scholarly journals Asymptotic analysis for dispersion relations and travel times in noise cross-correlations: spherically symmetric case

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180382
Author(s):  
Tianshi Liu ◽  
Haiming Zhang
Keyword(s):  
Asymptotic Analysis ◽  
Surface Waves ◽  
Green's Functions ◽  
Green’S Functions ◽  
Dispersion Relations ◽  
Body Waves ◽  
Spherically Symmetric ◽  
Travel Times ◽  
Cross Correlations ◽  
The Cross

The cross-correlations of ambient noise or earthquake codas are massively used in seismic tomography to measure the dispersion curves of surface waves and the travel times of body waves. Such measurements are based on the assumption that these kinematic parameters in the cross-correlations of noise coincide with those in Green's functions. However, the relation between the cross-correlations of noise and Green's functions deserves to be studied more precisely. In this paper, we use the asymptotic analysis to study the dispersion relations of surface waves and the travel times of body waves, and come to the conclusion that for the spherically symmetric Earth model, when the distribution of noise sources is laterally uniform, the dispersion relations of surface waves and the travel times of SH body-wave phases in noise correlations should be exactly the same as those in Green's functions.

Seismic Monitoring of Permafrost in Svalbard, Arctic Norway

2021 ◽  
Author(s):  
Julie Albaric ◽  
Daniela Kühn ◽  
Matthias Ohrnberger ◽  
Nadège Langet ◽  
Dave Harris ◽  
...  
Keyword(s):  
Surface Waves ◽  
Seismic Noise ◽  
Green's Functions ◽  
Seismic Velocity ◽  
Green’S Functions ◽  
Velocity Model ◽  
Body Waves ◽  
Ambient Seismic Noise ◽  
Seasonal Temperature ◽  
Velocity Variations

Abstract We analyze data from passive and active seismic experiments conducted in the Adventdalen valley of Svalbard in the Norwegian Arctic. Our objective is to characterize the ambient wavefield of the region and to investigate permafrost dynamics through estimates of seismic velocity variations. We are motivated by a need for early geophysical detection of potentially hazardous changes to permafrost stability. We draw upon several data sources to constrain various aspects of seismic wave propagation in Adventdalen. We use f-k analysis of five years of continuous data from the Spitsbergen seismic array (SPITS) to demonstrate that ambient seismic noise on Svalbard consists of continuously present body waves and intermittent surface waves appearing at regular intervals. A change in wavefield direction accompanies the sudden onset of surface waves when the average temperature rises above the freezing point, suggesting a cryogenic origin. This hypothesis is supported further by our analysis of records from a temporary broadband network, which indicates that the background wavefield is dominated by icequakes. Synthetic Green’s functions calculated from a 3D velocity model match well with empirical Green’s functions constructed from the recorded ambient seismic noise. We use a shallow shear-wave velocity model, obtained from active seismic measurements, to estimate the maximum depth of Rayleigh wave sensitivity to changes in shear velocity to be in the 50–100 m range. We extract seasonal variations in seismic velocities from ambient noise cross-correlation functions computed over three years of SPITS data. We attribute relative velocity variations to changes in the ice content of the shallow (2–4 m depth) permafrost, which is sensitive to seasonal temperature changes. A linear decreasing trend in seismic velocity is observed over the years, most likely due to permafrost warming.

Numerical evaluation of Green’s functions for axisymmetric boreholes using leaking modes

Geophysics ◽  
1987 ◽  
Vol 52 (8) ◽  
pp. 1099-1105 ◽  
Author(s):  
R. A. W. Haddon
Keyword(s):  
Wave Propagation ◽  
Fourier Transform ◽  
Elastic Wave ◽  
Numerical Evaluation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Complete Solution ◽  
Body Waves ◽  
Complex Frequency ◽  
Residue Theory

By choosing appropriate paths of integration in both the complex frequency (ω) and complex wavenumber (k) planes, exact Green’s functions for elastic wave propagation in axisymmetric boreholes are expressed completely as sums of modes. The integrations with respect to k are performed exactly using Cauchy residue theory. The remaining integrations with respect to ω are then carried out using the fast Fourier transform (FFT). The complete solution, including all possible body waves, is expressed simply as a superposition of modes without any contributions from branch line integrals. There are no spurious arrivals and, provided that the number of points in the FFT can be taken sufficiently large, no restrictions on distance. The method is fast, accurate, and easy to apply.

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