Methods for determining infrasound phase velocity direction with an array of line sensors
Diagram and photo of an optical fiber infrasound sensor (OFIS; modified from Zumberge et al., 2003). A laser illuminates two optical fibers that are helically wrapped around a sealed silicone tube. Differences in the coupling between the two optical fibers and the tube result in their responding differently to pressure-induced diameter changes, allowing an optical fiber interferometer to transform pressure changes into an optical signal. A photodetector converts the optical signal to an electrical one, which is analyzed in real time by a digital signal processor to generate a pressure recording (Zumberge et al., 2004).
Three-dimensional view of the relationship between the angles in Eq. (3). The OFIS is parallel to the -axis, and the vector is antiparallel to the incident ray vector.
(Color online) (a) Directivity and (b) frequency response for a long OFIS as a function of and frequency [Eqs. (1) and (3)]. In (a) is plotted in polar coordinates as a function of for three sample frequencies. In (b) is plotted in dB as a function of frequency for four sample angles. For comparison purposes, the omnidirectional plane-wave response for a rosette with eight diameter secondary rosettes is also shown for grazing angles in (b).
OFIS array configuration naming terminology. The dotted and dashed lines in (a) are azimuths of ambiguity. The dotted azimuths can only be resolved with the separation of the OFIS centers. The dashed azimuths cannot be resolved with instrument response discrimination or separation of the OFIS centers. The angles to the dashed lines in (b) and (c) indicate the effective azimuthal separation in terms of phase-velocity-direction resolution.
Analysis of a 3°–120° OFIS signal recorded at PFO on 2005/09/20 (263) 02:31:09 UTC using the WLD technique. The predicted OFIS time series are compared with that observed for two trial back azimuths and elevation angles: (a) and and (b) the correct and . IFT is the inverse Fourier transform function. The numbers next to each pair are the correlation coefficients.
Comparison of the WLD and SAD deconvolution techniques in removing the instrument responses from a 3°–120° OFIS. The resulting time series signal from both techniques is compared (with correlation coefficients) to the beamformed signal from a microbarometer array.
Cartoon of the infrasound band that has the most leverage in determining the phase velocity direction by means of instrument response discrimination for a OFIS arm and a heuristic noise level.
PFO surface OFIS and partially buried pipe array (I57US, part of the IMS network) used in this study. The gray rosette was not used. The arrays are drawn to scale but are shown collocated for aperture comparison purposes.
Comparison of real signal back azimuths and elevation angles (recorded by a 3-120° OFIS and collocated pipe array I57US) using three OFIS methods and TDB for the pipe array. The back azimuth is the clockwise angle with respect to north. The elevation angle is the vertical angle with respect to the horizontal. SNR is the average SNR (dB) recorded by the OFIS. The error bars are the vector sums of the asymmetric error bars determined for each technique. Statistics that summarize these results are presented in Table I.
(Color online) The analysis of infrasound created by an aircraft flying over PFO on 2005/09/18 (261) 19:52 UTC tracked by the OFIS array and the I57US high-frequency (HF) array to the southeast.
Misfit functions for the three OFIS techniques and TDB (I57US HF array) used to analyze the PFO signal in Figs. 5 and 6. The 95% confidence regions of the reference TDB method (white contour) and individual OFIS methods (gray contour) are shown. The dot indicates the best estimate of the phase velocity direction (global minimum).
Synthetic data experiments demonstrating the resolving power for phase velocity direction of different OFIS configurations using the WLD technique. The synthetic source signal is shown in (a). A misfit grid summarizing 360 different synthetic experiments (one experiment per degree input back azimuth) is shown for three different OFIS configurations in (b)–(d). White contours indicate the 95% confidence region, which ideally should enclose the unity-slope line that intersects the origin. The OFIS arms are in length.
Different configurations of OFIS arms of length (drawn to scale). The circle that defines the maximum aperture of these configurations is drawn for each configuration. Configurations in (a)–(d) have the same theoretical resolving power for phase velocity direction (spectral and time separation resolution). Configuration (e) has no time separation resolution but is almost equally effective with a 75% footprint reduction. However, this configuration cannot distinguish between signals propagating from a given back azimuth and its 180° counterpart.
Statistics for differences between the TDB and OFIS back azimuths and elevation angles from Fig. 9 (minus the outliers and low SNR measurements).
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