Elastodynamic Marchenko Green's function retrieval from two-sided reflection and transmission data

Abstract

Green’s functions in an unknown elastic layered medium can be retrieved from single-sided reflection data by solving a Marchenko equation. This methodology requires a priori knowledge of all forward-scattered (non-converted and converted) waveforms. Moreover, the medium should satisfy stringent monotonicity conditions, which are often not met in realistic scenarios. In this contribution, we show that the situation is significantly less cumbersome if two-sided reflection and transmission data are recorded (for instance in laboratory settings). A novel methodology is presented to retrieve elastodynamic Green’s functions from such data. Apart from the two-sided reflection and transmission responses, our methodology requires knowledge of the direct non-converted PP- and SS-transmissions (a priori knowledge of forward-scattered converted waveforms is not needed). We demonstrate the success of our methodology by conducting a numerical experiment in an elastic layered medium that violates the monotonicity conditions of the Marchenko equation for single-sided reflection data. The limitations of the methodology and the sensitivity to errors in our initial estimates require further investigation.