daniel-koehn
commented
9 years ago Problem solved, in case of GRAD_FORM = 2 the gradients for the non-conservative stress-velocity formulation according to Castellanos (2014) can be applied:
http://seiscope2.obs.ujf-grenoble.fr/IMG/pdf/PhD_Castellanos_2014.pdf
They require no integration of the data residuals before the backpropagation.
Different gradient formulations can be defined in denise.c
GRAD_FORM == 1 is based on the classical gradient derivation from the stress-displacement isotropic elastic equations of motion and reformulated for the stress-velocity code (e.g. Köhn et al. 2012). This approach has the disadvantage, that the data residuals have to be numerically integrated and are consequently very sensitive to noise.
EFWI with new gradient formulation GRAD_FORM == 2 for the stress-velocity formulation with compliance matrix (Vigh et al. 2014) is currently not converging, most likely due to an incorrect source implementation. The density update is also not implemented yet.
Gradient GRAD_FORM == 3 is based on the stress-velocity formulation with elastic tensor. Actually, this problem is not self-adjoint and therefore the gradients should be wrong. However, the P-wave and S-wave velocity updates seem to converge correctly for the Marmousi-II test problem. The density model shows a strong ambiguity and trade-offs with the S-wave velocity model.