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Seismic imaging by nonlinear inversion
Silva, Werter Oliveira
Silva, Werter Oliveira
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2024
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Imaging aims to create representations of internal object structures through indirect external physical measurements. In seismic exploration, for instance, seismic reflections on the Earth’s surface are mapped into discontinuities in physical properties, revealing geological structures. Various seismic imaging techniques exist, differing in their approach to wave propagation (acoustic or elastic; isotropic or anisotropic), wave equation type (one-way or all-way), application domain (post-stack or pre-stack), numerical implementation (frequency or time domain; integral or differential forms), and other factors.
Migrations usually assume a linear relationship between data and image based on the Born approximation, and the image consists of a scalar parameter that describes the spatial distribution of subsurface reflectors. Since seismic data includes not only primary reflections but also multiples that do not satisfy the Born approximation, imaging is normally preceded by multiple attenuation to meet the linear assumption and avoid creating fake reflectors and crosstalk noise. However, multiples provide additional illumination and resolution because they can sample subsurface image points at angles different from those of the primary waves. Therefore, multiple attenuation ignores additional information that could be used to improve the image.
In this thesis, I introduce an acoustic nonlinear inversion imaging method, based on a parameterization of the wave equation that preserves the nonlinearity between data and image, defined as a vector instead of a scalar function. This parameterization separates propagation and dynamic effects. Wave propagation is ruled by a background velocity model, lacking sharp contrasts, while the dynamics of reflections is controlled by the image vector parameter I seek to invert. The vectorial nature of the image reflects the directional dependence of the reflectivity and its nonlinear dependence to the data enables multiple-scattering modeling to fit unprocessed data, containing multiples and ghots in addition to primaries.
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