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Non‐monotone spectral projected gradient method applied to full waveform inversion
Author(s) -
Zeev Noam,
Savasta Olga,
Cores Debora
Publication year - 2006
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.2006.00554.x
Subject(s) - monotone polygon , inversion (geology) , gradient descent , mathematical optimization , gradient method , inverse problem , residual , least squares function approximation , descent direction , waveform , convex function , optimization problem , solver , convex optimization , convergence (economics) , mathematics , minification , algorithm , computer science , regular polygon , mathematical analysis , geology , estimator , geometry , structural basin , economic growth , paleontology , machine learning , artificial neural network , statistics , economics , telecommunications , radar
The seismic inversion problem is a highly non‐linear problem that can be reduced to the minimization of the least‐squares criterion between the observed and the modelled data. It has been solved using different classical optimization strategies that require a monotone descent of the objective function. We propose solving the full‐waveform inversion problem using the non‐monotone spectral projected gradient method: a low‐cost and low‐storage optimization technique that maintains the velocity values in a feasible convex region by frequently projecting them on this convex set. The new methodology uses the gradient direction with a particular spectral step length that allows the objective function to increase at some iterations, guarantees convergence to a stationary point starting from any initial iterate, and greatly speeds up the convergence of gradient methods. We combine the new optimization scheme as a solver of the full‐waveform inversion with a multiscale approach and apply it to a modified version of the Marmousi data set. The results of this application show that the proposed method performs better than the classical gradient method by reducing the number of function evaluations and the residual values.