Multivariate autoregressive representation of seismic P-wave signals with application to short-period discrimination

1978 ◽  
Vol 68 (3) ◽  
pp. 735-756 ◽  
Author(s):  
Ottar Sandvin ◽  
Dag Tjøstheim
Keyword(s):  
Time Series ◽  
Parametric Models ◽  
P Wave ◽  
Separate Analysis ◽  
Wave Signal ◽  
Nuclear Explosions ◽  
Spectral Density Matrix ◽  
Short Period ◽  
Vector Time Series ◽  
Multivariate Autoregressive

abstract It is shown that seismic P-wave vector signals as recorded by selected NORSAR subarrays can be described by multivariate parametric models of autoregressive type. These are models having the form X ¯ ( t ) − A 1 X ¯ ( t − 1 ) − ... − A p X ¯ ( t − p ) = W ¯ ( t ) Where X¯(t) (t) is the digitized short-period vector time series defined by the P-wave signal and W¯(t) (t) is a white noise vector time series. The multivariate autoregressive analysis is undertaken for 83 nuclear explosions and 72 earthquakes from Eurasia. For each event a separate analysis of the main signal and of the coda has been carried through. It is found that in most cases a reasonable statistical fit is obtained using a low-order autoregressive model. The autoregressive parameters characterize the spectral density matrix of the P-wave signal and therefore form a convenient basis for constructing short-period discriminants between earthquakes and explosions. Based on the classification results for our data base of Eurasian events, we find that the multivariate autoregressive parameters have a substantially larger discrimination potential than the short-period parameters suggested earlier in the literature. In fact our results indicate that, based on autoregressive parameters, it may now be possible to construct purely short-period discriminants which are comparable, if not superior, to the mb:Ms criterion.

Teleseismic p-wave transmission through slabs

1973 ◽  
Vol 63 (4) ◽  
pp. 1349-1373
Author(s):  
Norman H. Sleep
Keyword(s):  
P Wave ◽  
P Waves ◽  
Nuclear Explosions ◽  
Velocity Models ◽  
Shallow Earthquakes ◽  
Short Period ◽  
Systematic Effects ◽  
First Motion ◽  
Low Amplitude ◽  
Good Agreement

abstract Theoretical ray paths through velocity models constructed from numerically calculated thermal models of slabs were computed. The results were in good agreement with observed travel times. First motion amplitudes of P waves at teleseismic distances were measured from long- and short-period WWSSN records of intermediate focus earthquakes in the Tonga, Kermadec, and Kurile regions and of nuclear explosions and shallow earthquakes in the Aleutian region. These amplitudes were corrected for source mechanism. The Aleutian data were sufficient to show that intermediate focus earthquakes in that region occur in the colder regions of the slab. At short periods, for regions other than the Aleutians, shadowing effects which could be associated with the slab were not very marked, less than a factor of 2 reduction for epicentral distances between 30° and 50°. No systematic effects due to plates were found in the long-period data. Some stations in the predicted shadow zone of a Tonga earthquake recorded low amplitude precursors which probably were greatly defocused waves which ran the full length of the slab. Simple diffraction is incapable of explaining the short-period results.

Seismic magnitudes of underground nuclear explosions

1973 ◽  
Vol 63 (1) ◽  
pp. 105-131 ◽  
Author(s):  
P. W. Basham ◽  
R. B. Horner
Keyword(s):  
Computational Procedure ◽  
Test Site ◽  
P Wave ◽  
Nevada Test Site ◽  
Underground Nuclear Explosions ◽  
Nuclear Explosions ◽  
Novaya Zemlya ◽  
Yield Information ◽  
Short Period ◽  
Propagation Effects

abstract Using an Ms computational procedure that minimizes path-propagation effects, and with Ms values found to be empirically independent of test site and detonation medium among consolidated rock explosions, available yield information is employed to illustrate that the seismic scaling of explosions in realistic detonation environments produces teleseismic Rayleigh-wave displacements proportional to the 1.2-power of yield over the range from low yields to greater than three megatons. Ms values independent of network, path, and site can be employed to estimate unknown yields at uncalibrated test sites to within average errors judged to be about 20 per cent. P-wave magnitudes, in the form of a calibrated teleseismic measure of short-period P-wave displacements, show a theoretically supported dependence of displacement on the 1.1-power of yield over the range from 6 kt to 1 mt. Studied explosions separate into two categories: the Nevada Test Site granite explosions, LONG SHOT, the Sahara February 1965 explosion and (by empirical inference) Novaya Zemlya and Eastern Kazakh explosions exhibit P-wave displacements about a factor of 3 greater than explosions of the same yield in tuff, rhyolite, and shale. P-wave magnitudes of explosions are subject to such a diversity of source, propagation, and measurement phenomena that any estimation of unknown yields without a closely controlled site and network calibration can be subject to large errors.

