Prestack depth migration using variable large-step

Abstract

A variable large-step prestack depth extrapolation migration method is presented. In the extrapolation process adopting a large depth step can keep efficiency but at a cost of low accuracy. However, if the depth step is allowed to vary we can use a relative small depth step for accuracy where required and large depth step where possible to retain efficiency. The intermediate depth samples are obtained by applying phase-shift operator and interpolations. The Fourier finite-difference (FFD) operator is employed as the depth extrapolation operator. The variable large step method is also suitable to other extrapolation operators such as the split-step Fourier (SSF) operator and the phase-shift plus interpolation (PSPI) operator. To make this approach more efficient and economical, the method is applied to the synthesized areal shot-record migration. Two numerical examples have been used to assess the feasibility of this approach. Introduction As so far, prestack depth migration is the most efficient method for imaging complex structures. The wave equation prestack depth migration methods based on the wave extrapolations has got more and more realization in practical production in recent years. However, the methods are computationally expensive because the migration process involves a huge amount of computations required for the extrapolation process of the prestack data. The proposition of the synthesized areal shot-record migration [1] has improved the efficiency of the wave equation prestack depth migration. In the approach the point shot records are synthesized into an areal source response prior to shot-record migration, and subsequently an enormous data reduction can be obtained. The resulting areal shot record can be migrated using the same scheme as the one for conventional shot-record migration. The main advantage of the areal shot-record migration is that the extrapolations need not be done for all the individual shot records, but for the areal shot record only. A straight-forward approach to implementing prestack depth migration involves the use of a fixed depth step. While attractive for its simplicity, a fixed depth step can not take advantage of neither the depth varying frequency content, nor the increase in velocity with depth, usually found in seismic data. However, if the depth step is allowed to vary, the features may be utilized. Adopting large depth step is a straightforward way to improve the efficiency of prestack depth migration methods based on wave extrapolation. But the accuracy is influenced and the qualities of imaging go worse as the depth step increases. In many finite difference and finite element methods outside the seismic industry varying grid spacing and indeed adaptive curvilinear grids are commonplace. In the seismic industry these adaptive approaches are less common. Jastram and Behle [2] investigated varying the grid spacing for acoustic wavefield modeling and Mufti. In this paper, the author proposed a variable large depth step method which produces accurate migration images with high efficiency. The Fourier finite-difference operator [3] is employed as the depth extrapolation operator. The variable large step method is also suitable to other extrapolation operators such as the split-step Fourier operator [4] and the phase-shift plus interpolation operator [5]. In migration examples, we first use a 2-D slice of the SEG/EAGE 3-D salt model to test the method. A field data is then used to demonstrate the feasibility and efficiency of the method. International Conference on Information Sciences, Machinery, Materials and Energy (ICISMME 2015) © 2015. The authors Published by Atlantis Press 519 Migration with large-step wavefield extrapolation In the migration methods based on wave field depth extrapolation, it is easy to notice that the wave fields in different depths are similar except the phase. This suggests that we can utilize the phase-shift formula to deal with the intermediate wave fields during wave field extrapolations. The 2-D phase-shift formula[6] reads: ( ) ( ) ( ) z i k z p k z z p z x x ∆ = ∆ + θ ω ω exp , , , , , (1) where