Least-squares imaging and deconvolution using the hybrid norm conjugate-direction solver |

There are two ways to linearize this model. The first one is to use model perturbation and neglect the non-linear higher order terms in the following:

in which are the initial model and source wavelet respectively. are the pertubation of them, the linearized inversion will output . The other way of linearization is a two-stage linear least squares formulation; i.e. alternately fixing one term (

and then use the updated

Repeat this process (6) and (7) for several iterations.

As is in all non-linear inversion problems, the difficulty in these methods is to find a good starting model. Another issue is to add proper constrain on the wavelet , for example, the wavelet should have constant energy during inversion, but this constrain does not fit the linear inversion framework.

Least-squares imaging and deconvolution using the hybrid norm conjugate-direction solver |

2010-05-19