Removing Periodic Noise: Improved ProceduresFelix Gorschlüter, Jürgen Altmann

Experimentelle Physik III, Technische Universität Dortmund, D-44221 Dortmund, Germany

Exact Localisation of Underground Explosion

Teleseismic detections of an underground explosion result in localisation uncertainties on the order of 10 km. In order to find radioisotopes in the soil as indicators of a nuclear explosion, an CTBTO on-site inspection needs to localise the epi- or the hypocentre much better, maybe to around 0.1 km. For this purpose a local Seismic Aftershock Monitoring System (SAMS) can be set up shortly after the event in the area of interest determined from teleseismic signals. The purpose is to detect weak aftershocks which will occur for several weeks – from cracking and falling rocks around and in the cavity. Extreme sensitivity is required to detect the weak aftershock signals that can be masked by periodic noise.We have improved our procedures to find and remove such noise.

Impulse Signals and their Spectra

Aftershock events are single impulses which change form during propagation due to different seismic wave types with different velocities and to reflection at layer boundaries. Nevertheless, seismic signals received retain the impulsive character. Their spectrum is broad-band (see impulse figures below).

Masking by Periodic Noise

Seismic signals measured at the surface can be masked by periodic noise from machinery, road traffic, propeller aircraft or helicopters. In experiments, we have measured acoustic and seismic signals of tanks, trucks, propeller aircraft and helicopters.1-4

Spectra of periodic signals consist of discrete lines at the fundamental frequency and its harmonics.

Demonstration of periodic and impulse events:Signal (left) and spectrum (right) of a firecracker at about 100 m distance from microphone (top) and the seismic signal of a flying helicopter at about 1 km distance (bottom). In the spectra of the helicopter two harmonic series can be found stemming from the main (triangles) and the tail (circles) rotor, respectively.

Results

Fraction of spectral power sum removed by line subtraction. In rare cases up to 90% of squared magnitude is reduced. In other cases approximation of the highest lines failed – so most of the spectral power remains.

One problem here is that if the sampling rate of the data is low either frequency resolution is bad which results in blurred neighbouring lines or lines become broad if the frequency varies over longer time intervals.

Another problem is time varying Doppler shift in data (not shown here) which produces the same effect: Lines become broadened and a single sinusoid can no longer be approximated successfully.

Earlier work has shown that non-periodic data superposed with strong (~105 times the background magnitude) synthetic sine functions can be separated very successfully even with multiple lines in one spectrum.5 Further research will be done to improve separation of real signals.

Finding periodic content in large time seriesDuring on-site inspections of the CTBTO an area of ~1000 km² is covered with stations for seismic aftershock measurements. Typically each of these stations consists of six sensors so that a large quantity of data is generated over several weeks of measurement. As our line analysis algorithm is complex and works on single spectra it would take enormous calculation effort to feed all the data into it. It seems to be more reasonable to preselect time intervals with periodic content.Sequences of spectra still are too extensive and screen or print resolution is not sufficient to overview long time intervals and multiple sensors at once. To reduce the amount of data and still be able to find the periodic content the standard deviation is taken in several spectral power intervals. The underlying idea is that in case of a periodic signal the spectrum consists of lines which themselves are distinguished by some big values over a smaller underground.Spectra of noise and non-periodic signals do not show strong changes in magnitude between neighbouring values. So instead of regarding the whole power spectrum a set of bands is used. For this work we chose 20 bands, leaving out the lowest 2 frequencies (the zero-frequency value can be high if there is an offset in the data) and the high frequencies (as events are expected in lower frequencies and low pass filters reduced the magnitude here anyway). Each band comprises 20 frequencies starting at the 3 rd frequency.To reduce the amount of data per time we extract the maximum value of the standard deviation of each band for multiple spectra. This reduces the time resolution strongly but the information whether or not there is at least one spectrum with a high standard deviation in a certain band is still preserved.By starting with an overview of 1000 spectra per value and successive refinement (to compression by 100 and 10, finally looking at the actual spectra sequence) the operator can find the time periods with periodic content and apply the line fitting and removal there.

Overview presentation for the six sensors of one station, 20 bands. By showing the maxima of 1000 standard deviations more than 12 days measurement can be covered. Weak indications of periodic content can be seen at day 10, 3:30 h (shown below). (CTBTO test data)

More sensors with better time resolution (maximum out of 10 values → maximum error in time ~8 s) are shown. This kind of overview is also useful to decide whether events are local ones.

Line fitting and subtractionLines are characterized precisely (frequency, phase, amplitude) and their spectra subtracted sequentially in the complex domain. Compared to earlier4,5 phase is now taken care of fully.

Spectrum sequences (sampling rate 500 Hz, FFT with 512 Points) ofSpectrum sequences (sampling rate 500 Hz, FFT with 512 Points) of the original signal (above; probably a helicopter) and after application of the line finding and subtraction algorithm (below). At several times thethe line finding and subtraction algorithm (below). At several times the lines were removed successfully (dark parts in white curves), but linelines were removed successfully (dark parts in white curves), but line identification and removal did not always succeed.

Graph of the times and frequencies where lines are found and subtracted. AsGraph of the times and frequencies where lines are found and subtracted. As expected from comparison of the two sequences above there are both: peaks that are not subtracted (false negative) and subtracted peaks at non-line positions (falsenot subtracted (false negative) and subtracted peaks at non-line positions (false positive). The complete set of analysed peaks (above a certain level of magnitude) iscomplete set of analysed peaks (above a certain level of magnitude) is shown below.

Conclusions It is possible to reduce periodic content in real data

without manipulating the data significantly.

With the current set of parameters and thresholds lines in spectra of signals are not always found and fitted satisfactorily as well as lines are found and subtracted that are produced by noise.

There are possibilities for improvement:A) multiple line approximations at once (problem of neighbouring lines, especially for low sampling rates),B) handling of changing frequencies (revolution rate, varying Doppler shift) with linear frequency change with time,C) analysing the influence of both false positive (subtraction of virtual lines) and false negative (keeping lines in the spectrum), then adjusting of thresholds.

References

1 J. Altmann, S. Linev, A. Weiß, Acoustic-Seismic Detection and Classification of Military Vehicles – Developing Tools for Disarmament and Peace-keeping, Applied Acoustics 63 (10), 1085-1107, 2002.

2 J. Altmann, Acoustic and Seismic Signals of Heavy Military Vehicles for Co-operative Verification, Journal of Sound and Vibration 273 (4-5), 713-740, 2004

3 R. Blumrich, Sound Propagation and Seismic Signals of Aircraft Used for Airport Monitoring, Verification – Research Reports, no. 10, Hagen: ISL, 1998.

4 F. Gorschlüter, Messung, Erkennung und Unterdrückung periodischer akustischer und seismischer Störsignale, Diplomarbeit, FB Physik, TU Dortmund, 2009 (unpublished).

5 J. Altmann, F. Gorschlüter, Removing Periodic Noise to Detect Weak Impulse Events, poster presented at International Scientific Studies (ISS 09) Conference, Vienna, 10-12 June 2009.

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ConclusionsReferences

Finding periodic content in large time seriesLine fitting and subtractionExact Localisation of Underground ExplosionRemoving Periodic Noise: Improved Procedures