The relative performance of mb and alternative measures of elastic energy in estimating source size and explosion yield

1984 ◽  
Vol 74 (5) ◽  
pp. 1863-1882
Author(s):  
J. T. Bullitt ◽  
V. F. Cormier
Keyword(s):  
Elastic Energy ◽  
P Wave ◽  
Reference Station ◽  
Small Data ◽  
Federal Republic Of Germany ◽  
Underground Nuclear Explosions ◽  
Nuclear Explosions ◽  
Short Period ◽  
Alternative Measures ◽  
The Stability

Abstract A comparison has been made of the relative scatter of classical mb and alternative measures of P-wave energy from underground nuclear explosions at test sites in East Kazakh, USSR. The scatter of the energy measures is observed in teleseismic arrays of short-period Global Digital Seismic Network (GDSN) stations and the local broadband array at Graefenburg, Federal Republic of Germany. Four measures of A in log(A/T), spectral magnitudes, peak velocity, rms coda, and integrated velocity-squared are compared. The measures are constructed to be in equivalent units of the flux rate of radiated elastic energy. All measures are assumed to have the same slope in a linear regression of log(yield) versus log(measure). Three independent tests were made of the stability of the yield estimators: the scatter of the measures using: (1) Graefenburg array data; (2) GDSN data normalized to a reference station; and (3) GDSN data normalized to a reference event. The differences among the standard deviations are small (≦ 0.1 mb units), making it difficult using a small data base to conclude whether the performance of one estimator is significantly better than another. The relative order in the performance of the yield estimators, however, is preserved in each of the three tests. The coda measure is the most stable, followed by the spectral and time-domain A/T measures. The relations observed at Graefenburg between (1) the amplitude of direct P versus P coda, (2) the apparent azimuth of direct P, and (3) complexity, suggest that amplitude variations across an array are a product of scattering along the entire ray path as well as scattering, focusing, and defocusing localized in the lithosphere beneath the source and receiver sites.

Identification of multiple underground explosions using the relative amplitude method

1988 ◽  
Vol 78 (2) ◽  
pp. 885-897
Author(s):  
R. A. Clark ◽  
R. G. Pearce
Keyword(s):  
Body Wave ◽  
The Body ◽  
P Wave ◽  
Relative Amplitude ◽  
Time Data ◽  
Large Measure ◽  
Source Discrimination ◽  
Nuclear Explosions ◽  
Short Period ◽  
Wave Forms

Abstract The relative amplitude method is applied to the few available good quality teleseismic P-wave seismograms from five presumed double nuclear explosions and one known multiple chemical explosion, under the “naive” assumption that the observed multiple arrivals correspond to P, pP, and sP from a single earthquake—an interpretation which is indeed consistent with the body-wave arrival time data in most cases. The purpose is to investigate the ability of relative amplitudes to identify correctly such multiple events for which established discrimination criteria may give earthquake-like or ambiguous results. For five of the examples, observed relative amplitudes from only four azimuthally well-distributed array seismograms are sufficient to exclude the single-earthquake interpretation. Deliberate attempts to simulate earthquake teleseismic P wave-forms using multiple explosions are restricted to simulation studies, and one of these is analyzed here using the same approach. We conclude that relative amplitudes can act as a valuable aid to source discrimination in cases where complexity gives rise to fallibility of conventional discriminants, even where only a small number of well-distributed teleseismic short-period array seismograms are available, their signal-to-noise ratios being maximized by suitable array design and careful choice of array site. The network need not be dense, since closely spaced observations of the focal sphere generally embody a large measure of redundancy.

