scholarly journals Retrieval of long-wave tsunami Green’s function from the cross-correlation of continuous ocean waves excited by far-field random noise sources on the basis of a first-order Born approximation

2012 ◽  
Vol 64 (1) ◽  
pp. 43-48 ◽  
Author(s):  
Tatsuhiko Saito ◽  
Jun Kawahara
Keyword(s):  
Green's Function ◽  
Born Approximation ◽  
Cross Correlation ◽  
Random Noise ◽  
Ocean Waves ◽  
Far Field ◽  
Noise Sources ◽  
First Order ◽  
Long Wave ◽  
The Cross

scholarly journals On the Green's function emergence from interferometry of seismic wave fields generated in high-melt glaciers: implications for passive imaging and monitoring

2020 ◽  
Vol 14 (3) ◽  
pp. 1139-1171 ◽  
Author(s):  
Amandine Sergeant ◽  
Małgorzata Chmiel ◽  
Fabian Lindner ◽  
Fabian Walter ◽  
Philippe Roux ◽  
...  
Keyword(s):  
Green’S Function ◽  
Wave Field ◽  
Green's Function ◽  
Seismic Wave ◽  
Ambient Noise ◽  
Cross Correlation ◽  
Noise Sources ◽  
Wave Fields ◽  
Seismic Scattering ◽  
The Cross

Abstract. Ambient noise seismology has revolutionized seismic characterization of the Earth's crust from local to global scales. The estimate of Green's function (GF) between two receivers, representing the impulse response of elastic media, can be reconstructed via cross-correlation of the ambient noise seismograms. A homogenized wave field illuminating the propagation medium in all directions is a prerequisite for obtaining an accurate GF. For seismic data recorded on glaciers, this condition imposes strong limitations on GF convergence because of minimal seismic scattering in homogeneous ice and limitations in network coverage. We address this difficulty by investigating three patterns of seismic wave fields: a favorable distribution of icequakes and noise sources recorded on a dense array of 98 sensors on Glacier d'Argentière (France), a dominant noise source constituted by a moulin within a smaller seismic array on the Greenland Ice Sheet, and crevasse-generated scattering at Gornergletscher (Switzerland). In Glacier d'Argentière, surface melt routing through englacial channels produces turbulent water flow, creating sustained ambient seismic sources and thus favorable conditions for GF estimates. Analysis of the cross-correlation functions reveals non-equally distributed noise sources outside and within the recording network. The dense sampling of sensors allows for spatial averaging and accurate GF estimates when stacked on lines of receivers. The averaged GFs contain high-frequency (>30 Hz) direct and refracted P waves in addition to the fundamental mode of dispersive Rayleigh waves above 1 Hz. From seismic velocity measurements, we invert bed properties and depth profiles and map seismic anisotropy, which is likely introduced by crevassing. In Greenland, we employ an advanced preprocessing scheme which includes match-field processing and eigenspectral equalization of the cross spectra to remove the moulin source signature and reduce the effect of inhomogeneous wave fields on the GFs. At Gornergletscher, cross-correlations of icequake coda waves show evidence for homogenized incident directions of the scattered wave field. Optimization of coda correlation windows via a Bayesian inversion based on the GF cross coherency and symmetry further promotes the GF estimate convergence. This study presents new processing schemes on suitable array geometries for passive seismic imaging and monitoring of glaciers and ice sheets.

Passive scalar dispersion and mixing in a turbulent jet

1995 ◽  
Vol 292 ◽  
pp. 1-38 ◽  
Author(s):  
Chenning Tong ◽  
Z. Warhaft
Keyword(s):  
Reynolds Number ◽  
Cross Correlation ◽  
Thermal Field ◽  
Temperature Fluctuations ◽  
Passive Scalar ◽  
Turbulent Jet ◽  
Grid Turbulence ◽  
Far Field ◽  
The Cross ◽  
Heated Jet

The dispersion and mixing of passive scalar (temperature) fluctuations is studied in a turbulent jet. The temperature fluctuations were produced by heated fine wire rings placed axisymmetrically in the flow. Typically the ring diameters were of the same order as the jet, Dj, and they were placed in the self-similar region. However, other initial conditions were studied, including a very small diameter ring used to approximate a point source. Using a single ring to study dispersion (which is analogous to placing a line source in a planar flow such as grid turbulence), it was found that the intense local thermal field close to the ring disperses and fills the whole jet in approximately 1.5 eddy turnover times. Thereafter the thermal field evolves in the same way as for the traditional heated jet experiments. Two heated rings were used to study the mixing of two independently introduced scalar fields. Here an inference method (invoking the principle of superposition) was used to determine the evolution of the cross-correlation coefficient, ρ, and the segregation parameter, α, as well as the coherence and co-spectrum. While initially strongly dependent on ring locations and spacing, ρ and α reached asymptotic values of 1 and 0.04, respectively, also in about 1.5 eddy turnover times. These results are contrasted with mixing and dispersion in grid turbulence where the evolution is slower. Measurements in the far field of the jet (where ρ = 1) of the square of the scalar derivative conditioned on the scalar fluctuation itself, as well as other conditional statistics, showed strong dependence on the measurement location, as well as the direction in which the derivative was determined. The cross-correlation between the square of the scalar derivative and the signal showed a clear Reynolds-number trend, decreasing as the jet Reynolds number was varied from 2800 to 18 000. The far-field measurements, using the heated rings, were corroborated by new heated jet experiments.

The theory of deep holograms

1968 ◽  
Vol 304 (1478) ◽  
pp. 275-289 ◽  
Keyword(s):  
Born Approximation ◽  
Random Noise ◽  
Directional Selectivity ◽  
Two Dimensional ◽  
First Order ◽  
Auto Correlation ◽  
Auto Correlation Function ◽  
Colour Photography ◽  
Photographic Emulsions ◽  
Second Wave

A simple theory of the first-order properties of holograms in thick photographic emulsions is presented. Following a combination by Denisyuk of the basic method of wavefront recon­struction with Lippmann’s method of colour photography, such holograms are produced by the interference of an object wave with a coherent reference wave, falling on the emulsion from opposite sides. It is shown, by using the first Born approximation, that such deep holograms have three properties which distinguish them from two-dimensional or ‘plane’ holograms: (1) They have directional selectivity, that is to say the image will appear only if the hologram is illuminated in the reconstruction within a certain angular zone. (2) They have colour selectivity, that is to say they will reflect only within a certain narrow waveband close to the original wavelength. (3) The second wave, which is a disturbance in two-dimensional holograms is as good as completely suppressed. All three are of great practical value. It is shown that holograms which are produced by strongly diffused, wide-angle illumina­tion, and which have a random, noise-like appearance, contain the information in the form of the auto-correlation function of densities or scattering powers between different space-elements in the emulsion.

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