Extraction of phase and group velocities from ambient surface noise in a patch-array configuration

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. KS231-KS240 ◽  
Author(s):  
Malgorzata Chmiel ◽  
Philippe Roux ◽  
Thomas Bardainne
Keyword(s):  
Surface Wave ◽  
Group Velocity ◽  
Seismic Analysis ◽  
Vertical Component ◽  
Noise Sources ◽  
Array Design ◽  
Near Surface ◽  
Phase And Group Velocities ◽  
Group Velocities ◽  
Surface Noise

We have investigated the use of ambient-noise data to extract phase and group velocities from surface-noise sources in a microseismic monitoring context. The data were continuously recorded on 44 patch arrays with an interpatch distance on the order of 1 km. Typically, a patch-array design consists of a few tens of patches, each containing 48 strings of 12 single-vertical-component geophones densely distributed within the patch area. The specificity of the patch-array design allows seismic analysis at two different scales. Within each patch, highly coherent signals at small distances provide phase information at high frequency (up to 10 Hz), from which surface-wave phase velocities can be extracted. Between the pairs of patches, surface-wave group-velocity maps can be built using correctly identified and localized surface-noise sources. The technique can be generalized to every patch pair using different noise sources identified at the surface. We note that the incoherent but localized noise sources accelerate the convergence of the noise-correlation functions. This opens the route to passive seismic monitoring of the near surface from repetitive inversion of phase- and group-velocity maps.

Compressional‐wave velocities in attenuating media: A laboratory physical model study

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1162-1167 ◽  
Author(s):  
Joseph B. Molyneux ◽  
Douglas R. Schmitt
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Wave Velocity ◽  
Propagation Distance ◽  
Compressional Wave ◽  
Arrival Times ◽  
Wave Velocities ◽  
Amplitude Maximum ◽  
Phase And Group Velocities ◽  
Group Velocities

Elastic‐wave velocities are often determined by picking the time of a certain feature of a propagating pulse, such as the first amplitude maximum. However, attenuation and dispersion conspire to change the shape of a propagating wave, making determination of a physically meaningful velocity problematic. As a consequence, the velocities so determined are not necessarily representative of the material’s intrinsic wave phase and group velocities. These phase and group velocities are found experimentally in a highly attenuating medium consisting of glycerol‐saturated, unconsolidated, random packs of glass beads and quartz sand. Our results show that the quality factor Q varies between 2 and 6 over the useful frequency band in these experiments from ∼200 to 600 kHz. The fundamental velocities are compared to more common and simple velocity estimates. In general, the simpler methods estimate the group velocity at the predominant frequency with a 3% discrepancy but are in poor agreement with the corresponding phase velocity. Wave velocities determined from the time at which the pulse is first detected (signal velocity) differ from the predominant group velocity by up to 12%. At best, the onset wave velocity arguably provides a lower bound for the high‐frequency limit of the phase velocity in a material where wave velocity increases with frequency. Each method of time picking, however, is self‐consistent, as indicated by the high quality of linear regressions of observed arrival times versus propagation distance.

Errors Introduced in Estimation of Surface Wave Phase and Group Velocities Due to Wrong Assumptions: An Assessment Using a Simple Model For Love Wave

2021 ◽  
Author(s):  
Akash Kharita ◽  
Sagarika Mukhopadhyay
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Love Wave ◽  
Arrival Time ◽  
Epicentral Distance ◽  
Horizontal Distance ◽  
Wave Analysis ◽  
Time Period ◽  
Phase And Group Velocities ◽  
Group Velocities

<p>The surface wave phase and group velocities are estimated by dividing the epicentral distance by phase and group travel times respectively in all the available methods, this is based on the assumptions that (1) surface waves originate at the epicentre and (2) the travel time of the particular group or phase of the surface wave is equal to its arrival time to the station minus the origin time of the causative earthquake; However, both assumptions are wrong since surface waves generate at some horizontal distance away from the epicentre. We calculated the actual horizontal distance from the focus at which they generate and assessed the errors caused in the estimation of group and phase velocities by the aforementioned assumptions in a simple isotropic single layered homogeneous half space crustal model using the example of the fundamental mode Love wave. We took the receiver locations in the epicentral distance range of 100-1000 km, as used in the regional surface wave analysis, varied the source depth from 0 to 35 Km with a step size of 5 km and did the forward modelling to calculate the arrival time of Love wave phases at each receiver location. The phase and group velocities are then estimated using the above assumptions and are compared with the actual values of the velocities given by Love wave dispersion equation. We observed that the velocities are underestimated and the errors are found to be; decreasing linearly with focal depth, decreasing inversely with the epicentral distance and increasing parabolically with the time period. We also derived empirical formulas using MATLAB curve fitting toolbox that will give percentage errors for any realistic combination of epicentral distance, time period and depths of earthquake and thickness of layer in this model. The errors are found to be more than 5% for all epicentral distances lesser than 500 km, for all focal depths and time periods indicating that it is not safe to do regional surface wave analysis for epicentral distances lesser than 500 km without incurring significant errors. To the best of our knowledge, the study is first of its kind in assessing such errors.</p>

