Astronomy and Astrophysics – Astronomy
Scientific paper
Apr 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008geoji.173..233h&link_type=abstract
Geophysical Journal International, Volume 173, Issue 1, pp. 233-248.
Astronomy and Astrophysics
Astronomy
18
Fourier Analysis, Wavelet Transform, Inverse Theory, Spatial Analysis, Controlled Source Seismology, Theoretical Seismology
Scientific paper
Seismic data recovery from data with missing traces on otherwise regular acquisition grids forms a crucial step in the seismic processing flow. For instance, unsuccessful recovery leads to imaging artefacts and to erroneous predictions for the multiples, adversely affecting the performance of multiple elimination. A non-parametric transform-based recovery method is presented that exploits the compression of seismic data volumes by recently developed curvelet frames. The elements of this transform are multidimensional and directional and locally resemble wave fronts present in the data, which leads to a compressible representation for seismic data. This compression enables us to formulate a new curvelet-based seismic data recovery algorithm through sparsity-promoting inversion. The concept of sparsity-promoting inversion is in itself not new to geophysics. However, the recent insights from the field of `compressed sensing' are new since they clearly identify the three main ingredients that go into a successful formulation of a recovery problem, namely a sparsifying transform, a sampling strategy that subdues coherent aliases and a sparsity-promoting program that recovers the largest entries of the curvelet-domain vector while explaining the measurements. These concepts are illustrated with a stylized experiment that stresses the importance of the degree of compression by the sparsifying transform. With these findings, a curvelet-based recovery algorithms is developed, which recovers seismic wavefields from seismic data volumes with large percentages of traces missing. During this construction, we benefit from the main three ingredients of compressive sampling, namely the curvelet compression of seismic data, the existence of a favourable sampling scheme and the formulation of a large-scale sparsity-promoting solver based on a cooling method. The recovery performs well on synthetic as well as real data by virtue of the sparsifying property of curvelets. Our results are applicable to other areas such as global seismology.
Hennenfent Gilles
Herrmann Felix J.
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