Version 1
: Received: 8 July 2022 / Approved: 11 July 2022 / Online: 11 July 2022 (11:19:01 CEST)
How to cite:
Van Der Neut, J.; Brackenhoff, J.; Meles, G.; Slob, E.; Wapenaar, K. Marchenko Green's Function Retrieval in Layered Elastic Media from Two-Sided Reflection and Transmission Data. Preprints2022, 2022070159. https://doi.org/10.20944/preprints202207.0159.v1
Van Der Neut, J.; Brackenhoff, J.; Meles, G.; Slob, E.; Wapenaar, K. Marchenko Green's Function Retrieval in Layered Elastic Media from Two-Sided Reflection and Transmission Data. Preprints 2022, 2022070159. https://doi.org/10.20944/preprints202207.0159.v1
Van Der Neut, J.; Brackenhoff, J.; Meles, G.; Slob, E.; Wapenaar, K. Marchenko Green's Function Retrieval in Layered Elastic Media from Two-Sided Reflection and Transmission Data. Preprints2022, 2022070159. https://doi.org/10.20944/preprints202207.0159.v1
APA Style
Van Der Neut, J., Brackenhoff, J., Meles, G., Slob, E., & Wapenaar, K. (2022). Marchenko Green's Function Retrieval in Layered Elastic Media from Two-Sided Reflection and Transmission Data. Preprints. https://doi.org/10.20944/preprints202207.0159.v1
Chicago/Turabian Style
Van Der Neut, J., Evert Slob and Kees Wapenaar. 2022 "Marchenko Green's Function Retrieval in Layered Elastic Media from Two-Sided Reflection and Transmission Data" Preprints. https://doi.org/10.20944/preprints202207.0159.v1
Abstract
Bysolving a Marchenko equation, Green'sfunctions at anarbitrary (inner) depth level inside an unknown elasticlayered medium canberetrieved from single-sidedreflection data, which are tobecollected at the top of the medium. So far, an exact solutioncouldonlybeobtained if the medium obeys stringent monotonicityconditions and if all forward-scattered (non-converted and converted) transmissionsbetween the acquisition level and the innerdepth level are known a-priori. We introduceanalternativeMarchenko equation byrevising the window operators that are applied in itsderivation. We also introduceanauxiliary equation for transmission data, which are tobecollected at the bottom of the medium, and a coupled equation, which is based on bothreflection and transmission data. We show that the joint system of the Marchenko equation, the auxiliary equation and the coupled equation canbesuccesfullyinvertedwhenbroadbandreflection and transmission data are available. Thisresults in a novelmethodology for elastodynamicGreen's function retrieval from two-sided data. Apart from these data, ourapproachrequiresP- and S-wave transmission times between the innerdepth level and the top of the medium, as well as two angle-dependent amplitude scaling factors, whichcanbeestimated from the data byenforcingenergyconservation.
Keywords
Marchenko equation; Green's function retrieval; elastodynamic wave propagation
Subject
Physical Sciences, Applied Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.