Measurement of interstation phase and group velocities and Q using Wiener filtering

1982 ◽  
Vol 72 (1) ◽  
pp. 73-91
Author(s):  
Steven R. Taylor ◽  
M. Nafi Toksöz
Keyword(s):  
Surface Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Amplitude Spectrum ◽  
Wiener Filter ◽  
Wave Path ◽  
Phase And Group Velocities ◽  
Filtering Technique ◽  
Surface Wave Data ◽  
Group Velocities

abstract A method for calculating interstation phase and group velocities and attenuation coefficients using a Wiener (least-squares) filtering technique is presented. The interstation Green's (or transfer) function is estimated from surface wave data from two stations laying along the same great circle path. The estimate is obtained from a Wiener filter which is constructed to estimate the signal recorded at the station further from the source from the signal recorded at the nearer station. The interstation group velocity is obtained by applying the multiple-filtering technique to the Green's function, and the interstation phase velocity from the phase spectrum of the Green's function. The amplitude spectrum of the Green's function is used to calculate average attenuation between the two stations. Using synthetic seismograms contaminated by noise, it is shown that the Q values calculated from the Green's function are significantly more stable and accurate than those obtained by taking spectral ratios. The method is particularly useful for paths involving short station separations and is applied to a surface wave path crossing the Iranian Plateau.

Estimation of elastic stiffness coefficients of an orthorhombic physical model using group velocity analysis on transmission data

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. R27-R39 ◽  
Author(s):  
Faranak Mahmoudian ◽  
G. F. Margrave ◽  
P. F. Daley ◽  
J. Wong ◽  
D. C. Henley
Keyword(s):  
Physical Model ◽  
Group Velocity ◽  
Body Wave ◽  
Elastic Stiffness ◽  
Laboratory Model ◽  
Theoretical Dependence ◽  
Stiffness Coefficients ◽  
Phase Velocities ◽  
Phase And Group Velocities ◽  
Group Velocities

We acquired 3C ultrasonic transmission seismograms, measured group velocities associated with the three quasi-body wave types, and determined density-normalized stiffness coefficients ([Formula: see text]) over an orthorhombic physical (laboratory) model. The estimation of [Formula: see text] is based on an approximate relationship between the nine orthorhombic [Formula: see text] and group velocities. Estimation of the anisotropic [Formula: see text] is usually done using phase velocities with well-known formulas expressing their theoretical dependence on [Formula: see text]. However, on time-domain seismograms, arrivals are observed traveling with group velocities. Group velocity measurements are found to be straightforward, reasonably accurate, and independent of the size of the transducers used. In contrast, the accuracy of phase velocities derived from the [Formula: see text] transform analysis was found to be very sensitive to small differences in picked arrival times and to transducer size. Theoretical phase and group velocities, calculated in a forward manner from the [Formula: see text] estimates, agreed with the originally measured phase and group velocities, respectively. This agreement confirms that it is valid to use easily measured group velocities with their approximate theoretical relationship to the [Formula: see text] to determine the full stiffness matrix. Compared to the phase-velocity procedure, the technique involving group velocities is much less prone to error due to time-picking uncertainties, and therefore is more suitable for analyzing physical model seismic data.

EXPERIMENTAL STUDIES OF SOURCE‐GENERATED SEISMIC NOISE

Geophysics ◽  
1971 ◽  
Vol 36 (6) ◽  
pp. 1138-1149 ◽  
Author(s):  
R. N. Jolly ◽  
J. F. Mifsud
Keyword(s):  
Seismic Noise ◽  
Experimental Studies ◽  
Near Surface ◽  
The Third ◽  
Wave Velocities ◽  
Leaky Modes ◽  
Phase And Group Velocities ◽  
Group Velocities ◽  
Surface Layer Thickness ◽  
High Phase

Source‐generated seismic noise has been studied in several areas of Oklahoma and Texas having distinctly different near‐surface layering and velocities. Surface‐wave velocities, particularly those of the propagating modes, are closely related to near‐surface layer thickness and velocity. Modal structure is strongly influenced by the shooting parameters, of which charge depth is the most important. The Rayleigh or first propagating mode and the third propagating mode are readily identifiable on the noise records and agree satisfactorily with theory, if frequency‐dependent attenuation and modal overlapping are taken into account. Leaky modes are identifiable on the basis of their high phase and group velocities but to date have defied quantitative comparison with theory.

