The proposed CGG (Conjugate Guided Gradient) inversion method
is a modified CG (Conjugate Gradient) inversion method,
which guides the gradient vector during the iteration
and allows the user to impose various constraints for residual, model, or both of them.
The guiding is implemented by weighting the residual vector
and the gradient vector, either separately or together.
Weighting the residual vector with the residual itself
corresponds to guiding the solution search toward the -norm minimization;
weighting the gradient vector with the model itself corresponds to
guiding the solution search toward a priori information imposed.
Testing the CGG algorithm for the velocity-stack inversion
of synthetic and real data demonstrates
that the guiding with residual weighting gives
a robust model estimation comparable to the IRLS method
and the guiding with model weighting produces a parsimonious velocity spectrum
also comparable to the IRLS method.
So we can say that the CGG method can be use to achieve the same goals as the IRLS method does,
but with less computation by solving the linear problem instead of solving nonlinear problem
and more flexibility in choice of weighting parameters.
Therefore, the CGG method seems to be a good alternative to the
IRLS method for robust and parsimonious model estimation inversion of seismic data.

Conjugate guided gradient (CGG) method for robust inversion and its application to velocity-stack inversion