Signal Processing and Frequency-Wavenumber Spectrum Analysis for a Large Aperture Seismic Array

Capon, Jack

doi:10.1016/b978-0-12-460813-9.50007-2

Cited by 57 publications

(49 citation statements)

References 23 publications

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“…Research progressed through the 1970s concentrating on the detection of earthquake waves in records contaminated by noise, such as microtremors and pulsation (e.g., Capon, 1969). The success of research was facilitated by 1 Downloaded 06/25/14 to 134.153.184.170.…”

Section: Prefacementioning

confidence: 99%

The Microtremor Survey Method

Okada¹

2003

534

274

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Section: Prefacementioning

confidence: 99%

The Microtremor Survey Method

Okada¹

2003

534

274

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“…Modifications to the conventional SPAC processing have been developed to permit its use with arrays that deviate from the standard circular and equidistant configuration (Bettig et al, 2001;Ohori et al, 2002;Cho et al, 2004;Köhler et al, 2007). This idea was originally proposed by Aki (1957) and mathematically demonstrated by Capon (1973), who proved that identical results are obtained when using a single pair of sensors to record an omnidirectional wave field or an array of n sensors to record one single plane wave of unique azimuth. The integration of complex coherencies is adapted to sum over the sources azimuth ϕ with the sensors orientation θ fixed.…”

Section: Introductionmentioning

confidence: 96%

Statistical Validity Control on SPAC Microtremor Observations Recorded with a Restricted Number of Sensors

Claprood¹,

Asten²

2010

Bulletin of the Seismological Society of America

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The interpretation of an observed spatially averaged coherency (SPAC) spectrum assumes spatial and temporal stationarity of the microtremor wave field. This hypothesis gains in importance when recording coherency spectra (COHs) with a limited number of sensors. SPAC observations were recorded at three separate sites in Launceston (Australia) using a pair of sensors, triangular arrays, and hexagonal arrays to study the effect of the number of sensors, length of time series, and frequency interval for evaluating the shear-wave velocity (SWV) profile.The imaginary component of the observed complex COH is separated into roughened and smoothed parts. The root mean square of the roughened imaginary COH (rms (Im)) is an expression of the statistical noise in the observed coherency, while the behavior of the smoothed imaginary COH gives some indication of the distribution of the microtremor wave field. The mean square of residuals (MSR) between observed and theoretical COHs is an indication of the confidence level on the SWV profile interpreted. MSR values evaluated at pairs of sensors of different orientations give some indication of the azimuth distribution of the microtremor wave field and provide some guidelines on the field procedure when using a limited number of sensors to record SPAC observations. Observed COHs at site KPK demonstrate the importance of recording longer time series to increase the stability of the observed COHs. The increasing level of statistical noise with increasing frequency at site DBL suggests the SPAC method can be used with a single pair of sensors by restricting its upper frequency limit to the first minimum of the COH. Low values of MSR on observed COHs from most pairs of sensors further strengthen that hypothesis. SPAC observations at site RGB give further insights into the capabilities of the SPAC method to evaluate the SWV profile in limited azimuth microtremor wave-field distribution.Online Material: Color versions of figures showing observed coherency spectra for all possible pairs of sensors and interstation separations.

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“…The simplest processing method is singlestation analysis of three-component data to give spectra for the ratio of horizontal to vertical particle motion, a method based on a study by Nogoshi and Igarashi ͑1971͒ that was later popularized by Nakamura ͑1989͒. Bard ͑1998͒ reviewed the method in detail, and it is now widely used for qualitative or semiquantitative mapping of sediment thickness over bedrock, particularly in earthquake hazard zonation studies ͑Lachet and Bard, 1994;Lermo and Chavez-Garcia, 1994;Ibs-von Seht and Wohlenburg, 1999;Scherbaum et al, 2003;Lang and Schwartz, 2005͒. The second and third processing methods are conventional and high-resolution beam-forming or frequency-wavenumber ͑ f -k͒ array methods pioneered by Lacoss et al ͑1969͒ andCapon ͑1969͒. They have been used recently by Liu et al ͑2000͒, Scherbaum et al ͑2003͒, Wathelet et al ͑2004͒, Ohrnberger et al ͑2004͒, and Kind et al ͑2005͒. An important variant on these beam-forming methods is a frequency-slowness transform method ͑McMechan and Yedlin, 1981͒, adapted by Park et al ͑1999͒ for active surface-wave studies; it was further developed by Louie ͑2001͒ for use with microtremor data acquired with linear rather than 2D arrays.…”

Section: Introductionmentioning

confidence: 98%

On bias and noise in passive seismic data from finite circular array data processed using SPAC methods

2006

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The finite nature of typical small seismic arrays used in conjunction with spatial autocorrelation ͑SPAC͒ processing for observing the microtremor wavefield causes predictable perturbations of the SPAC spectrum when sources of seismic noise are confined to a restricted range of azimuths. Such perturbations are especially evident at higher frequencies where wavelengths are on the order of the array radius. The effects are readily modeled and show that the triangular array geometries commonly used for microtremor studies require azimuthal distributions of wave energy on the order of 60°or greater to have a high probability of being free of such perturbations. The imaginary component of the SPAC spectrum, which is ideally zero for a sufficiently dense circular array and/or a sufficiently isotropic wavefield, is in practice often nonzero and provides three quality-control indicators: ͑1͒ an indication of insufficient spatial averaging, ͑2͒ an empirical measure of the level of statistical uncertainty in SPAC spectral estimates, and ͑3͒ an indication of departures from planewave stationarity of the seismic noise wavefield.

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Signal Processing and Frequency-Wavenumber Spectrum Analysis for a Large Aperture Seismic Array

Cited by 57 publications

References 23 publications

The Microtremor Survey Method

The Microtremor Survey Method

Statistical Validity Control on SPAC Microtremor Observations Recorded with a Restricted Number of Sensors

On bias and noise in passive seismic data from finite circular array data processed using SPAC methods

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