A comprehensive comparison between the refraction microtremor and seismic interferometry methods for phase-velocity estimation

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. EN99-EN108 ◽  
Author(s):  
Zongbo Xu ◽  
T. Dylan Mikesell ◽  
Jianghai Xia ◽  
Feng Cheng
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Wave Velocity ◽  
Velocity Estimation ◽  
Seismic Interferometry ◽  
S Wave ◽  
Noise Sources ◽  
Surface Wave Dispersion ◽  
Near Surface ◽  
Refraction Microtremor

Passive-source seismic-noise-based surface-wave methods are now routinely used to investigate the near-surface geology in urban environments. These methods estimate the S-wave velocity of the near surface, and two methods that use linear recording arrays are seismic interferometry (SI) and refraction microtremor (ReMi). These two methods process noise data differently and thus can yield different estimates of the surface-wave dispersion, the data used to estimate the S-wave velocity. We have systematically compared these two methods using synthetic data with different noise source distributions. We arrange sensors in a linear survey grid, which is conveniently used in urban investigations (e.g., along roads). We find that both methods fail to correctly determine the low-frequency dispersion characteristics when outline noise sources become stronger than inline noise sources. We also identify an artifact in the ReMi method and theoretically explain the origin of this artifact. We determine that SI combined with array-based analysis of surface waves is the more accurate method to estimate surface-wave phase velocities because SI separates surface waves propagating in different directions. Finally, we find a solution to eliminate the ReMi artifact that involves the combination of SI and the [Formula: see text]-[Formula: see text] transform, the array processing method that underlies the ReMi method.

scholarly journals Dispersion and attenuation of a longitudinal wave propagating in a metamaterial defined as a mass-to-mass chain

2019 ◽  
pp. 6-18
Author(s):  
V I Erofeev ◽  
D A Kolesov ◽  
V L Krupenin
Keyword(s):  
Phase Velocity ◽  
Longitudinal Wave ◽  
Group Velocity ◽  
Mass Density ◽  
Deformable Body ◽  
Mass Model ◽  
Positive Direction ◽  
Normal Dispersion ◽  
Phase And Group Velocities ◽  
Group Velocities

We study the features of propagation of a longitudinal wave in an acoustic (mechanical) metamaterial, modeled as a one-dimensional chain, containing equal masses, connected by elastic elements (springs), and having the same rigidity. Each mass contains within itself a series connection of another mass and viscous element (damper). The mass-to-mass model is free from the drawbacks of a number of other mechanical models of metamaterials: i.e. it eliminates the need to have the property of a deformable body to possess a negative mass, density, and (or) a negative elastic modulus. It is shown that the model under consideration makes it possible to describe the dispersion and frequency-dependent attenuation of a longitudinal wave, the character of which essentially depends on the ratio of the external and internal mass of the metamaterial. The behavior of the phase and group velocities of the wave is studied, as well as the evolution of its profile, both in the low-frequency and high-frequency ranges. The mass ratios were found at which the phase velocity exceeds the group velocity (normal dispersion) in magnitude and those at which the group velocity exceeds the phase velocity (anomalous dispersion) in a wide frequency range. Having the same asymptotic values when the frequency tends to infinity, the phase and group velocities have significant differences in behavior, namely, that the phase velocity is a monotonic function of frequency, and the group velocity has a maximum. In addition, in the region of normal dispersion, the group velocity may be negative, i.e. the so-called “reverse wave” effect is true, when, despite the fact that the phase velocity is directed in the positive direction of the spatial axis, the energy in such a wave is transferred in the negative direction.

Shear-wave group-velocity surfaces in low-symmetry anisotropic media

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. C1-C7 ◽  
Author(s):  
Vladimir Grechka
Keyword(s):  
Group Velocity ◽  
Body Wave ◽  
Transverse Isotropy ◽  
Shear Waves ◽  
Anisotropic Media ◽  
The Body ◽  
Velocity Models ◽  
Phase And Group Velocities ◽  
Low Symmetry ◽  
Group Velocities

Shear waves excited by natural sources constitute a significant part of useful energy recorded in downhole microseismic surveys. In rocks, such as fractured shales, exhibiting symmetries lower than transverse isotropy (TI), the shear wavefronts are always multivalued in certain directions, potentially complicating the data processing and analysis. This paper discusses a basic tool — the computation of the phase and group velocities of all waves propagating along a given ray — that intends to facilitate the understanding of geometries of the shear wavefronts in homogeneous anisotropic media. With this tool, arbitrarily complex group-velocity surfaces can be conveniently analyzed, providing insights into possible challenges to be faced when processing shear waves in anisotropic velocity models that have symmetries lower than TI. Among those challenges are complicated multipathing and the presence of cones of directions, known as internal refraction cones, in which no fast shear waves propagate and the entire shear portion of the body-wave seismic data consists of several branches of the slow shear wavefronts.

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