Wavefield focusing using a generalised, potentially asymmetric homogeneous Green's function

Marchenko-type integrals typically relate so-called focusing functions and Green's functions via the reflection response measured on the open surface of a volume of interest. Originating from one dimensional inverse scattering theory, the extension to two and three dimensions set in motion various new developments regarding imaging in complex...

Green’s function representations for Marchenko imaging without up/down decomposition

Marchenko methods are based on integral representations which express Green’s functions for virtual sources and/or receivers in the subsurface in terms of the reflection response at the surface. An underlying assumption is that inside the medium the wave field can be decomposed into downgoing and upgoing waves and that evanescent waves can be...

Accounting for free-surface multiples in Marchenko imaging

Imagine placing a receiver at any location in the earth and recording the response at that location to sources on the surface. In such a world, we could place receivers around our reservoir to better image the reservoir and understand its properties. Realistically, this is not a feasible approach for understanding the subsurface. We have...

Seismic reflection imaging, accounting for primary and multiple reflections

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

Recent work on retrieving the Green’s function with the Marchenko equation shows how these functions 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...

Marchenko imaging

Traditionally, the Marchenko equation forms a basis for 1D inverse scattering problems. A 3D extension of the Marchenko equation enables the retrieval of the Green’s response to a virtual source in the subsurface from reflection measurements at the earth’s surface. This constitutes an important step beyond seismic interferometry. Whereas seismic...

Green's function retrieval from reflection data, in absence of a receiver at the virtual source position

The methodology of Green’s function retrieval by cross-correlation has led to many interesting applications for passive and controlled-source acoustic measurements. In all applications, a virtual source is created at the position of a receiver. Here a method is discussed for Green’s function retrieval from controlled-source reflection data,...

Seismic reflector imaging using internal multiples with Marchenko-type equations

We present an imaging method that creates a map of reflection coefficients in correct one-way time with no contamination from internal multiples using purely a filtering approach. The filter is computed from the measured reflection response and does not require a background model. We demonstrate that the filter is a focusing wavefield that...

Interferometric redatuming of autofocused primaries and internal multiples

Recently, an iterative scheme has been introduced to retrieve the down- and upgoing Green's functions at an arbitrary level ?F inside an acoustic medium as if there were a source at the surface. This scheme requires as input the reflection response acquired at the surface and the direct arrival of the transmission response from the surface to...

Three-dimensional Marchenko equation for Green's function retrieval “beyond seismic interferometry”

In recent work we showed with heuristic arguments that the Green's response to a virtual source in the subsurface can be obtained from reflection data at the surface. This method is called “Green's function retrieval beyond seismic interferometry”, because, unlike in seismic interferometry, no receiver is needed at the position of the virtual...

Electromagnetic interferometry in wavenumber and space domains in a layered earth

With interferometry applied to controlled-source electromagnetic data, the direct field and the airwave and all other effects related to the air-water interface can be suppressed in a data-driven way. Interferometry allows for retreival of the scattered field Green’s function of the subsurface or, in other words, the subsurface reflection...

Three-Dimensional Single-Sided Marchenko Inverse Scattering, Data-Driven Focusing, Green’s Function Retrieval, and their Mutual Relations

The one-dimensional Marchenko equation forms the basis for inverse scattering problems in which the scattering object is accessible from one side only. Here we derive a three-dimensional (3D) Marchenko equation which relates the single-sided reflection response of a 3D inhomogeneous medium to a field inside the medium. We show that this equation...

Increasing the sensitivity of controlled-source electromagnetics with synthetic aperture

Controlled-source electromagnetics (CSEM) has been used as a derisking tool in the hydrocarbon exploration industry. We apply the concept of synthetic aperture to the lowfrequency electromagnetic field in CSEM. Synthetic aperture sources have been used in radar imaging for many years. Using the synthetic aperture concept, big synthetic sources...

Tutorial on seismic interferometry: Part 2 — Underlying theory and new advances

In the 1990s, the method of time-reversed acoustics was developed. This method exploits the fact that the acoustic wave equation for a lossless medium is invariant for time reversal. When ultrasonic responses recorded by piezoelectric transducers are reversed in time and fed simultaneously as source signals to the transducers, they focus at the...

Synthetic aperture controlled source electromagnetics

Controlled?source electromagnetics (CSEM) has been used as a de?risking tool in the hydrocarbon exploration industry. Although there have been successful applications of CSEM, this technique is still not widely used in the industry because the limited types of hydrocarbon reservoirs CSEM can detect. In this paper, we apply the concept of...

On seismic interferometry, the generalized optical theorem, and the scattering matrix of a point scatterer

We have analyzed the far-field approximation of the Green's function representation for seismic interferometry. By writing each of the Green's functions involved in the correlation process as a superposition of a direct wave and a scattered wave, the Green's function representation is rewritten as a superposition of four terms. When the...

Retrieving electric resistivity data from self-potential measurements by cross-correlation

We show that the two-point cross-correlation of self-potential field recordings is equal to the electric resistivity between the two points. This holds under the condition that spatially and temporally uncorrelated noise sources exist throughout the volume. These sources should have a known amplitude spectrum and their correlated strengths...

Unified Green’s Function Retrieval by Cross Correlation

It has been shown by many authors that the cross correlation of two recordings of a diffuse wave field at different receivers yields the Green’s function between these receivers. Recently the theory has been extended for situations where time-reversal invariance does not hold (e.g., in attenuating media) and where source-receiver reciprocity...