in Figure 41 is essentially unfocused for the boxcar
origin. The vertical-geophone responses to the
taper.
M60 tank were dominated by the presence of
Figure 41 is an extreme example of beamformer
Rayleigh surface wave energy with spectral peaks
failure; however, it was not uncommon to encoun-
at 11 and 30 Hz and a propagation velocity of
220 m s1. Most wavenumber estimates used the
ter similar problems in less coherent frequency
bins with more reasonable OBAFFT parameters.
highly coherent secondary maxima in the vicinity
The failure of the beamformer to focus is most
of the 11-Hz frequency bins. It was difficult to
likely due to the highly biased nature of the fre-
obtain reliable wavenumber estimates in the vicin-
quency-domain phase angle caused by energy
ity of the 30-Hz spectral maxima. It is hypoth-
leakage from neighboring frequency bins. Such
esized that the low coherence in the vicinity of 30
bias effects are particularly problematic with the
Hz is due to interference at the sensor between
boxcar window. The above examples show the
acoustic and seismic waves.
extent to which the introduction of a high degree
Maximum-likelihood wavenumber estimates
of bias and variance in the frequency domain
of .45 caliber blank pistol shots exhibited two
estimate impacts the wave number estimate.
distinct propagation modes. The first wave phase
arrives with a propagation velocity of 338 m s1
Considering the wavenumber results in this
section and those given in other sections, we make
and is interpreted as an acoustic excitation of the
several generalizations concerning the impact of
ground in the vicinity of the geophone. The second
the OBAFFT parameters on ML beamformer. In
wave phase arrives with a propagation velocity of
approximately 220 m s1 and is interpreted as a
virtually all the examples discussed, the applica-
tion of a strongly tapered, low-resolution, low-
Rayleigh surface wave that is excited by acoustic-
bias, time-domain window function (such as the
to-seismic coupling near the source. Wavenumber
Blackman taper) produced a higher resolution
estimates of vertically delivered sledgehammer
wavenumber estimate with lower background
blows also exhibited surface wave propagation
energy levels when compared with wavenumber
modes that had the same phase velocity.
estimates using high-resolution, high-bias, time-
In general, direction and velocity estimates ob-
domain tapers (such as the boxcar function).
tained from wavenumber spectra showed good
Specifying large numbers of blocks in the
agreement with known source positions and ve-
OBAFFT estimation of the spatial correlation ma-
locity estimates produced by time-domain move-
trix mitigated the impact of the high-bias window
out analyses. However, it was observed that
functions. Improvements in beamformer perfor-
changes in the parameters used to estimate the
mance were observed even when blocks were
spatial correlation matrix could produce wave-
overlapped by as much as 95%. The unexpected
number bias effects. These spatial frequency bias
benefit of using highly overlapped blocks in the
effects were strongly dependent on the type of
estimate of the spatial correlation matrix may be
window taper applied to the time series data and
explained by noting that the phase angle for a
the number of blocks used in the estimate of the
given frequency bin in each block varies rapidly
spatial correlation matrix. It was observed that
between blocks and therefore has a much smaller
low-resolution, low-bias window types produced
degree of correlation between blocks as compared
the highest resolution wavenumber spectra with
with power spectra estimates. The variance analy-
the least wavenumber bias and highest signal-to-
sis was helpful in partially explaining the
noise ratios. Utilizing large numbers of blocks in
beamformer's dependence on the OBAFFT pa-
the estimate of spatial correlation matrix miti-
rameters. A more complete explanation will have
gated the impact of window taper choice. In some
to consider the phase angle bias effects as well.
cases improvements were found in the wave-num-
ber spectra even when block overlaps were as high
as 95%.
6. CONCLUSIONS
Capon's minimum variance (maximum likeli-
LITERATURE CITED
hood) beamformer produces reliable direction es-
timates for a U.S. Army M60 tank moving at 4.5
Albert, D.G. (1989) Preliminary analysis of acous-
m s1 using an array of vertical-component geo-
tic-to-seismic coupling experiments at Grayling,
phone signals. Accurate direction estimates were
Michigan. Paper presented at the 17th Meeting
obtained at ranges from 50 to 500 m from the array
of NATORSG.11, 2327 May 1988, Issy-les-
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