Challenges for seismic imaging using explicit wavefield extrapolation

Abstract

For imaging complicated subsurface structures, downward-continuation imaging algorithms are more powerful than their ray-based counterparts, such as the Kirchhoff methods. Space-frequency explicit wavefield extrapolation is an attractive downward-continuation algorithm because it accounts for strong lateral velocity variations. In this method, the wavefield at each output point is computed using a different extrapolator that is calculated using the velocity at that location. This algorithm, however, has the following limitations: (1) numerical instability of the wavefield extrapolator: (2) computational expense; and (3) inability of short operators to handle the steep dips. The numerical instability arises because the amplitude and phase spectra of the ideal operator, in the wave number-frequency domain, have discontinuities at boundaries separating the wavelike and evanescent regions. The numerical instability also increases as the spatial extent of the extrapolator decreases. Shorter operators are often more desirable than long ones because they are computationally more efficient, but they cannot handle the steep dips. In this presentation, I will discuss different approaches that can be used to design stable operators. Also, I will show how short operators can handle the high angles of propagation. I will use impulse response examples to illustrate the stability and the accuracy of the designed wavefield extrapolators. Then, the designed wavefield extrapolators will be used to image two synthetic datasets that have strong velocity variation and strong topographic variations. Finally, the algorithm will be implemented in pre-stack time and depth migrations of real data examples.