Data Assimilation Meetings at Reading

Date Meeting type Speakers
26 November 2014
Maths 314
Invited speaker Paul Childs (Schlumberger)
Weak Constraints and Seismic Imaging
Seismic inversion aims to determine subsurface structures and provide information for hydrocarbon exploration. Mathematically, seismic waves are described by a linear wave equation. In seismic exploration, we collect a large amount of data on the boundary of the domain under investigation (land or sea surface) resulting from seismic experiments. Seismic inversion is a PDE constrained inversion problem where the constraint is the wave equation, solved for many right hand sides. Established practice is to solve the constraint PDEs exactly in space and time, using methods of iterative inversion pioneered by Tarantola et al in the 1980s. The inversion procedure is ill-posed without additional prior information, which is often lacking. Inversion suffers from a large null space and from multiple local minima in the objective function. Recently, researchers at UBC proposed using weak constraints (a.k.a the penalty method) to improve robustness in seismic inversions. In this talk we shall review established practice in seismic inversion (using strong constraints), and review initial work on the use of weak constraints for seismic inversion in the frequency domain. Lastly we make the connection to data assimilation but also discuss the important differences.

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