Diffuse fields in ultrasonics and seismology

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. SI5-SI9 ◽  
Author(s):  
Richard L. Weaver ◽  
Oleg I. Lobkis
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Ultrasonic Waves ◽  
Passive Imaging ◽  
Basic Principles ◽  
Diffuse Fields ◽  
Recent Developments ◽  
History Of ◽  
Scattered Fields

We review the history of diffuse ultrasonic waves in solids with emphasis on recent developments in field-field correlations and their identification with Green’s function. The basic principles appear to be well understood now, and the identity between these two waveforms has been proven under a variety of assumed conditions that guarantee a diffuse field. Promise for practical passive imaging is good; nevertheless, measurements sometimes fail to fully agree with theory. We ascribe this in some cases to incomplete convergence — insufficient amounts of data have been processed. In other cases, it is probably because of a lack of perfect diffuseness; ambient nonmultiply scattered fields are often not equipartitioned and imperfectly diffuse.

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.

ESTIMATION OF IMPACT LOAD IN THICK PLATE BY USING THEORETICAL GREEN FUNCTION AND EXPERIMENTAL MEASUREMENT OF VIBRATION

2008 ◽  
Vol 22 (09n11) ◽  
pp. 1377-1382
Author(s):  
H. W. Kim ◽  
S. K. Lee
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Thick Plate ◽  
Impact Load ◽  
Plate Theory ◽  
Time History ◽  
Force Transducer ◽  
Good Prediction ◽  
History Of ◽  
The Impact

The classic plate theory (CPT) as a theoretical solution to an impact load has been used in a thin plate. However, The CPT is not any more useful solution for the impact load in the industrial power plant, which is generally constructed by the thick plate. In this paper a novel and effective approach is developed to determine the time history of the impact load on a thick aluminum plate based on the analysis of the acoustic waveforms measured by a sensor array located on the thick plate surface in combination with the theoretical Green's function for the plate. The Green's functions are derived based on either the exact elastodynamic or theory the approximate shear deformation plate theory (SDPT). If the displacement is measured on the plate, then the time history of impact load can be calculated by deconvolving the measured displacement with the theoretical Green's function. The reconstructed time history for impact load is compared with the time history of the impact load measured by the force transducer. A good prediction is found. This technique presents a valuable method for identification of source and may be applied to in-service structures under impact to signals recorded from acoustic emission of propagating cracks.

Detection of near-surface defects in rails combining Green's function retrieval of ultrasonic diffuse fields and sign coherence factor imaging

2020 ◽  
Vol 62 (4) ◽  
pp. 216-221
Author(s):  
Haiyan Zhang ◽  
Mintao Shao ◽  
Guopeng Fan ◽  
Hui Zhang ◽  
Wenfa Zhu
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Surface Defects ◽  
Signal To Noise Ratio ◽  
Near Surface ◽  
Coherence Factor ◽  
Array Transducer ◽  
Diffuse Fields ◽  
Ultrasonic Phased Array ◽  
Cross Correlations

A method combining Green's function retrieval theory and sign coherence factor (SCF) imaging is presented to detect near-surface defects in rails. The defects are close to the ultrasonic phased array and near-surface acoustic information of defects is obscured by the non-linear effects of the initial wave signal in directly acquired responses. To overcome this problem, cross-correlations of the diffuse field signals captured by the array transducer are performed to reconstruct the Green's function. SCF imaging is used to further improve the spatial resolution and signal-to-noise ratio (SNR) of near-surface defects in rails. Experiments are conducted on two rails containing two and four defects, respectively. The results show that these defects can be clearly identified when using the reconstructed Green's function. However, the images of near-surface defects are masked and cannot be distinguished when using directly captured signals and total focus imaging. The proposed method reduces the background noise and allows for effective imaging of near-surface defects in rails.

Extraction of thermal Green's function using diffuse fields: a passive approach applied to thermography

2016 ◽  
Author(s):  
Margherita Capriotti ◽  
Simone Sternini ◽  
Francesco Lanza di Scalea ◽  
Stefano Mariani
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Diffuse Fields

scholarly journals Wavenumber Imaging of Near-Surface Defects in Rails using Green’s Function Reconstruction of Ultrasonic Diffuse Fields

Sensors ◽  
2019 ◽  
Vol 19 (17) ◽  
pp. 3744 ◽  
Author(s):  
Hui Zhang ◽  
Haiyan Zhang ◽  
Jiayan Zhang ◽  
Jianquan Liu ◽  
Wenfa Zhu ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Phased Array ◽  
Surface Defects ◽  
Measured Signal ◽  
Near Surface ◽  
Diffuse Fields ◽  
Ultrasonic Phased Array ◽  
The Cross ◽  
Function Reconstruction

Wavenumber imaging with Green’s function reconstruction of ultrasonic diffuse fields is used to realize fast imaging of near-surface defects in rails. Ultrasonic phased array has been widely used in industries because of its high sensitivity and strong flexibility. However, the directly measured signal is always complicated by noise caused by physical limitations of the acquisition system. To overcome this problem, the cross-correlations of the diffuse field signals captured by the probe are performed to reconstruct the Green’s function. These reconstructed signals can restore the early time information from the noise. Experiments were conducted on rails with near-surface defects. The results confirm the effectiveness of the cross-correlation method to reconstruct the Green’s function for the detection of near-surface defects. Different kinds of ultrasonic phased array probes were applied to collect experimental data on the surface of the rails. The Green’s function recovery is related to the number of phased array elements and the excitation frequency. In addition, the duration and starting time of the time-windowed diffuse signals were explored in order to achieve high-quality defect images.

Principles of Economics

2015 ◽  
pp. 302-333
Author(s):  
Célestin Monga
Keyword(s):  
Economic Literature ◽  
Basic Principles ◽  
Economic Man ◽  
Economic Experience ◽  
Modeling Techniques ◽  
Recent Developments ◽  
History Of ◽  
Human Thinking ◽  
Economic Thinking ◽  
Made In

Mainstream economists have promoted the idea of universally representative agents, which allows for simple modeling techniques to describe and predict human thinking and decision-making. Yet, there has been a debate in the economic literature on the existence of the rational “economic man” in Africa. The continent’s long history of oppression, its sub-optimal economic performance, and colonial fantasies, have contributed to the development of a discourse of otherness fed by prejudices. This chapter tackles some of these epistemological dilemmas and policy issues in that debate through a reconsideration of the basic principles of economics. A didactic approach is followed, popularized by Gregory Mankiw, and a list of ten principles different from the ones he proposed is produced. This chapter offers a series of counter-narratives to conventional economic thinking, and highlights how some of the recent developments in economics are consistent with analyses made in the study of Africa’s economic experience.

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