Iterative inversion for velocity using waveform data

Summary. In this paper, velocity inversion using waveform data is investigated. A linearized approach is used in which a linear sensitivity operator must be derived. This operator can be computed economically using reciprocity of the Green's function. In order to avoid a large matrix inversion, several descent algorithms are described. Data errors and a priori model information are incorporated using covariance operators. A fast and reasonably accurate forward modelling scheme is required and here the Gaussian beam method for a slowly varying heterogeneous medium is used. Several types of linearizations can be done including the Born approximation, a linearization in terms of the field, and the Rytov approximation, a linearization in terms of the log field. Field linearizations are expected to be useful for small‐scale heterogeneities which result in scattering effects that are additive in the field. For small perturbations from a homogeneous background, a linearized inversion in terms of the field is equivalent to a sequence of Kirchhoff migrations. Log field linearizations may be more robust for large‐scale heterogeneities where forward scattering predominates, but phase unwrapping may be difficult numerically. Several numerical examples using a field linearization are performed in which transmitted body waves through a model with small velocity variations are used. The results using the waveform data identify the trial structures and are comparable or slightly better than the travel‐time inversion results.