Starting with initial values of
, we are able to solve for
using equation 5. Then we solve for the model increment
. After a number of iterations, summation of
converges to the estimated value. The Gauss-Newton method is efficient. In most cases, approximately 20 iterations provide an acceptable convergence. Fitting more component frequencies helps minimize the residual. Geological factors can help the user decide how many components to include in the model. In addition, providing good initial values helps the algorithm avoid being trapped in a local minimum.
Automated spectral recomposition with application in stratigraphic interpretation