Vol.9 No.2 2016
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Research paper : Constructing a system to explore shallow velocity structures using a miniature microtremor array (I. CHO et al.)−92−Synthesiology - English edition Vol.9 No.2 (2016) section).When the feasibility of this idea was investigated using real data, it was found that the expected results as demonstrated by theory could be obtained (refer to Reference [20] for technical details). Let us look at Fig. 6 for an explanation. The figure is the dispersion curve of phase velocity obtained by a miniature array of a radius of 0.6 m. The purple triangle shows the phase velocity that has been corrected for noise effect and the blue cross shows one that has not been corrected. Normally for the dispersion curve, the phase velocity increases as the frequency decreases (called normal dispersion), and this is in reflection of the fact that S-wave velocity increases with the increase of depth. In the dispersion curve of the same figure, the phase velocities suddenly increase at 7.5 Hz or less. On the other hand, the phase velocities increase as the frequency increases above 7.5 Hz, and the trend called reverse dispersion is seen. This reflects the fact that there is a high velocity layer near the surface. In fact, there is a clay layer with extremely slow S-wave velocity embedded at a depth of about 5 m around the measurement point in the figure, and it is known that the S-wave velocity is faster near the surface.Figure 6 shows the lines that correspond to the wavelengths of 25 m (red), 40 m (purple), and 100 m (green), as the reference indices that show up to which depth the data can be obtained using the miniature array. The intersection points of the dispersion curve and these lines represent the frequencies and phase velocities that correspond to each wavelength. It can be seen from this figure that the phase velocities of slightly less than the wavelength of 100 m are obtained if the noise is not corrected, and phase velocities of wavelengths surpassing 100 m are obtained if corrected for noise. Here, by visual inspection of the noise-corrected results (shown by crosses), the phase velocity surpassing the wavelength of 100 m is identified. A wavelength of 100 m is about 167 times the radius of the array. The adequacy of this visual inspection was verified by separately executing with an array of a radius of about 5 m.Up to now, the performance of the miniature array has been described while explaining how to read the figure. However, what we wish to present in Fig. 6 is the evaluation of reliability based on the analytical limit of the phase velocity. In the figure, the upper limit for analysis is shown as a yellow broken line. This is the limit for analysis that is set strictly based on the developed technology, which separates the microtremor record into the components of surface waves (signals) crossing the array and the components of noise unrelated to such signals. If the upper limit is sufficiently high compared to the estimated value of phase velocity, it can be judged that the estimated value of phase velocity is safe to use. In the figure, the long wavelengths are automatically read up to the phase velocity surpassing the wavelength of 40 m (yellow square), based on this upper limit for analysis. That is, in this case, the objective quality control of the analysis result was done based on the data from the miniature array only, and it was automatically determined that the data up to at least the wavelength of 40 m can be “used.” Of course, this information is provided regardless of whether the recipients are experts or non-experts.In this way, we came to be able to obtain the phase velocity of the Rayleigh waves as new data to determine S-wave velocity by using miniature arrays. This is the core of sophisticating i-bidou. Objective quality control, automation of the analysis, and therefore, the use by general users are made possible by the theoretical development allowing the data-based evaluation of the upper limits for analysis.Reading (visual)Reading (automatic)(after noise correction)Phase velocity (before noise correction)the upper limit for analysisWavelength 100 mWavelength 40 mWavelength 25 m3025201510500.20.40.60.81.0Phase velocity (km/s)Frequency (Hz)Fig. 6 Phase velocity (dispersion curve) by miniature arrays and evaluation of automatic reading and the upper limit for analysis

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