Spatial autocorrelation method for simple microtremor array survey at rock/stiff-soil sites


 It is shown that the phase velocities of Rayleigh waves can be identified with a very simple microtremor array even at a rock or stiff-soil site. The main problem at rock/stiff-soil sites is the low signal-to-noise ratio, which is addressed in this study by applying a zero-crossing method, which is one form of a technique called spatial autocorrelation (SPAC). This method uses zero-crossing frequencies of the SPAC-coefficient spectrum to identify the phase velocities, modelled by the zeroth-order Bessel function of the first kind. A simple array, such as a linear array, can cause biases called directional aliasing, depending on the wavefield directionality. A systematic, theoretical examination of directional aliasing was made in this study to determine a practical shape for microtremor arrays, as well as to develop an improved scheme for reading the zero-crossing points of a SPAC coefficient curve. It is shown that, for an L-shaped array consisting of two independent linear arrays, the SPAC-coefficient curve can include biases in the frequency range immediately higher than the first zero-crossing point. In this study, based on these results, later zero-crossing points were not read depending on the indicator of possible biases, or the amplitude of the SPAC-coefficient curve immediately after the zero-crossing point. This systematic study also reveals that, for L-shaped arrays, although the first zero-crossing point is sometimes obscured (e.g., it appears to just touch the zero line rather than cross it), the biases of directional aliasing decrease as the intersection angle of the two linear arrays approaches a right angle. Therefore, an L-shaped array with a right angle is selected in this study as the simplest practical array, and a criterion for reading the first zero-crossing point is devised. It is shown that obscured zero-crossing points can be appropriately read in general by checking the systematic change in the zero-crossing frequency with array radius. Once the first zero-crossing point is thus appropriately read, we can identify accurate phase velocities. To test the feasibility of these theoretical findings, microtremor array data were acquired at 15 sites in the northern Kanto region, Japan, with an average S-wave velocity to a depth of 30 m (Vs30) based on velocity log data ranging from 182 to 1433 m/s (i.e., 14 sites with rock/stiff-soil and a site with relatively soft soil). The microtremor arrays were L-shaped, consisting of two independent linear arrays with lengths of 24 m. Each linear array consisted of seven unequally spaced 4.5-Hz geophones. Microtremors were recorded for about 20 minutes for each measurement. The soil parameters Vs10, Vs20, and Vs30 and S-wave velocity structure models were evaluated based on the obtained phase-velocity dispersion curves. The analysis results for the microtremor array data were in good agreement with values based on velocity logging.