Multilinear Filtering of Nonstationary Array Data and Inversion

English Abstract:

For various geoscience applications, observations and measurements provide array data that necessitate filtering and inversion for parameters of interest. Although most geophysical processes are nonlinear and nonstationary, simplifications are often implemented in practical data array computations. Starting with linear filtering and inversion of stationary array data, the mathematical convolution can often be generalized to multilinear tensor formulation for filtering and inversion of nonstationary data. Multilinear and tensor algebras can then be exploited to optimize the transformation to conventional matrix algebra and hence take advantage of linear equation solvers available in numerical libraries. These strategies and procedures will be briefly discussed using simple numerical examples with special attention to the computational aspects of Kirchhoff least-squares imaging using seismic data. Some open questions are also included for further research and development.