The dynamic acoustic inverse problem in laterally homogeneous media

Inverse problems are ubiquitous in many fields of science and can only be solved directly in very specific simple cases. There are many kinematic and dynamic inverse solution methods that require a good starting model to be able to proceed to a correct reconstruction. We investigated the application of the Gelfand- Levitan method to the problem of finding acoustic parameters from seismic data. The method allows for a direct reconstruction of the model from the data if the medium is laterally homogeneous. A synthetic numerical example shows that we can reconstruct a smooth version of a given 1D model up to a predictable depth for typical marine data that include multiples.