General algorithms for multiscale approximation

2017 ◽  
Author(s):  
Gilcélia Regiâne de Souza ◽  
Jorge Stolfi
Keyword(s):  
Multiscale Approximation

Multiscale adjoint waveform-difference tomography using wavelets

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. WA79-WA95 ◽  
Author(s):  
Yanhua O. Yuan ◽  
Frederik J. Simons
Keyword(s):  
Forward Modeling ◽  
Spectral Element ◽  
Orthogonal Wavelet ◽  
Final Model ◽  
Long Wavelength ◽  
Full Waveform ◽  
Industry Standard ◽  
Multiscale Approximation ◽  
Minimization Algorithms ◽  
Orthogonal Wavelet Transform

Full-waveform seismic inversions based on minimizing the distance between observed and predicted seismograms are, in principle, able to yield better-resolved earth models than those minimizing misfits derived from traveltimes alone. Adjoint-based methods provide an efficient way of calculating the gradient of the misfit function via a sequence of forward-modeling steps, which, using spectral-element codes, can be carried out in realistically complex media. Convergence and stability of full-waveform-difference adjoint schemes are greatly improved when data and synthetics are progressively presented to the algorithms in a constructive multiscale approximation using a (bi)orthogonal wavelet transform. Wavelets provide the nonredundant spectral decomposition that paves the way for the inversion to proceed successively from long-wavelength fitting to detailed exploration of the phases in the seismogram. The choice of wavelet class and type, the initial depth of the multiscale decomposition, and the minimization algorithms used at every level continue to play crucial roles in our procedure, but adequate choices can be made that test successfully on 2C elastic seismograms generated in toy models, as well as in the industry-standard 2D Marmousi model. Although for simplicity our inversion ignored surface waves by prior tapering and filtered removal, those also appeared to be very well matched in the final model.

Multiscale Approximation of Vortex Patches

2000 ◽  
Vol 60 (2) ◽  
pp. 477-502 ◽  
Author(s):  
Albert Cohen ◽  
Raphael Danchin
Keyword(s):  
Multiscale Approximation

Multiscale Approximation and Reproducing Kernel Hilbert Space Methods

2015 ◽  
Vol 53 (2) ◽  
pp. 852-873 ◽  
Author(s):  
Michael Griebel ◽  
Christian Rieger ◽  
Barbara Zwicknagl
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Multiscale Approximation
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