scholarly journals Interferometric correlogram-space analysis

Geophysics ◽  
2011 ◽  
Vol 76 (1) ◽  
pp. SA9-SA17 ◽  
Author(s):  
Oleg V. Poliannikov ◽  
Mark E. Willis
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
The Other ◽  
Seismic Interferometry ◽  
Controlled Source ◽  
Space Analysis

Controlled-source seismic interferometry is a method of obtaining a virtual shot gather from a collection of physical shot gathers. The set of traces corresponding to two common receiver gathers from many physical shots is used to synthesize a virtual shot located at one of the receivers and a receiver at the other. An estimate of the Green’s function between these two receivers is obtained by first crosscorrelating corresponding pairs of traces from each of the shots and then stacking the resulting crosscorrelograms. We studied the structure of crosscorrelograms obtained from a VSP acquisition geometry using surface sources and downhole receivers. The model is purely acoustic and contains flat or dipping layers and/or point inclusions that act as diffractors. We propose a semblance analysis based on moveout curves for both point diffractors and flat or dipping layers, which can be used to improve the quality of redatumed traces either by rejecting certain events prior to stacking or by enhancing them.

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

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. 75A211-75A227 ◽  
Author(s):  
Kees Wapenaar ◽  
Evert Slob ◽  
Roel Snieder ◽  
Andrew Curtis
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Seismic Interferometry ◽  
Virtual Source ◽  
Bending Waves ◽  
Complex Source ◽  
Recent Developments ◽  
Diffusion Phenomena ◽  
Quantum Mechanical Scattering ◽  
Moving Media

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 position of the original source, even when the medium is very complex. In seismic interferometry the time-reversed responses are not physically sent into the earth, but they are convolved with other measured responses. The effect is essentially the same: The time-reversed signals focus and create a virtual source which radiates waves into the medium that are subsequently recorded by receivers. A mathematical derivation, based on reciprocity theory, formalizes this principle: The crosscorrelation of responses at two receivers, integrated over differ-ent sources, gives the Green’s function emitted by a virtual source at the position of one of the receivers and observed by the other receiver. This Green’s function representation for seismic interferometry is based on the assumption that the medium is lossless and nonmoving. Recent developments, circumventing these assumptions, include interferometric representations for attenuating and/or moving media, as well as unified representations for waves and diffusion phenomena, bending waves, quantum mechanical scattering, potential fields, elastodynamic, electromagnetic, poroelastic, and electroseismic waves. Significant improvements in the quality of the retrieved Green’s functions have been obtained with interferometry by deconvolution. A trace-by-trace deconvolution process compensates for complex source functions and the attenuation of the medium. Interferometry by multidimensional deconvolution also compensates for the effects of one-sided and/or irregular illumination.

scholarly journals Parallel Simulation of Audio- and Radio-Magnetotelluric Data

Minerals ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 42 ◽  
Author(s):  
Nikolay Yavich ◽  
Mikhail Malovichko ◽  
Arseny Shlykov
Keyword(s):  
Numerical Modeling ◽  
Green’S Function ◽  
Green's Function ◽  
Mineral Exploration ◽  
Iterative Solvers ◽  
Contraction Operator ◽  
Magnetotelluric Data ◽  
Controlled Source ◽  
Em Simulation ◽  
Preconditioned Iterative

This paper presents a novel numerical method for simulation controlled-source audio-magnetotellurics (CSAMT) and radio-magnetotellurics (CSRMT) data. These methods are widely used in mineral exploration. Interpretation of the CSAMT and CSRMT data collected over an area with the complex geology requires application of effective methods of numerical modeling capable to represent the geoelectrical model of a deposit well. In this paper, we considered an approach to 3D electromagnetic (EM) modeling based on new types of preconditioned iterative solvers for finite-difference (FD) EM simulation. The first preconditioner used fast direct inversion of the layered Earth FD matrix (Green’s function preconditioner). The other combined the first with a contraction operator transformation. To illustrate the effectiveness of the developed numerical modeling methods, a 3D resistivity model of Aleksandrovka study area in Kaluga Region, Russia, was prepared based on drilling data, AMT, and a detailed CSRMT survey. We conducted parallel EM simulation of the full CSRMT survey. Our results indicated that the developed methods can be effectively used for modeling EM responses over a realistic complex geoelectrical model for a controlled source EM survey with hundreds of receiver stations. The contraction-operator preconditioner outperformed the Green’s function preconditioner by factor of 7–10, both with respect to run-time and iteration count, and even more at higher frequencies.

scholarly journals Wiener estimation of the Green’s function

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. W31-W44 ◽  
Author(s):  
Anton Ziolkowski
Keyword(s):  
Green’S Function ◽  
Impulse Response ◽  
Green's Function ◽  
Seismic Data ◽  
Wiener Filter ◽  
Electromagnetic Data ◽  
Transient Electromagnetic ◽  
Marine Seismic ◽  
Measured Response

I consider the problem of finding the impulse response, or Green’s function, from a measured response including noise, given an estimate of the source time function. This process is usually known as signature deconvolution. Classical signature deconvolution provides no measure of the quality of the result and does not separate signal from noise. Recovery of the earth impulse response is here formulated as the calculation of a Wiener filter in which the estimated source signature is the input and the measured response is the desired output. Convolution of this filter with the estimated source signature is the part of the measured response that is correlated with the estimated signature. Subtraction of the correlated part from the measured response yields the estimated noise, or the uncorrelated part. The fraction of energy not contained in this uncorrelated component is defined as the quality of the filter. If the estimated source signature contains errors, the estimated earth impulse response is incomplete, and the estimated noise contains signal, recognizable as trace-to-trace correlation. The method can be applied to many types of geophysical data, including earthquake seismic data, exploration seismic data, and controlled source electromagnetic data; it is illustrated here with examples of marine seismic and marine transient electromagnetic data.

