Improving explicit seismic depth migration with a stabilizing Wiener filter and spatial resampling

We present a new approach to the design and implementation of explicit wavefield extrapolation for seismic depth migration in the space-frequency domain. Instability of the wavefield extrapolation operator is addressed by splitting the operator into two parts, one to control phase accuracy and a second to improve stability. The first partial operator is simply a windowed version of the exact operator for a half step. The second partial operator is designed, using the Wiener filter method, as a band-limited, least-squares inverse of the first. The final wavefield extrapolation operator for a full step is formed as a convolution of the first partial operator with the complex conjugate of the second. This resulting wavefield extrapolation operator can be designed to have any desired length and is generally more stable and more accurate than a simple windowed operator of similar length. Additional stability is gained by reducing the amount of evanescent filtering and by spatially downsampling the lower temporal frequencies. The amount of evanescent filtering is controlled by building two operator tables, one corresponding to significant evanescent filtering and the other to very little evanescent filtering. During the wavefield extrapolation process, most steps are taken with the second table while the first is invoked only for roughly every tenth step. Also, the data are divided into frequency partitions that are optimally resampled in the spatial coordinates to further enhance the performance of the extrapolation operator. Lower frequencies are downsampled to a larger spatial sample size. Testing of the algorithm shows accurate, high-angle impulse responses and run times comparable to the phase shift method of time migration. Images from trial depth migrations of the Marmousi model show very high resolution.