 |
| Titel |
Inversion with a sparsity constraint: Application to mantle tomography |
| VerfasserIn |
J. Charléty, G. Nolet, S. Voronin, I. Loris, F. J. Simons, I. Daubechies, K. Sigloch |
| Konferenz |
EGU General Assembly 2012
|
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250063450
|
|
|
|
|
|
| Zusammenfassung |
| There is an increasing interest in using sparsity as information to find a solution of a linear problem. Usually smoothness or minimum energy model are the information chosen to select a preferred model among all possible solution.
Wavelet decomposition of models in an over-parameterized Earth and L1-norm minimization in wavelet space is a promising strategy to deal with the very heterogeneous data coverage in the Earth without sacrificing detail in the solution where this is resolved. However, L1-norm minimizations are nonlinear, and may pose problems of convergence speed when applied to large data sets.
We investigate the use of a L1 norm penalty for the model while solving the normal equation with a L2 norm. The idea originates from the image processing field and is based on FISTA (fast iterative soft thresholding algorithm). The L2 norm inversion is performed with a projected Landweber algorithm and the L1 norm constraint is dealt with a thresholding operator.
We invert 430,554 P delay times measured by cross-correlation in different frequency windows. The data are dominated by observations with US Array, leading to a major difference in the resolution beneath North America and the rest of the world. This is a subset of the data set inverted by Sigloch et al (Nature Geosci, 2008), excluding only a small number of ISC delays at short distance and all amplitude data. The model is a cubed Earth model with 3,637,248 voxels spanning mantle and crust, with a resolution everywhere better than 70 km. A total of 1912 event corrections are added as unknowns to be solved for. We will present our final results for both a synthetic model to test resolution as well as convergence, and for the real data. This new results will be compared with those obtained by LSQR with damping and smoothing terms. |
|
|
|
|
|
|