• Geophysics and Geophysical Exploration
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• v.12 no.1
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• pp.121-131
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• 2009

In recent years, microtremor array observations have been used for estimation of shear-wave velocity structures. One of the methods is the conventional spatial autocorrelation (SPAC) method, which requires simultaneous recording at least with three or four sensors. Modified SPAC methods such as 2sSPAC, and linear array methods, allow estimating shear-wave structures by using only two sensors, but suffer from instability of the spatial autocorrelation coefficient for frequency ranges higher than 1.0 Hz. Based on microtremor measurements from four different size triangular arrays and four same-size triangular and linear arrays, we have demonstrated the stability of SPAC coefficient for the frequency range from 2 to 4 or 5 Hz. The phase velocities, obtained by fitting the SPAC coefficients to the Bessel function, are also consistent up to the frequency 5 Hz. All data were processed by the SPAC method, with the exception of the spatial averaging for the linear array cases. The arrays were deployed sequentially at different times, near a site having existing Parallel Seismic (PS) borehole logging data. We also used the imaginary part of the SPAC coefficients as a data-quality indicator. Based on perturbations of the autocorrelation spectrum (and in some cases on visual examination of the record waveforms) we divided data into so-called 'reliable' and 'unreliable' categories. We then calculated the imaginary part of the SPAC spectrum for 'reliable', 'unreliable', and complete (i.e. 'reliable' and 'unreliable' datasets combined) datasets for each array, and compared the results. In the case of insufficient azimuthal distribution of the stations (the linear array) the imaginary curve shows some instability and can therefore be regarded as an indicator of insufficient spatial averaging. However, in the case of low coherency of the wavefield the imaginary curve does not show any significant instability.

• Geophysics and Geophysical Exploration
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• v.18 no.3
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• pp.162-166
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• 2015

• Geophysics and Geophysical Exploration
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• v.9 no.1
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• pp.73-85
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• 2006

Array observations of the vertical component of microtremors are frequently conducted to estimate a subsurface layered-earth structure on the assumption that microtremors consist predominantly of the fundamental mode Rayleigh waves. As a useful tool in the data collection, processing and analysis, the spatial autocorrelation (SPAC) method is widely used, which in practice requires a circle array consisting of M circumferential stations and one centre station (called "M-station circle array", where M is the number of stations). The present paper considers the minimum number of stations required for a circle array for efficient data collection in terms of analytical efficacy and field effort. This study first rearranges the theoretical background of the SPAC algorithm, in which the SPAC coefficient for a circle array with M infinite is solely expressed as the Bessel function, $J_0(rk)$ (r is the radius and k the wavenumber). Secondly, the SPAC coefficient including error terms independent of the microtremor energy field for an M-station circle array is analytically derived within a constraint for the wave direction across the array, and is numerically evaluated in respect of these error terms. The main results of the evaluation are: 1) that the 3-station circle array when compared with other 4-, 5-, and 9-station arrays is the most efficient and favourable for observation of microtremors if the SPAC coefficients are used up to a frequency at which the coefficient takes the first minimum value, and 2) that the Nyquist wavenumber is the most influential factor that determines the upper limit of the frequency range up to which the valid SPAC coefficient can be estimated.

• Geophysics and Geophysical Exploration
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• v.25 no.1
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• pp.14-25
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• 2022

The passive surface wave method measures seismic signals from ambient noises or vibrations of natural phenomena without using an artificial source. Since passive sources are usually in lower frequencies than artificial ones being able to ensure the information on deeper geological structures, the passive surface wave method can investigate deeper geological structures. In the passive method, frequency dispersion curves are obtained after data acquisition, and the dispersion curves are analyzed by assuming 1D-layered earth, which is like the method of active surface wave survey. However, when computing dispersion curves, the passive method first obtains and analyzes coherence curves of received signals from a set of receivers based on spatial autocorrelation. In this review, we explain how passive surface wave methods measure signals, and make data processing and interpretation, before analyzing field application cases.

• Geophysics and Geophysical Exploration
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• v.7 no.1
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• pp.14-18
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• 2004

High levels of ambient noise and safety factors often limit the use of 'active-source' seismic methods for geotechnical investigations in urban environments. As an alternative, shear-wave velocity-depth profiles can be obtained by treating the background microtremor wave field as a stochastic process, rather than adopting the traditional approach of calculating velocity based on ray path geometry from a known source. A recent field test in Melbourne demonstrates the ability of the microtremor method, using only Rayleigh waves, to resolve a velocity inversion resulting from the presence of a hard, 12 m thick basalt flow overlying 25 m of softer alluvial sediments and weathered mudstone. Normally the presence of the weaker underlying sediments would lead to an ambiguous or incorrect interpretation with conventional seismic refraction methods. However, this layer of sediments is resolved by the microtremor method, and its inclusion is required in one-dimensional layered-earth modelling in order to reproduce the Rayleigh-wave coherency spectra computed from observed seismic noise records. Nearby borehole data provided both a guide for interpretation and a confirmation of the usefulness of the passive Rayleigh-wave microtremor method. Sensitivity analyses of resolvable modelling parameters demonstrate that estimates of shear velocities and layer thicknesses are accurate to within approximately $10\%\;to\;20\%$ using the spatial autocorrelation (SPAC) technique. Improved accuracy can be obtained by constraining shear velocities and/or layer thicknesses using independent site knowledge. Although there exists potential for ambiguity due to velocity-thickness equivalence, the microtremor method has significant potential as a site investigation tool in situations where the use of traditional seismic methods is limited.