Most of algorithms in the geophysical inverse problems can be categorized into two types: global inversion and sequential inversion. Global inversion methods are usually referred to as full waveform inversion and sequential inversion methods are mostly known as velocity estimation followed by reflectivity imaging.

Global approaches use the direct inversion approach Tarantola (1987). The objective function represents a measure of the difference between the recorded data, and the data predicted by a particular choice of model parameters. To be able to describe all the features in the data, the model space must assume its most complex form for the particular formulation of the forward problem. In sequential approaches the data is first reduced to a form that contains only relevant information, that is, in a formation that depends only on the subset of the model space that we want to invert for. The objective function measures only the misfit between a particular attribute of the data and the attribute predicted by a particular choice of parameters in the associated subset of the model space.

It is important to note that the data reduction involved in the sequential approach assumes that the complementary part of the model space necessary to perform the data reduction has already been estimated, also by means of an appropriate sequential approach. On the other hand, global inversion approaches make no distinction between low- and high-wavenumber components of the model. As pointed out by Claerbout 1985, this distinction is important because of the band limitation of surface seismic data. While only the low-wavenumber part of the velocity field can be reliably obtained (usually by velocity estimation), the retrieval of the reflectivity (impedance contrasts) is restricted to the high-wavenumber components. The independence between the two parts of the impedance spectrum provides a theoretical justification for the separability of the estimation process of the two parts of the model (low- and high-wavelengths). One difficulty that arises from the simultaneous inversion of the velocities and reflectivities is that whereas the effect of reflectivity perturbations can be partly linearized, the effect of velocity perturbations is highly nonlinear (Hindlet and Kolb, 1988). Another disadvantage of the direct inversion approach is its high cost; the complete physical process must be simulated at each new iteration.

2/5/2001