Wavefield extrapolation and prestack depth migration in anelastic inhomogeneous media

Abstract

Wavefield depth extrapolation and prestack depth migration in complex anelastic media are studied. Kjartansson's frequency‐independent Q law is used to describe the absorption of seismic energy. The macromodel used is analogous to the macromodel used for current migration schemes except that an additional frequency‐independent Q macromodel needs to be provided. Absorption in the forward one‐way propagator is introduced by assuming a complex phase velocity, and the inverse one‐way propagator is obtained using the reciprocity theorem for one‐way wavefields in dissipative media. The stability of the inverse propagator is achieved by limiting the angle of propagation of wavefields. A table‐driven explicit operator scheme for imaging complex 2D anelastic media is presented. High‐accuracy, short convolution operators are designed by the weighted least‐squares method, and two kinds of imaging conditions are proposed. Numerical examples of depth extrapolation in laterally varying media, the migration of a spatial impulse with dispersion as well as shot record depth migration demonstrate the potential of the proposed explicit forward operator, the explicit inverse operator and the prestack depth migration scheme, respectively.

A single-sided representation for the homogeneous Green's function of a unified scalar wave equation

“…3 For a medium with losses, the bar in G Ã ðx 0 ; x; xÞ denotes that the back propagation is carried out in the adjoint medium. 26,27 Because of the exponential growth of this Green's function with distance, care must be taken when the response at S is contaminated with noise. …”

Jacobian matrix for the inversion of P- and S-wave velocities and its accurate computation method

“…Inversion of seismic data is an important approach to improve the precision of lithology interpretation. Therefore, the application of the seismic wave reflection coefficients to the inversion of P-and S-wave velocities or to the inversion of petrophysical characteristics remains a hot topic for geophysical research [9][10][11][12][13][14][15][16][17][18][19][20].…”

“…Inversion of seismic data is an important approach to improve the precision of lithology interpretation. Therefore, the application of the seismic wave reflection coefficients to the inversion of P-and S-wave velocities or to the inversion of petrophysical characteristics remains a hot topic for geophysical research [9][10][11][12][13][14][15][16][17][18][19][20].Since the middle 1980s, the AVO (Amplitude Versus Offset) [9][10][11][12][13][14][15][16][17][18][19][20] or AVA (Amplitude Versus incident Angle) techniques [9-20] have been stuided extensively. Their theoretical foundation is Zoeppritz equations [8,9,14], which accurately describe the relations of reflected wave amplitudes to incidence angle of waves, velocity of waves, and density of media.…”

Implementation aspects of attenuation compensation in reverse‐time migration

“…They apply wavefield extrapolation based on one‐way (e.g., Mittet et al . ; Zhang and Wapenaar ; Mittet ) and two‐way wave equation (e.g., Deng and McMechan ; Zhang, Zhang, and Zhang ; Fletcher, Nichols, and Cavalca ; Zhu, Harris, and Biondi ). Conventionally, two‐way wave equations for reverse‐time migration (RTM) include damping viscoscalar wave equation (Deng and McMechan ; Yan and Liu ) and viscoelastic wave equation based on the standard linear solid model (Deng and McMechan ).…”