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

Notice that Algorithm 3 is different from the original CG method (Algorithm 1) only at the step of gradient computation; the modification of the gradient is performed by changing the residual before the gradient is computed from it. By choosing the weight as a function of the residual of the previous iteration step, as we did in the IRLS method, we can guide the gradient vector to the gradient vector of the -norm. Thus the result obtained by weighting the residual in the CGG method could be interpreted as a localized LS solution in the subspace composed by the -norm gradient vectors, not in the whole solution space. The minimum -norm location is unlikely to be located along the gradient direction of the different -norm which is guided by the applied weight. Therefore, it is more likely that the solution will be close to the minimum -norm location which is guided by the applied weight.

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

2011-06-26