Pre-stack Depth Migration Based On Nonstationary Phase Shift Method

Migration is the eternal topic of seismic data processing, how to accurately image at complex structure region is increasingly urgent need for research and production. Based on this, thesis proposes one-way wave equation based on second order approximation is derived by finite difference operator, the common offset shot gathers are acquired by forward simulating model, then prestack depth migration is done by nonstationary phase shift (NSPS) method..In the thesis, we derive an analytic form for NSPS in the limit of an exhaustive set of reference velocities. NSPS in this limiting form can be written as generalized Fourier integrals which reduce to ordinary phase shift in the constant velocity limit. The phase-shift method of wavefield extrapolation applies a phase shift in the Fourier domain to deduce a scalar wavefield at one depth level given its value at another. The phase-shift operator varies with frequency and wavenumber, and assumes constant velocity across the extrapolation step. NSPS,which allows the phase shift to vary laterally depending upon the local propagation velocity,meanwhile ,it avoids shortcomings of unchanges with velocity in traditional phase shift. Also, it has the physical interpretation of forming the scaled, linear superposition of laterally variable impulse responses. To transform NSPS between Fourier domain and mixed domain can further improve the efficiency and scope of application of the algorithm. At last ,by simulating some models and testing the depth migration algorithm ,the results significantly show that the stability and accuracy has been greatly improved.In the pre-stack depth migration algorithm, using piecewise uniform approximation has further improved the speed of operation. Wavefield extrapolation can be regarded as the crosscorrelation of the wavefield with the expected response of a point diffractor at the new depth level. The crosscorrelation becomes spatially variant, even for constant velocity, and hence is a nonstationary filter,which can be well applied in the wave field extrapolation of NSPS.