Unified elimination of 1D acoustic multiple reflection

Migration, velocity and amplitude analysis are the employed processing steps to find the desired subsurface information from seismic reflection data. The presence of free-surface and internal multiples can mask the primary reflections for which many processing methods are built. The ability to separate primary from multiple reflections is desirable. Connecting Marchenko theory with classical one-dimensional inversion methods allows to understand the process of multiple reflection elimination as a data-filtering process. The filter is a fundamental wave field, defined as a pressure and particle velocity that satisfy the wave equation. The fundamental wave field does not depend on the presence or absence of free-surface multiples in the data. The backbone of the filtering process is that the fundamental wave field is computed from the measured pressure and particle velocity without additional information. Two different multiples-free datasets are obtained: either directly from the fundamental wave field or by applying the fundamental wave field to the data. In addition, the known schemes for Marchenko multiple elimination follow from the main equation. Numerical examples show that source and receiver ghosts, free-surface and internal multiples can be removed simultaneously using a conjugate gradient scheme. The advantage of the main equation is that the source wavelet does not need to be known and no pre-processing is required. The fact that the reflection coefficients can be obtained is an interesting feature that could lead to improved amplitude analysis and inversion than would be possible with other processing methods.