Inversion strategies for visco-acoustic waveform inversion
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Résumé
Visco-acoustic waveform inversion can potentially yield quantitative images of the distribution of both velocity and the attenuation parameters from seismic data. Intrinsic <it>P</it>-wave attenuation has been of particular interest, but has also proven challenging. Frequency-domain inversion allows attenuation and velocity relations to be easily incorporated, and allows a natural multiscale approach. The Laplace–Fourier approach extends this to allow the natural damping of waveforms to enhance early arrivals. Nevertheless, simultaneous inversion of velocity and attenuation leads to significant ‘cross-talk’ between the resulting images, reflecting a lack of parameter resolution and indicating the need for pre-conditioning and regularization of the inverse problem. We analyse the cross-talk issue by partitioning the inversion parameters into two classes; the velocity parameter class, and the attenuation parameter class. Both parameters are defined at a reference frequency, and a dispersion relation is assumed that describes these parameters at any other frequency. We formulate the model gradients at a forward modelling frequency, and convert them to the reference frequency by employing the Jacobian of the coordinate change represented by the dispersion relation. We show that at a given modelling frequency, the Fréchet derivatives corresponding to these two parameter classes differ only by a 90° phase shift, meaning that the magnitudes of resulting model updates will be unscaled, and will not reflect the expected magnitudes in realistic (<it>Q</it>−1 &Lt; 1) media. Due to the lack of scaling, cross-talk will be enhanced by poor subsurface illumination, by errors in kinematics, and by data noise. To solve these issues, we introduce an attenuation scaling term (the inverse of a penalty term) that is used to pre-condition the gradient by controlling the magnitudes of the updates to the attenuation parameters. Initial results from a suite of synthetic cross-hole tests using a three-layer randomly heterogenous model with both intrinsic and extrinsic (scattering) attenuation demonstrate that cross-talk is a significant problem in attenuation inversion. Using the same model, we further show that cross-talk can be suppressed by varying the attenuation scaling term in our pre-conditioning operator. This strategy is effective for simultaneous inversion of velocity and attenuation, and for sequential inversion (a two-stage approach in which only the velocity models are recovered in the first stage). Further regularization using a smoothing term applied to the attenuation parameters is also effective in reducing cross-talk, which is often highly oscillatory. The sequential inversion approach restricts the search space for attenuation parameters, and appears to be important in retrieving a reliable attenuation model when strong time-damping is applied. In a final test with our synthetic model, we successfully carry out visco-acoustic inversions of noise-contaminated data.
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Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Apprise à partir de 10 348 étiquettes directes de Codex et de 10 348 étiquettes directes de Gemma. Le mode candidate est l'union des têtes enseignantes seuillées; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont ni des étiquettes humaines ni des étiquettes directes de modèles de pointe.
Scores Codex et Gemma par catégorie
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,000 | 0,000 |
| Méta-épidémiologie (sens strict) | 0,000 | 0,000 |
| Méta-épidémiologie (sens large) | 0,000 | 0,000 |
| Bibliométrie | 0,000 | 0,000 |
| Études des sciences et des technologies | 0,000 | 0,000 |
| Communication savante | 0,000 | 0,001 |
| Science ouverte | 0,000 | 0,000 |
| Intégrité de la recherche | 0,000 | 0,000 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,003 | 0,001 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
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