Pc. Liu et al., NONLINEAR MULTIPARAMETER INVERSION USING A HYBRID GLOBAL SEARCH ALGORITHM - APPLICATIONS IN REFLECTION SEISMOLOGY, Geophysical journal international, 122(3), 1995, pp. 991-1000
Many interesting inverse problems in geophysics are non-linear and mul
timodal. Parametrization of these problems leads to an objective funct
ion, or measure of agreement between data and model predictions, that
has a complex topography with many local minima. Optimization algorith
ms that rely on local gradients in the objective function or that sear
ch the model space locally may become trapped in these local minima. B
y combining simulated annealing with the downhill simplex method, a hy
brid global search algorithm is presented in this paper for non-linear
, multimodal, inverse problems. The hybrid algorithm shares the advant
ages of both local search methods that perform well if the local model
is suitable, and global methods that are able to explore efficiently
the full model space. The hybrid algorithm also utilizes a larger and
more complex memory to store information on the objective function tha
n simulated annealing algorithms. The effectiveness of this new scheme
is evaluated in three problems: minimization of the multidimensional
Rosenbrock function, non-linear, 1-D, acoustic waveform inversion, and
residual statics. The performance of the hybrid algorithm is compared
with simulated annealing and genetic algorithms and is shown to conve
rge more rapidly and to have a higher success rate of locating the glo
bal minimum for the cases investigated.