No abstract

A B S T R A C TTrue amplitude migration is one of the most important procedures of seismic data processing. As a rule it is based on the decomposition of the velocity model of the medium into a known macrovelocity component and its sharp local perturbations to be determined. Under this decomposition the wavefield can be considered as the superposition of an incident and reflected/scattered waves. The single scattering approximation introduces the linear integral operator that connects the sharp local perturbations of the macrovelocity model with the multishot/multioffset data formed from reflected/scattered waves. We develop the pseudoinverse of this operator using the Gaussian beam based decomposition of acoustic Green's functions. The computation of this pseudoinverse operator is done pointwise by shooting Gaussian beams from the target area towards the acquisition system.The numerical implementation of the pseudoinverse operator was applied to the synthetic data Sigsbee2A. The results obtained demonstrate the high quality of the true amplitude images computed both in the smooth part of the model and under the salt body.

This paper presents a new approach to a local time-space grid refinement for a staggered-grid finitedifference simulation of waves. The approach is based on approximation of a wave equation at the interface where two grids are coupled. As no interpolation or projection techniques are used, the finite-difference scheme preserves second order of convergence. We have proved that this approach is low-reflecting, the artificial reflections are about 10 −4 of an incident wave. We have also shown that if a successive refinement is applied, i.e. temporal and spatial steps are refined at different interfaces, this approach is stable. Mathematics Subject Classifications (2010) 86A15· 86-08 · 35L40 · 65M06 · 65M50 · 65M55 V. Lisitsa (B) · V. Tcheverda

Numerical simulations of wave propagation produce different errors and the most well known is numerical dispersion, which is only valid for homogeneous media. However, there is a lack of error studies for heterogeneous media or even for the canonical case of media that have two constant velocity layers. The error associated with media that have two layers is called an interface error, and it typically converges to zero with a lower order of convergence compared to the theoretical convergence rate of the finite-difference schemes (FDS) for homogeneous media. We evaluated a detailed numerical study of the interface error for three staggered-grid FDS that are commonly used in the simulation of seismic-wave propagation. We determined that a standard staggered-grid scheme (SSGS) (also known as the Virieux scheme), a rotated staggered-grid scheme (RSGS), and a Lebedev scheme (LS) preserve the second order of convergence at horizontal/vertical solid-solid interfaces when the medium parameters have been properly modified, such as by harmonic averaging of finely layered media for the stiffness tensor and arithmetic mean for the density. However, for a fluid-solid interface aligned with the grid line, a second-order convergence can only be achieved by an SSGS. In addition, the presence of a fluid-solid interface reduces the order of convergence for the LS and the RSGS to a first order of convergence. The presence of inclined interfaces makes high-order (second and more) convergence impossible.

No abstract