Research Note: Analysis of the Born Approximation

ABSTRACT The Born approximation has been extensively used to approximate scattered waves in a variety of areas in physics. The Born approximation utilizes specific terms of a series expansion and the general issues of convergence of the series and accuracy of the approximations are difficult to ascertain. I use a simple one‐interface model to examine these issues for both acoustic and elastic wavefields. The series converges in the normal incidence case, although to a value that is less accurate than that of the first‐order approximation. Also, for normal incidence and two‐dimensional acoustic waves, the series contains only odd terms. At non‐normal incidence angles the inclusion of higher order terms does increase accuracy over a reasonable range of incidence angles, but ultimately diverges from the exact reflection coefficient at large reflection angles. The series for elastic waves contains both odd and even terms, and the effects of mode conversions begin with the even second‐order term. Adding the second‐order term for the elastic case provides a more accurate prediction than the first‐order term alone, yet it is unclear if additional terms will continue to improve the accuracy of the approximation for non‐normal incidence.