On estimating the impulse response between receivers in a controlled ultrasonic experiment

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. SI79-SI84 ◽  
Author(s):  
K. van Wijk
Keyword(s):  
Data Processing ◽  
Laboratory Experiment ◽  
Green’S Function ◽  
Detailed Analysis ◽  
Elastic Medium ◽  
Impulse Response ◽  
Green's Function ◽  
Geophysical Data ◽  
Seismic Interferometry ◽  
Band Limited

A controlled ultrasonic laboratory experiment provides a detailed analysis of retrieving a band-limited estimate of the Green's function between receivers in an elastic medium. Instead of producing a formal derivation, this paper appeals to a series of intuitive operations, common to geophysical data processing, to understand the practicality of seismic interferometry. Whereas the retrieval of the full Green's function is based on the crosscorrelation of receivers in the presence of equipartitioned signal, an estimate of the impulse response is recovered successfully with 40 sources in a line covering six wavelengths at the surface.

Various evaluations of a diffractive transmitted field of light through a one-dimensional metallic grating with subwavelength slits

Open Physics ◽  
2010 ◽  
Vol 8 (3) ◽  
Author(s):  
Bin Hu ◽  
Ben-Yuan Gu ◽  
Bi-Zhen Dong ◽  
Yan Zhang ◽  
Ming Liu
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Exact Result ◽  
The Other ◽  
Optimal Designs ◽  
Optical Elements ◽  
One Dimensional ◽  
Precise Result ◽  
Metallic Grating ◽  
Cylindrical Waves

AbstractWe compare the Fresnel-Kirchhoff diffraction formula, the superposition of cylindrical waves, and the twodimensional (2D) Green’s function diffraction formula with a rigorous vector algorithm in calculating the near and intermediately transmitted field of light through a one-dimensional metallic grating with subwavelength slits. It is found that the results calculated by the 2D Green’s function diffraction formula coincide well with the precise result. The other evaluations deviate from the exact result by varying proportions. Our findings may provide a useful and precise way to analyze the transmitted field features of a metallic grating and subsequent possibility of achieving optimal designs for metallic optical elements with subwavelength scale.

scholarly journals Marchenko imaging

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. WA39-WA57 ◽  
Author(s):  
Kees Wapenaar ◽  
Jan Thorbecke ◽  
Joost van der Neut ◽  
Filippo Broggini ◽  
Evert Slob ◽  
...  
Keyword(s):  
Green’S Function ◽  
Inverse Scattering ◽  
Green's Function ◽  
Seismic Interferometry ◽  
Virtual Source ◽  
Target Zone ◽  
Scattering Problems ◽  
Inverse Scattering Problems ◽  
Marchenko Equation ◽  
Internal Multiples

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 interferometry requires a receiver at the position of the virtual source, for the Marchenko scheme it suffices to have sources and receivers at the surface only. The underlying assumptions are that the medium is lossless and that an estimate of the direct arrivals of the Green’s function is available. The Green’s function retrieved with the 3D Marchenko scheme contains accurate internal multiples of the inhomogeneous subsurface. Using source-receiver reciprocity, the retrieved Green’s function can be interpreted as the response to sources at the surface, observed by a virtual receiver in the subsurface. By decomposing the 3D Marchenko equation, the response at the virtual receiver can be decomposed into a downgoing field and an upgoing field. By deconvolving the retrieved upgoing field with the downgoing field, a reflection response is obtained, with virtual sources and virtual receivers in the subsurface. This redatumed reflection response is free of spurious events related to internal multiples in the overburden. The redatumed reflection response forms the basis for obtaining an image of a target zone. An important feature is that spurious reflections in the target zone are suppressed, without the need to resolve first the reflection properties of the overburden.

Relationship of the self‐potential Green’s function to solutions of controlled source direct‐current potential problems

Geophysics ◽  
1979 ◽  
Vol 44 (11) ◽  
pp. 1879-1881 ◽  
Author(s):  
David V. Fitterman
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Direct Current ◽  
Streaming Potential ◽  
The Self ◽  
Simple Relationship ◽  
Controlled Source ◽  
Source Mechanisms ◽  
Vertical Contact ◽  
Self Potential

This note presents a simple relationship between the self‐potential (SP) Green’s function and the solution of the controlled‐source direct‐current (dc) potential problem which allows a simplified means of determining the SP Green’s function. An example of its application to the vertical contact problem will be presented. The case of a streaming potential source mechanism will be considered, although any of the SP source mechanisms described by Nourbehecht (1963) could be substituted.

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