Direct downward continuation from topography using explicit wavefield extrapolation

Downward-continuation migration algorithms are powerful tools for imaging complicated subsurface structures. However, they usually assume that extrapolation proceeds from a flat surface, whereas most land surveys are acquired over irregular surfaces. Our method downward continues data directly from topography using a recursive space-frequency explicit wavefield-extrapolation method. The algorithm typically handles strong lateral velocity variations by using the velocity value at each spatial position to build the wavefield extrapolator in which the depth step usually is kept fixed. To accommodate topographic variations, we build space-frequency wavefield extrapolators with laterally variable depth steps (LVDS). At each spatial location, the difference between topography and extrapolation depth is used to determine the depth step. We use the velocity and topographic values at each spatial lateral position to build extrapolators. The LVDS approach does not add more data nor does it require preprocessing prior to extrapolation. We implemented the LVDS method and applied it to a source profile prestack migration technique. We also implemented the previously developed zero-velocity layer approach to use for comparison. For both algorithms, we modeled the acoustic source as an approximate free-space Green’s function, not as a simple extrapolated spatial impulse. Tests on a synthetic data set modeled from rough topography and comparisons with the zero-velocity layer approach confirm the method’s effectiveness in imaging shallow and deep structures beneath rugged topography.