Accurate Absorbing Boundary Conditions And Reverse-time Migration Of Acoustic Wave Equation Using Non-reflecting Recursive Algorithm

Artificial boundaries must be introduced to limit the area of computation in both seismic modeling and migration using wave equation method. Usually, there are two types of methods handling the artificial boundary problems. One is the attenuating boundary conditions approach and the other is the absorbing boundary conditions (ABC) method based on the one-way approximation wave theory. Using the attenuating boundary conditions often means too much time-consuming and low absorbing efficiency to low frequency signal. Therefore the absorbing boundary conditions with relatively simpler computations are widely used to eliminate the unwanted boundary reflections. However the lower order traditional absorbing boundary conditions are only effective for the incident waves with smaller incident angles. A fourth-order absorbing boundary condition equation based on Higden's ABC is deduced in this thesis, and a new algorithm is presented to automatically select the Higden's parameters. Using the fourth-order absorbing boundary conditions can absorb the incident wave with incident angles nearly from 0 to 90 degrees. Numerical tests confirm the effectiveness of the new approach.Unwanted interlayer reflections are unavoidable when using the full wave equation to perform the reverse-time migration. It is desirable to use a non-reflecting two-way wave equation or a non-reflecting algorithm for wavefield extrapolation. Here, a non-reflecting wavefield extrapolation algorithm is proposed for reverse-time migration by introducing the impedance to the acoustic wave equation. The impedances on grid points are optimally computed based on the criteria of minimum reflected energy. Numerical tests for both seismic modeling and reverse-time migration demonstrate that the new non-reflecting recursive algorithm can sufficiently suppress the unwanted interlayer multiples.