Migration by Analytic Continuation through a Variable Background Medium

Zhdanov, M.S. and Tjan, T., 1994. Migration by analytic continuation through a variable background medium. Journal of Seismic Exploration, 3: 283-297. Conventional migration of wavefields is based on depth extrapolation of the upgoing field in reverse time. This extrapolation provides us with a means to determine the positions of reflectors and diffraction points and, therefore, to produce an image of a geological cross-section. However, conventional depth extrapolation allows us 10 restore only some transformation of the field in the subsurface rather than the true field. For example, this approach rules out the proper imaging of multiple reflections. Meanwhile. there is reason to expect that a different reconstruction of the seismic wavefield reconstruction by analytic continuation can yield a more comprehensive image of a medium. An exact depth extrapolation based on analytic continuation could contribute to the restoration of the true process of seismic wave propagation in a medium. In this case, multiples do not 'pass' the layers where they have been formed and, hence, they cannot generate any fictitious reflecting boundaries. Here, we describe a method for doing migration of seismic wave fields in the frequency domain by analytic continuation through a medium with vertically variable velocity.