Propagation of waves in a randomly inhomogeneous medium with strongly developed fluctuations. III. Arbitrary power-law noise correlation function

1988 ◽  
Vol 74 (3) ◽  
pp. 241-250 ◽  
Author(s):  
L. Ts. Adzhemyan ◽  
A. N. Vasil'ev ◽  
Yu. M. Pis'mak
Keyword(s):  
Correlation Function ◽  
Inhomogeneous Medium ◽  
Power Law ◽  
Noise Correlation ◽  
Arbitrary Power ◽  
Power Law Noise ◽  
Noise Correlation Function ◽  
Propagation Of Waves

Wave scattering in a randomly inhomogeneous medium with long-range noise correlation function ?1/r

1990 ◽  
Vol 84 (2) ◽  
pp. 848-856
Author(s):  
L. S. Adzhemyan ◽  
A. N. Vasil'ev ◽  
M. M. Perekalin ◽  
Kh. Yu. Reittu
Keyword(s):  
Correlation Function ◽  
Inhomogeneous Medium ◽  
Long Range ◽  
Wave Scattering ◽  
Noise Correlation ◽  
Noise Correlation Function

Relative Time Corrections for Historical Analog Seismograms Using the Single-Day Ambient Noise Correlation Function

2020 ◽  
Vol 110 (6) ◽  
pp. 3185-3195
Author(s):  
Thomas Lee ◽  
Miaki Ishii ◽  
Paul Okubo
Keyword(s):  
Correlation Function ◽  
Noise Correlation ◽  
Relative Time ◽  
P Waves ◽  
Arrival Times ◽  
Volcano Observatory ◽  
Local Earthquake ◽  
Noise Correlation Function ◽  
Using Data ◽  
Time Accuracy

ABSTRACT This study examines analog seismograms that were generated when most seismic stations had their own clock for timing, making precise comparison of time between different stations difficult. Availability of accurate relative timing facilitates differential travel-time analyses, such as seismic tomography and local earthquake relocations, to be performed using data originally recorded on paper or other physical media. These analyses allow for the investigation of longer-term processes like the earthquake cycle or climate change. We take advantage of the continuous nature of seismic noise to determine the relative time correction between two stations by leveraging the symmetry of the noise correlation function. This procedure is applied to two Global Positioning System-timed stations in the Hawaiian Volcano Observatory network demonstrating subsecond time accuracy. The technique is then applied to analog records from comparable stations between 7 and 10 August in 1988, and relative time corrections of up to about 6 s are obtained. These corrections are confirmed by the relative arrival times of teleseismic P waves of earthquake doublets.

scholarly journals Recovering and monitoring the thickness, density and elastic properties of sea ice from seismic noise recorded in Svalbard

2021 ◽  
Author(s):  
Agathe Serripierri ◽  
Ludovic Moreau ◽  
Pierre Boue ◽  
Jérôme Weiss ◽  
Philippe Roux
Keyword(s):  
Mechanical Properties ◽  
Correlation Function ◽  
Sea Ice ◽  
Elastic Properties ◽  
Arctic Sea Ice ◽  
The Arctic ◽  
Ice Thickness ◽  
Noise Correlation ◽  
Sea Ice Thickness ◽  
Noise Correlation Function

Abstract. Due to global warming, the decline in the Arctic sea ice has been accelerating over the last four decades, with a rate that was not anticipated by climate models. To improve these models, there is the need to rely on comprehensive field data. Seismic methods are known for their potential to estimate sea-ice thickness and mechanical properties with very good accuracy. However, with the hostile environment and logistical difficulties imposed by the polar regions, seismic studies have remained rare. Due to the rapid technological and methodological progress of the last decade, there has been a recent reconsideration of such approaches. This paper introduces a methodological approach for passive monitoring of both sea-ice thickness and mechanical properties. To demonstrate this concept, we use data from a seismic experiment where an array of 247 geophones was deployed on sea ice in a fjord at Svalbard, between March 1 and 24, 2019. From the continuous recording of the ambient seismic field, the empirical Green's function of the seismic waves guided in the ice layer was recovered via the so-called 'noise correlation function'. Using specific array processing, the multi-modal dispersion curves of the ice layer were calculated from the noise correlation function, and then inverted for the thickness and elastic properties of the sea ice via Bayesian inference. The evolution of sea-ice properties was monitored for 24 days, and values are consistent with the literature, as well as with measurements made directly in the field.

TESTING POWER-LAW RELAXATION SCENARIOS IN A METASTABLE LIQUID

2012 ◽  
Vol 26 (29) ◽  
pp. 1250146 ◽  
Author(s):  
BHASKAR SEN GUPTA ◽  
SHANKAR P. DAS
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Hard Sphere ◽  
Numerical Solutions ◽  
Packing Fraction ◽  
Equilibrium Density ◽  
Density Correlation ◽  
Density Correlation Function ◽  
Basic Model ◽  
The One

The renormalized dynamics described by the equations of nonlinear fluctuating hydrodynamics (NFH) treated at one loop order gives rise to the basic model of the mode coupling theory (MCT). We investigate here by analyzing the density correlation function, a crucial prediction of ideal MCT, namely the validity of the multi step relaxation scenario. The equilibrium density correlation function is calculated here from the direct solutions of NFH equations for a hard sphere system. We make first detailed investigation for the robustness of the correlation functions obtained from the numerical solutions by varying the size of the grid. For an optimum choice of grid size we analyze the decay of the density correlation function to identify the multi-step relaxation process. Weak signatures of two step power law relaxation is seen with exponents which do not match predictions from the one loop MCT. For the final relaxation stretched exponential (KWW) behavior is seen and the relaxation time grows with increase of density. But apparent power law divergences indicate a critical packing fraction much higher than the corresponding MCT predictions for a hard sphere fluid.

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