Comparison of absorbing boundary conditions: A correlation of reflection coefficients and determination of the optimum grid interval for migration

Abstract

Modeling and migration couple is one of the most important steps in seismic data processing and interpretation. Absorbing boundary conditions used in the modeling were studied with the wave-equation by different authors. In this study, reflection coefficient analyses of recent solutions are compared to each other for the different incident angles of seismic waves to the modeling boundaries. According to the reflection coefficients correlation, the A3 condition is the most appropriate solution which greatly reduces artificial reflections from the boundaries. However, multi-transmitting Formula is better for relatively high angles between 32–58° with the usage of a special parameter. On the contrary, this formula is not an appropriate condition for angles lower than 32°, although it allows setting the boundary at any preferred angle. Considering that most of the boundaries are set in low angles, A3 solution is still most preferential condition. In this study, it is also aimed to find out the optimum grid intervals for minimizing the ill-posedness arose from the combination of the 45° finite difference migration equation and the B 2 absorbing boundary condition for migration. Appropriate values are determined as ωΔx = 0.2 and ωΔz = 0.4 or neighbouring coarser values. It is also concluded that finer mesh spacing can increase the ill-posedness, in contrast to existence of some fine grid size values providing well-posedness. In addition, ill-posedness is obviously standard after ωΔ x = 0.6 for all values of ωΔ z.