On the retrieval of forward-scattered waveforms from acoustic reflection and transmission data with the Marchenko equation

A Green's function in an acoustic medium can be retrieved from reflection data by solving a multidimensional Marchenko equation. This procedure requires a priori knowledge of the initial focusing function, which can be interpreted as the inverse of a transmitted wavefield as it would propagate through the medium, excluding (multiply)...

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

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...

Marchenko Green’s Function Retrieval in Layered Elastic Media from Two-Sided Reflection and Transmission Data

By solving a Marchenko equation, Green’s functions at an arbitrary (inner) depth level inside an unknown elastic layered medium can be retrieved from single-sided reflection data, which are collected at the top of the medium. To date, it has only been possible to obtain an exact solution if the medium obeyed stringent monotonicity conditions and...

On the benefits of auxiliary transmission data for Marchenko-based Green’s function retrieval

Green’s functions in an unknown medium can be retrieved from single-sided reflection data by solving a multidimensional Marchenko equation. This methodology requires knowledge of the direct wavefield throughout the medium, which should include forward-scattered waveforms. In practice, the direct field is often computed in a smooth background...

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

With the Marchenko method it is possible to retrieve Green's functions between virtual sources in the subsurface and receivers at the surface from reflection data at the surface and focusing functions. A macro model of the subsurface is needed to estimate the first arrival; the internal multiples are retrieved entirely from the reflection data....

Wavefield focusing with reduced cranial invasiveness

Wavefield focusing can be achieved by Time-Reversal Mirrors, which involve in- and output signals that are infinite in time and waves propagating through the entire medium. Here, an alternative solution for wavefield focusing is presented. This solution is based on a new integral representation where in- and output signals are finite in time,...

Wavefield finite time focusing with reduced spatial exposure

Wavefield focusing is often achieved by time-reversal mirrors, where wavefields emitted by a source located at the focal point are evaluated at a closed boundary and sent back, after time-reversal, into the medium from that boundary. Mathematically, time-reversal mirrors are derived from closed-boundary integral representations of reciprocity...