Numerical modelling of wavefields in three-dimensional inhomogeneous media

Summary. Numerical modelling is one of the most efficient methods for an investigation of the relationship between structural features and peculiarities of observed wavefields. It is practically the only method for 2-D and 3-D inhomogeneous media.
An algorithm based on ray theory has been developed for calculations of travel times and amplitudes of seismic waves in 3-D inhomogeneous media with curved interfaces. It was applied for numerical modelling of kinematic and dynamic characteristics of seismic waves propagating in laterally inhomogeneous media.
Travel-time and amplitude patterns were studied in the 2-D and 3-D models of a geosyncline, in which velocity distribution was given by an analytical function of the coordinates. For a more complicated model representing a subducting high-velocity lithospheric plate in a transition zone between oceanic and continental upper mantle, the velocity distribution was given by discrete values on a 2-D non-rectangular grid. It was shown that when a source was placed above the lithospheric plate, a shadow zone appeared along a strike of the structure, i.e. in the direction which is perpendicular to a strong lateral velocity gradient. Travel-time residuals were calculated along the seismological profile for a 3-D velocity distribution in the upper mantle beneath Central Asia, obtained as a result of inversion of travel times by the Backus-Gilbert method. They were found to be in a good agreement with the observed data.