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)...

Applicability of the wide-band limit in DFT-based molecular transport calculations

Transport properties of molecular junctions are notoriously expensive to calculate with ab initio methods, primarily due to the semi-infinite electrodes. This has led to the introduction of different approximation schemes for the electrodes. For the most popular metals used in experiments, such as gold, the wide-band limit (WBL) is a...

Source depopulation potential and surface-wave tomography using a crosscorrelation method in a scattering medium

We use seismic prospecting data on a 40 × 40 regular grid of sources and receivers deployed on a 1 km × 1 km area to assess the feasibility and advantages of velocity analysis of the shallow subsurface by means of surface-wave tomography with Green's functions estimated from crosscorrelation. In a first application we measure Rayleigh-wave...

Seismic migration of blended shot records with surface-related multiple scattering

This paper focuses on the concept of using blended data and multiple scattering directly in the migration process, meaning that the blended input data for the proposed migration algorithm includes blended surface-related multiples. It also means that both primary and multiple scattering contribute to the seismic image of the subsurface....

Tutorial on seismic interferometry: Part 1 — Basic principles and applications

Seismic interferometry involves the crosscorrelation of responses at different receivers to obtain the Green's function between these receivers. For the simple situation of an impulsive plane wave propagating along the x-axis, the crosscorrelation of the responses at two receivers along the x-axis gives the Green's function of the direct wave...

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...

Surface and borehole ground-penetrating-radar developments

During the past 80 years, ground-penetrating radar (GPR) has evolved from a skeptically received glacier sounder to a full multicomponent 3D volume-imaging and characterization device. The tool can be calibrated to allow for quantitative estimates of physical properties such as water content. Because of its high resolution, GPR is a valuable...

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...

An iterative method for the computation of nonlinear, wide-angle, pulsed acoustic fields of medical diagnostic transducers

The development and optimization of medical ultrasound transducers and imaging modalities require a computational method that accurately predicts the nonlinear acoustic pressure field. A prospective method should provide the wide-angle, pulsed field emitted by an arbitrary planar source distribution and propagating in a three-dimensional, large...

Virtual reflector representation theorem (acoustic medium)

The virtual reflector method simulates new seismic signals by processing traces recorded by a plurality of sources and receivers. The approach is based on the crossconvolution of the recorded signals and makes it possible to obtain the Green’s function of virtual reflected signals as if in the position of the receivers (or sources) there were a...

The effect of a neighboring metal layer on the high-frequency characteristics of a thin magnetic stripe

The spin-wave spectrum of a ferromagnetic stripe placed above a metallic layer with finite conductivity is studied by using the magnetostatic Green’s function formalism. It is shown that the frequency and linewidth of the resonances are uniquely determined by complex, mode-dependent demagnetization factors. The formalism developed is used to...

Keldysh action of a multiterminal time-dependent scatterer

We present a derivation of the Keldysh action of a general multichannel time-dependent scatterer in the context of the Landauer–Büttiker approach. The action is a convenient building block in the theory of quantum transport. This action is shown to take a compact form that only involves the scattering matrix and reservoir Green’s functions. We...

On the relation between seismic interferometry and the migration resolution function

Seismic interferometry refers to the process of retrieving new seismic responses by crosscorrelating seismic observations at different receiver locations. Seismic migration is the process of forming an image of the subsurface by wavefield extrapolation. Comparing the expressions for backward propagation known from migration literature with the...

Impedance of a planar solenoid with a thin magnetic core

The high-frequency impedance of a planar solenoid with a thin magnetic core is theoretically investigated using the magnetostatic Green’s function formalism. It is shown that the electrical behavior of the solenoid depends on how the magnetic field induced by the current-carrying coil is coupled to the different magnetostatic modes of the core....

Seismic interferometry: Reconstructing the earth's reflection response

In 1968, Jon Claerbout showed that the reflection response of a 1D acoustic medium can be reconstructed by autocorrelating the transmission response. Since then, several authors have derived relationships for reconstructing Green's functions at the surface, using crosscorrelations of (noise) recordings that were taken at the surface and that...

Green's function representations for seismic interferometry

The term seismic interferometry refers to the principle of generating new seismic responses by crosscorrelating seismic observations at different receiver locations. The first version of this principle was derived by Claerbout (1968), who showed that the reflection response of a horizontally layered medium can be synthesized from the...

Nonreciprocal Green’s function retrieval by cross correlation

The cross correlation of two recordings of a diffuse acoustic wave field at different receivers yields the Green’s function between these receivers. In nearly all cases considered so far the wave equation obeys time-reversal invariance and the Green’s function obeys source-receiver reciprocity. Here the theory is extended for nonreciprocal Green...

Retrieving the Green’s function in an open system by cross correlation: A comparison of approaches (L)

We compare two approaches for deriving the fact that the Green’s function in an arbitrary inhomogeneous open system can be obtained by cross correlating recordings of the wave field at two positions. One approach is based on physical arguments, exploiting the principle of time-reversal invariance of the acoustic wave equation. The other approach...