valued plane of tangential components of the slowness vector, along which w e wish to compute the R/T coeecients. For example, the parameter ...

A trajectory mechanics approach for the study of wave propagation in an anisotropic elastic medium

Geophysical Journal International, 2019

SUMMARY We derive equations describing the path and traveltime of a coherent elastic wave propagating in an anisotropic medium, generalizing expressions from conventional high-frequency asymptotic ray theory. The methodology is valid across a broad range of frequencies and allows for subwavelength variations in the material properties of the medium. The primary difference from current ray methods is the retention of a term that is neglected in the derivation of the eikonal equation. The additional term contains spatial derivatives of the properties of the medium and of the amplitude field, and its presence couples the equations governing the evolution of the amplitude and phase along the trajectory. The magnitude of this term provides a measure of the validity of expressions based upon high-frequency asymptotic methods, such as the eikonal equation, when modelling wave propagation dominated by a band of frequencies. In calculations involving a layer with gradational boundaries, we f...