Wavelet estimation using a very fast simulated annealing and spline based parameterization
Abhijit Gangopadhyay, Long Jin · 2008
We describe a stochastic method of wavelet estimation combining a global optimization technique based on a Very Fast Simulated Annealing (VFSA), and spline parameterization. Our method inverts for the amplitude of the wavelet at several nodes and uses a spline interpolation scheme to estimate its amplitude in between those nodes. Our method retains all the distinct advantages of VFSA in that it searches a wider model space, chooses a random starting model and thereby has minimal dependence on the initial model, and does not require assumptions for the phase. Work is ongoing to incorporate statistical methods of computing uncertainties associated with the estimated wavelets which will provide an additional advantage to our method. We illustrate our method in this paper with example estimations of zero and hybrid phase wavelets. We also compute the mean of estimated zero phase wavelets resulting from several VFSA runs. Our results in their current form demonstrate that the method is stable in appropriately constructing the wavelet.