Do we need up/down decomposition for Marchenko imaging?

Marchenko redatuming, imaging, monitoring and multiple elimination methods are based on Green’s function representations, with the underlying assumption that the wave field in the subsurface can be decomposed into downgoing and upgoing waves and that evanescent waves can be neglected. In this paper we show that up/down decomposition in the...

A lossless earth Green's function representation between any two subsurface points from surface reflection GPR data

We present a three-dimensional scheme that can be used to compute the electromagnetic impulse response between any two subsurface points from surface reflection data measured at a single surface of a lossless medium. The scheme first computes a virtual vertical radar profile using the Marchenko scheme from which focusing wavefields are...

Creating virtual vertical radar profiles from surface reflection ground penetrating radar data

On the Marchenko equation for multicomponent single-sided reflection data

Recent work on the Marchenko equation has shown that the scalar 3-D Green’s function for a virtual source in the subsurface can be retrieved from the single-sided reflection response at the surface and an estimate of the direct arrival. Here, we discuss the first steps towards extending this result to multicomponent data. After introducing a...

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...

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...

Interferometry by deconvolution of multicomponent multioffset GPR data

Interferometric techniques are now well known to retrieve data between two receivers by the cross correlation of the data recorded by these receivers. Cross-correlation methods for interferometry rely mostly on the assumption that the medium is loss free and that the sources are all around the receivers. A recently developed method introduced...