Direct estimation of the Rayleigh wave phase velocity in microtremors

Shiraishi, Hidetaka; Matsuoka, Toshifumi; Asanuma, Hiroshi

doi:10.1029/2006gl026723

Cited by 9 publications

(4 citation statements)

References 7 publications

(9 reference statements)

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“…Phase velocity is inversely proportional to the derivative of the cross-coherence phase with respect to frequency. We assumed that CCFs can be expressed as the superposition of the Bessel function J 0 (·) and an angle-dependent error term [13]. Averaging over angle between the reference receiver and the rest of the array reduced the error term significantly.…”

Section: Overview Of Wave Dispersion Estimation Methodsmentioning

confidence: 99%

Estimation of EEG signal dispersion during seizure propagation

Stamoulis

Chang

Madsen

2009

2009 16th International Conference on Digital Signal Processing

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Localization of the seizure focus in the brain is a challenging problem in the field of epilepsy. The complexity of the seizure-related EEG waveform, its non-stationarity and degradation with distance due to the dispersive nature of the brain as a propagation medium, make localization difficult. Yet, precise estimation of the focus is critical, particularly when surgical resection is the only therapeutic option. The first step to solving this inverse problem is to estimate and account for frequency- or mode-specific signal dispersion, which is present in both scalp and intracranial EEG recordings during seizures. We estimated dispersion curves in both types of signals using a spatial correlation method and mode-based semblance analysis. We showed that, despite the assumption of spatial stationarity and a simplified array geometry, there is measurable inter-modal and intra-modal dispersion during seizures in both types of EEG recordings, affecting the estimated arrival times and consequently focus localization.

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Section: Overview Of Wave Dispersion Estimation Methodsmentioning

confidence: 99%

Estimation of EEG signal dispersion during seizure propagation

Stamoulis

Chang

Madsen

2009

2009 16th International Conference on Digital Signal Processing

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“…His derivation pathway is, however, different from ours, and does not easily provide an interface with the general theory of directional aliasing which we present below. Shiraishi et al [2006] also arrived at a similar expression, but they relied on the strong premise that waves arrive from a finite number of discrete azimuths.…”

Section: Theoretical Evaluation Of Error Factorsmentioning

confidence: 99%

“…Slight deviations from the circular and equidistant seismic‐array configuration tend to pose few serious obstacles to the use of the SPAC method. Attempts have been made, in recent years, to make use of seismic arrays of irregular shapes [e.g., Bettig et al , 2001; Ohori et al , 2002; Maresca et al , 2006; Shiraishi et al , 2006; Köhler et al , 2007]. The most extreme case is that of an array of just two seismic sensors, with one sensor around the circumference plus another at its center, which has reportedly produced reasonable results [e.g., Aki , 1957; Morikawa et al , 2004; Chávez‐García and Luzón , 2005; Chávez‐García et al , 2005, 2006, 2007a, 2007b].…”

Section: Introductionmentioning

confidence: 99%

Assessing the applicability of the spatial autocorrelation method: A theoretical approach

2008

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[1] We present a rigorous theoretical framework that allows one to assess the range of applicability of the spatial autocorrelation (SPAC) method, a technique of microtremor exploration that is widely used to infer phase velocities of Rayleigh waves using vertical-motion records from a circular array of seismic sensors. The magnitude of systematic errors (biases) that depend on the number of seismic sensors deployed around the circle, and the magnitude of systematic errors that arise from the presence of incoherent noise, are both evaluated analytically, and their general properties are discussed. The relationship between the magnitude of stochastic errors, inherent in the analysis results, and the duration of measurement (or to put it more accurately, the data's degree of freedom) is also elucidated. The validity of our theory is corroborated by checks against the results of both real data analysis and numerical experiments, and an example is given of how the theory can be adapted to account for practical situations encountered in the field. Discussions on the range of applicability of the SPAC method, which have heretofore often fallen back on empirical observations, have now obtained a theoretical ground on which to stand, providing a basis for strategies to make maximal use of the SPAC method's capabilities.Citation: Cho, I., T. Tada, and Y. Shinozaki (2008), Assessing the applicability of the spatial autocorrelation method: A theoretical approach,

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“…Since Aki ( 1957 ) proposed a new approach to estimate phase velocities of surface waves, spatial auto-correlation (SPAC) method has been a very useful tool to estimate ground structure because of its simple post-process (Aki 1957 ). After that, many researchers both in and out of Japan continued to publish papers to extend Aki’s theory and developed a variety of array methods (Okada 2003 ; Morikawa et al 2004 ; Cho et al 2006 ; Chávez-García et al 2005 , 2007 ; Shiraishi et al 2006 ; Tada et al 2009 ). However, all those improved methods are based on the assumption that the layers under surface are horizontal.…”

Section: Introductionmentioning

confidence: 99%

A new significance on the vertical component ratio of the power spectra between two sites in the application of array methods

Zhang

Morikawa

2015

J Seismol

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Array methods like spatial auto-correlation (SPAC) method and the centerless circular array (CCA) method have provided a convenient means of inferring the phase velocity of surface waves. However, these methods are under the assumption of horizontally layered medium (lateral homogeneity) while the ground structure is actually likely to be inclined. Hence, it is expected to obtain more detailed information of ground structure such as inclination by making better use of the records. In recent years, the seismic interferometry theory has also been widely used to estimate ground structure. According to seismic interferometry theory, the cross correlation of motion between two sites is proportional to the imaginary part of the Green’s function (IOG) between the two sites in diffuse wavefield. In this study, we can obtain the ratio of IOG between two sites by taking the ratio of power spectra between the same two sites. We propose this ratio as an indicator of the lateral heterogeneity between two sites. Through numerical simulation and a field test, we demonstrate that the significance of ratio of power spectra can be interpreted from the sight of ratio of IOG successfully.

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Direct estimation of the Rayleigh wave phase velocity in microtremors

Cited by 9 publications

References 7 publications

Estimation of EEG signal dispersion during seizure propagation

Estimation of EEG signal dispersion during seizure propagation

Assessing the applicability of the spatial autocorrelation method: A theoretical approach

A new significance on the vertical component ratio of the power spectra between two sites in the application of array methods

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