Recent applications of bandpass filtering Page: 3 of 15

Recent Applications of Bandpass Filtering

Abstract
Bandpass filtering has been applied recently in two widely different seismic
applications: S.R. Taylor and A.A. Velasco in their source-path amplitude-correction
(SPAC) algorithm and N.K. Yacoub in his maximum spectral energy algorithm for
picking teleseismic P-wave arrival times. Though the displacement spectrum is the
intermediate product in both cases, the filters and scaling corrections used to
estimate it are entirely different. We tested both and found that the scaling used by
Taylor and Velasco worked in all cases tested whereas Yacoub's did not. We also
found that bandpass filtering as implemented by Taylor and Velasco does not work
satisfactorily; however, the Gaussian filter used by Yacoub does work. The bandpass
filter of Taylor and Velasco works satisfactorily when the results are centered in the
band; however, a comb filter with the same number of poles and zeroes as the
bandpass used by Taylor and Velasco works better than the bandpass filter.

Introduction
Bandpass filtering, after years of being
overshadowed by the fast Fourier transform
(FFT), is enjoying renewed popularity for use in
seismic signal processing. Researchers at Los
Alamos National Laboratory (LANL) are
currently using it in their SPAC algorithm
(Taylor and Velasco, 1998) for characterizing
seismic events. In another form, Yacoub (1998) is
using bandpass filtering in his maximum spectral
energy technique for picking teleseismic P-wave
arrival times. In both of these algorithms,
accurate estimates of spectral amplitudes are
crucial to the final application, yet the filters
applied in these two cases are as different as the
approaches employed to scale the filtered time
series. Ironically, these diverse implementations
are occurring at a time when a strong drive to
standardize processing techniques exists within
the Comprehensive Test Ban Treaty (CTBT)
monitoring community so that the same concerns
are not raised repeatedly. With a view toward
standardizing on one technique, not necessarily
either of the two mentioned above, we have
evaluated both approaches along with some
alternatives.
Background
In the SPAC signal-processing algorithm, the
objective is to model the seismic-source function

and the attenuation along the propagation path.
For this application, a simple yet accurate proce-
dure for estimating the signal's displacement
spectrum is needed. The first step in the procedure
adopted for SPAC is to filter the signal, as re-
corded in velocity, with a set of eight filters that
are more or less logarithmically spaced over the
interval of 0.5 to 6.0 Hz. Each of these filters is a
zero-phase, Butterworth bandpass filter that is
one octave wide with four poles. The final steps
are to compute the root-mean-square (RMS) value
of each of the filtered time-series and then to
convert them to a spectral displacement by divid-
ing by o(2nf) and multiplying by a scaling
parameter derived from Parseval's theorem. The
scaling parameter is

T/

(1)

where T is the length of the signal, and E is the
total energy in a filter's bandpass. In this case,
the total energy of the filter is approximately
twice the bandwidth. The final results are as-
signed to the low-frequency corner (low-cut) of
each of the bandpass filters in an attempt to ac-
count for the possibility that the high-frequency
decay (roll-off) of the signal could result in the
RMS amplitudes being biased high relative to
the log-averaged frequency-domain amplitudes.
In the maximum spectral energy algorithm, the
objective is to measure a reliable arrival-time for

M. D. Denny

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Denny, M D. Recent applications of bandpass filtering, report, March 15, 1999; California. (https://digital.library.unt.edu/ark:/67531/metadc784805/m1/3/ocr/: accessed May 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.

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