The pseudo-acoustic equations of the scalar wavefield in anisotropic media

Abstract

The pseudo-acoustic equations of the scalar wavefield in anisotropic mediaIn this paper we present a new formulation of scalar pseudo-acoustic wave equation in arbitrary anisotropic media TI (Transverse Isotropy) type for 2D and 3D cases. These equations, based on precise dispersion relation, determine eigenvalue -temporal frequency as the function of wavenumber and anisotropy parameters. Here we present a few snapshots obtained for different signals by one-way equation.Key words: forward modelling, TI, Transverse Isotropy, pseudo-acoustic equation, one-way equation, dispersion relation.Pseudoakustyczne równanie skalarnego pola falowego w ośrodkach anizotropowych W artykule przedstawiono nowe sformułowanie skalarnych pseudospektralnych równań falowych w dowolnych ośrodkach anizotropowych typu TI (Transverse Isotropy) dla przypadków 2D i 3D. Równania bazują na dyspersyjnych relacjach wyznaczających wartości własne -częstotliwości w funkcji liczb falowych i parametrów anizotropii na podstawie pełnego systemu równań akustycznych. Zaprezentowano kilka przypadków propagacji falowej określonej jednostronnym równaniem w formie migawkowych zdjęć dla różnych typów sygnału.Słowa kluczowe: anizotropia, poprzeczna izotropia (TI), modelowanie, jednostronne równanie falowe, relacja dyspersyjna.Forward modelling of seismic waves in anisotropic media should be executed by solving a full system of elastic wave equations using numerical techniques such as finite-difference, spectral and pseudo-spectral method [3,7,9,10,11,17,19,20,23]. Due to the very time-consuming calculation system of modelling three component acoustic field and insufficient data concerning elastic parameters, in practical seismic research the tendency to simplify the theory and to limit oneself to the considerations of a few models of anisotropy can be noted. Alkhalifah T. [1, 2] introduced for P (compressional) wave fourth-order pseudo-acoustic scalar equations in the space-time domain. In this equation for vertical transverse isotropy (VTI) shear wave velocity V S = 0 is assumed. Alkhalifah's approximation was an inspiration for many studies [4-6, 21, 22].In this paper, we present pseudo-acoustic wave equations, first and second order, versus time in the wavenumbers domain for transverse isotropic media (TI). Some numerical examples were presented as snapshots of propagating wavefields.

Modeling and seismic migration in anisotropic media as a function of azimuthal angle – HTI(Y)

“…The stability of the extrapolation algorithm requires the convergence of Neumann series analogously to relation (21).…”