First Born and Rytov approximations: Modeling and inversion conditions in a canonical example

First Born and, more recently, first Rytov approximations are widely used for solving complex forward and inverse seismic scattering problems. The exact pressure‐field response from a one‐dimensional velocity slab included in an infinite constant velocity medium is expressed analytically. This solution is used for testing these two approximations in modeling and in inversion. Conditions of applicability and parameter estimates lead to the following results: The first Rytov approximation is best suited for modeling and inverting the transmitted, or forward scattered, part of the wave field, whereas the first Born approximation is best suited for modeling and inverting the primary reflected, or backscattered, part of the wave field. If the long wavelength condition holds, linearization of the field with respect to slowness squared is preferable over linearization with respect to slowness, allowing for a very large velocity contrast between the slab and the reference medium. However, if the weak heterogeneity condition holds (i.e., small velocity contrast), the linearization choice is reversed. Numerical examples show and display these differences quantitatively.