Non-linear Least-squares Reverse-time Migration

Migration attempts to produce an image of the subsurface by reversing the propagation effects in seismic data. Although in principle this requires the inverse of a modelling operator, in practice the adjoint of the modelling operator is used instead. This applies to nearly all migration methods, including reverse-time migration. In cases where the data are subject to significant aliasing, truncation, or noise, the adjoint of a modelling operator is not a good approximation to the inverse, and this degrades the resolution of the final migrated image. At last year’s meeting we presented a matrix formulation of least-squares reverse-time migration which provides an improved approximation to the inverse of the modelling operator, and which in turn results in more accurate amplitudes and higher resolution. Unfortunately, the matrix formulation, while very efficient in 2D, is currently computationally impractical for 3D data. In this paper, we present a non-linear least-squares reverse-time migration algorithm which generates the predicted data directly from the reflectivity without assuming they are linearly related. This algorithm retains the benefits of our previous approach, but is also feasible in 3D. In addition, the new formulation opens up the possibility of generating improved velocity estimates as part of the migration process.