Minimum-phase property and reconstruction of elastodynamic dereverberation matrix operators

Minimum-phase property and reconstruction of elastodynamic dereverberation matrix operators

Reinicke, Christian (Aramco Overseas Company B.V.)
Dukalski, Marcin (Aramco Overseas Company B.V.)
Wapenaar, C.P.A. (TU Delft Applied Geophysics and Petrophysics)

2023

Minimum-phase properties are well-understood for scalar functions where they can be used as physical constraint for phase reconstruction. Existing scalar applications of the latter in geophysics include, for example the reconstruction of transmission from acoustic reflection data, or multiple elimination via the augmented acoustic Marchenko method. We review scalar minimum-phase reconstruction via the conventional Kolmogorov relation, as well as a less-known factorization method. Motivated to solve practice-relevant problems beyond the scalar case, we investigate (1) the properties and (2) the reconstruction of minimum-phase matrix functions. We consider a simple but non-trivial case of 2 × 2 matrix response functions associated with elastodynamic wavefields. Compared to the scalar acoustic case, matrix functions possess additional freedoms. Nonetheless, the minimum-phase property is still defined via a scalar function, that is a matrix possesses a minimum-phase property if its determinant does. We review and modify a matrix factorization method such that it can accurately reconstruct a 2 × 2 minimum-phase matrix function related to the elastodynamic Marchenko method. However, the reconstruction is limited to cases with sufficiently small differences between P- and S-wave traveltimes, which we illustrate with a synthetic example. Moreover, we show that the minimum-phase reconstruction method by factorization shares similarities with the Marchenko method in terms of the algorithm and its limitations. Our results reveal so-far unexplored matrix properties of geophysical responses that open the door towards novel data processing tools. Last but not least, it appears that minimum-phase matrix functions possess additional, still-hidden properties that remain to be exploited, for example for phase reconstruction.

Fourier analysis
Numerical solutions
Time-series analysis
Inverse theory
Wave propagation
Wave scattering and diraction

http://resolver.tudelft.nl/uuid:27476485-3654-448f-a34e-67977a633411

https://doi.org/10.1093/gji/ggad111

2023-09-20

0956-540X

Geophysical Journal International, 235 (1), 1-11

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2023 Christian Reinicke, Marcin Dukalski, C.P.A. Wapenaar