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| Titel |
2D multi-parameter elastic seismic imaging by frequency-domain L1-norm full waveform inversion |
| VerfasserIn |
Romain Brossier, Stéphane Operto, Jean Virieux |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250038412
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| Zusammenfassung |
| Full waveform inversion (FWI) is becoming a powerful and efficient tool to derive
high-resolution quantitative models of the subsurface. In the frequency-domain,
computationally efficient FWI algorithms can be designed for wide-aperture acquisition
geometries by limiting inversion to few discrete frequencies. However, FWI remains an
ill-posed and highly non-linear data-fitting procedure that is sensitive to noise, inaccuracies of
the starting model and definition of multiparameter classes.
The footprint of the noise in seismic imaging is conventionally mitigated by stacking
highly redundant multifold data. However, when the data redundancy is decimated in the
framework of efficient frequency-domain FWI, it is essential to assess the sensitivity of the
inversion to noise. The impact of the noise in FWI, when applied to decimated data sets, has
been marginally illustrated in the past and least-squares minimisation has remained the most
popular approach.
We investigate in this study the sensitivity of frequency-domain elastic FWI to noise for
realistic onshore and offshore synthetic data sets contaminated by ambient random white
noise. Four minimisation functionals are assessed in the framework of frequency domain FWI
of decimated data: the classical least-square norm (L2), the least-absolute-values norm (L1),
and some combinations of both (the Huber and the so-called Hybrid criteria). These
functionals are implemented in a massively-parallel, 2D elastic frequency-domain FWI
algorithm. A two-level hierarchical algorithm is implemented to mitigate the non-linearity of
the inversion in complex environments. The first outer level consists of successive
inversions of frequency groups of increasing high-frequency content. This level defines a
multi-scale approach while preserving some data redundancy by means of simultaneous
inversion of multiple frequencies. The second inner level used complex-valued
frequencies for data preconditioning. This preconditioning controls the amount
of the data involved in the inversion from the first-arrival time and allows us to
mitigate the weight of the complex late arrivals during the first iterations of the
inversion.
We applied our FWI approach to the SEG/EAGE overthrust model and the
shallow-water Valhall model which is representative of oil and gas fields in North
Sea. Results show that the L1 norm provides the most reliable models for both
applications, even when only few discrete frequencies are used in the inversion and
outliers pollute the data. The L2 norm can provide reliable results in the presence of
uniform white noise only if the data redundancy is increased by refining the frequency
sampling interval in the inversion, at the expense of the computational efficiency.
The Huber and the Hybrid criteria are shown to be sensitive to a threshold, which
controls the transition between the L1 and L2 behaviours, and which requires tedious
trial-and-error investigations for reliable estimation. We show that the L1 norm
provides a robust alternative to the classical approach based on the L2 norm for the
inversion of decimated data sets in the framework of efficient frequency-domain FWI. |
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