Monday, April 22 2019
12:30pm - 1:30pm
Computational Mathematics Colloquium
CCM Colloquium: Regularization methods in seismic inversion problems: from model-driven to data-driven

Seismic inversion is essentially ill-posed because of inaccurate and insufficient data. Existing methods for improving stability and reducing the size of solution space are usually model-driven. These methods, such as total variation (TV), Tikhonov (TK), minimum gradient support (MGS), joint TV and TK (JTT), piecewise smooth (PS), piecewise linear (PL), etc., often rely on sophisticated mathematical models associated with prior knowledge or expectation of the structure, distribution and correlation of different parameters. In general, model-driven methods are established only for particular usage situations, which are known to have poor adaptivity. Also, because of their abstraction and simplification, these methods often have difficulty achieving satisfactory accuracy and resolution for complex geology. To overcome the limitations of the model-driven methods, we present a data-driven inversion framework based on dictionary learning and sparse representation (DLSR). We first let the system learn a dictionary from well-log data using K-singular value decomposition (K-SVD) algorithm. Such a learned dictionary captures structural features and correlations between different physical parameters. Then, in the inversion process, we replace the constraints of mathematical models with that of sparse representation over the learned dictionary on model parameters. This inversion framework is data-driven and has better adaptivity due to the incorporation of learning mechanism. Numerical experiments show that our algorithm has better performance than the conventional model-driven methods in improving the resolution and accuracy of solutions. Especially for multiparameter inversion problem, some physical parameters that are insensitive to observed data but extremely important for reservoir identification could be estimated much better by cooperative sparse representation (CSR) technique.
Speaker:Bin She
Affiliation:Department of Mathematical and Statistical Sciences, University of Colorado Denver
Location:SCB 4119

Download as iCalendar