Iterative inversion for velocity using waveform data

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 tenns of the field is equivalent to a sequence of Kirchhoff migrations. Log field linearizations may be more robust for largescale 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.