On Green’s functions, propagator matrices, focusing functions and their mutual relations

Green’s functions and propagator matrices are both solutions of the wave equation, but whereas Green’s functions obey a causality condition in time (G = 0 for t < 0), propagator matrices obey a boundary condition in space. Marchenko-type focusing functions focus a wave field in space at zero time. We discuss the mutual relations between Green...

Beyond Marchenko: Obtaining virtual receivers and virtual sources in the subsurface

By solving the Marchenko equations, the Green’s function can be retrieved between a virtual receiver in the subsurface to points at the surface (no physical receiver is required at the virtual location). We extend the idea of these equations to retrieve the Green’s function between any two points in the subsurface; i.e, between a virtual source...

Autofocusing imaging: Imaging with primaries, internal multiples and free-surface multiples

Recent work on autofocusing with the Marchenko equation has shown how the Green's function for a virtual source in the subsurface can be obtained from reflection data. The response to the virtual source is the Green's function from the location of the virtual source to the surface. The Green's function is retrieved using only the reflection...

Creating the green's response to a virtual source inside a medium using reflection data with internal multiples

Seismic interferometry is a technique that allows one to reconstruct the full wavefield originating from a virtual source inside a medium, assuming a receiver is present at the virtual source location. We discuss a method that creates a virtual source inside a medium from reflection data measured at the surface, without needing a receiver inside...

3D Marine CSEM Interferometry by Multidimensional Deconvolution in the Wavenumber Domain for a Sparse Receiver Grid

We use interferometry by multidimensional deconvolution in combination with synthetic aperture sources in 3D to suppress the airwave and the direct field, and to decrease source uncertainty in marine Controlled-Source electromagnetics. We show with this numerical study that the method works for very large receiver spacing distances, even though...

Data-driven green's function retrieval from reflection data: Theory and example

Recently we introduced a new approach for retrieving the Green's response to a virtual source in the subsurface from reflection data at the surface. Unlike in seismic interferometry, no receiver is needed at the position of the virtual source. Here we present the theory behind this new method. First we introduce the Green's function G and a so...

Synthesized 2D CSEM-interferometry Using Automatic Source Line Determination

Interferometry by multidimensional deconvolution applied to Controlled-Source Electromagnetic data replaces the medium above the receivers by a homogeneous halfspace, suppresses the direct field and redatums the source positions to the receiver locations. In that sense, the airwave and any other interactions of the signal with the air-water...

Creating Virtual Sources Inside an Unknown Medium from Reflection Data: A New Approach to Internal Multiple Elimination

It has recently been shown that the response to a virtual source in the subsurface can be derived from reflection data at the surface and an estimate of the direct arrivals between the virtual source and the surface. Hence, unlike for seismic interferometry, no receivers are needed inside the medium. This new method recovers the complete...