Implementation of the Marchenko multiple elimination algorithm

Abstract

The Marchenko multiple elimination and transmission compensation schemes retrieve primary reflections in the two-way traveltime domain without model information or using adaptive subtraction. Both schemes are derived from projected Marchenko equations and similar to each other, but use different time-domain truncation operators. The Marchenko multiple elimination scheme retrieves a new dataset without internal multiple reflections. The transmission compensated Marchenko multiple elimination scheme does the same and additionally compensates for transmission losses in the primary reflections. Both schemes can be solved with an iterative algorithm based on a Neumann series. At each iteration, a convolution or correlation between the projected focusing function and the measured reflection response are performed and after each convolution or correlation, a truncation in the time domain is applied. After convergence, the resulting projected focusing function is used for retrieving the transmission compensated primary reflections and the projected Green’s function is used for the physical primary reflections. We demonstrate that internal multiples are removed by using time-windowed input data that only contain primary reflections. We evaluate both schemes in detail and develop an iterative implementation that reproduces the presented numerical examples. The software is part of our open-source suite of programs and fits into the Seismic Unix software suite of the Colorado School of Mines.

Marchenko multiple elimination and full-wavefield migration in a resonant pinch-out model

“…Two truncation effects play a role here. One is the end of aperture effects, and the other is time truncation effects to solve equations 1 and 2; see Thorbecke et al (2021) for more details.…”

“…The need to know the initial part of the downgoing focusing function was removed in van der Neut and Wapenaar (2016) to remove the effect of the overburden on the target reflections. This is done by propagating the initial downgoing parts of all focusing functions at a certain depth level back to one physical receiver at the acquisition surface.…”

“…(4) which is the result from the T-MME scheme (Zhang et al, 2019b). Details on the numerical implementation and numerical illustrations of the MME and T-MME schemes can be found in Thorbecke et al (2021).…”

“…Many different approaches to data-driven redatuming and imaging without artifacts from multiples were derived and tested on synthetic and field data. Overburden removal (van der Neut and Wapenaar, 2016) led to different kinds of Marchenko multiple elimination (MME) schemes. The first kind uses either "double focusing" (Staring and Wapenaar, 2020), which includes source-receiver redatuming or "double dereverberations" (Staring et al, 2021), with the sources and receivers kept at the acquisition surface.…”

Marchenko redatuming, imaging, and multiple elimination and their mutual relations

“…Note that the space-independent window functionΘ v b cuts through offset-dependent events in the data. This aspect of the method is analysed in detail by Thorbecke et al (2021). For a field data example we refer to Zhang and Slob (2020b).…”