DETECTION OF P‐WAVES FROM WEAK SOURCES AT GREAT DISTANCES

Geophysics ◽  
1964 ◽  
Vol 29 (2) ◽  
pp. 197-211 ◽  
Author(s):  
Jon F. Claerbout
Keyword(s):  
Time Series ◽  
Prediction Error ◽  
P Wave ◽  
Pass Band ◽  
Multiple Time ◽  
Multiple Time Series ◽  
P Waves ◽  
Short Period ◽  
Band Pass ◽  
Detection Of Signals

Optimum (Wiener sense) filters for suppression of noise in multiple time series are computed by a new method due to E. A. Robinson. Filters for prediction error and interpolation error have been used to detect P‐wave signals from three teleseismic events. These filters facilitate detection of signals in noise with low signal‐to‐noise ratios. The instrumentation consists of short‐period Benioff seismometers, both three‐component stations and surface arrays of verticals. It was found that microseismic noise in the pass band of these instruments is more accurately termed “Brownian motion of a surface” than “random waveforms with characteristic direction(s) of propagation.” Thus, single time‐series filters work almost as well as multiple time‐series matrix filters. Prediction‐error filters gave results substantially more satisfactory than simple band‐pass filters.

scholarly journals Testing collinearity of vector time series

2019 ◽  
Vol 22 (2) ◽  
pp. 97-116
Author(s):  
Tucker S McElroy ◽  
Agnieszka Jach
Keyword(s):  
Time Series ◽  
Density Matrix ◽  
Spectral Density ◽  
Time Series Data ◽  
Series Data ◽  
Test Statistics ◽  
Rank Reduction ◽  
Spectral Density Matrix ◽  
Schur Complements ◽  
Vector Time Series

Summary We investigate the collinearity of vector time series in the frequency domain, by examining the rank of the spectral density matrix at a given frequency of interest. Rank reduction corresponds to collinearity at the given frequency. When the time series is nonstationary and has been differenced to stationarity, collinearity corresponds to co-integration at a particular frequency. We examine rank through the Schur complements of the spectral density matrix, testing for rank reduction via assessing the positivity of these Schur complements, which are obtained from a nonparametric estimator of the spectral density. New asymptotic results for the test statistics are derived under the fixed bandwidth ratio paradigm; they diverge under the alternative, but under the null hypothesis of collinearity the test statistics converge to a non-standard limiting distribution. Subsampling is used to obtain the limiting null quantiles. A simulation study and an empirical illustration for 6-variate time series data are provided.

scholarly journals Discrimination of teleseismic events in Central Asia with a local network of short period stations

1994 ◽  
Vol 37 (3) ◽  
Author(s):  
T. Tiira ◽  
M. Tarvainen
Keyword(s):  
Spectral Ratio ◽  
Difficult Problem ◽  
P Wave ◽  
Local Network ◽  
Separation Function ◽  
Data Set ◽  
Underground Nuclear Explosions ◽  
Nuclear Explosions ◽  
Discrimination Capability ◽  
Short Period

The difficult problem of distinguishing underground nuclear explosions from earthquakes at teleseismie distances was approached using short period seismic data from 6 stations in South and Central Finland. The events were nuclear tests mostly from the Semipalatinsk and Lop Nor test sites and earthquakes from adjacent areas. The magnitude range of the events was from 4.1 to 6.6. The features of the two classes of events were examined by computing spectral ratio, third moment of frequency (TMF) and complexity from P wave signals. The spectral discrimination parameters were extracted from spectra computed in 5 different ways in order to obtain all possible information even from weak events. The standard FFT spectra were computed from. raw data, after noise adaption and data adaption, from correlograms and using combinations of adaption and correlation: methods. This was done to employ not only the spectral differences of the events but also the temporal variation of energy and lack of it as a function of frequency. The optimum frequeney windows for spectral ratio and TMF were defined using stacked spectra of about 10 events from both classes. No single discriminant could classify all the events. Their performance varied significanfly for different stations, but on average the spectral discriminants had slightly higher discrimination capability than complexity. The distributions of all discriminants were studied and a group separation function was formed using an optimum set of discriminants. Instead of discriminant values their relative positions in the corresponding distributions of nuelear tests and earthquakes were used as inputs to the function. A weight for each discriminant was derived from the amount of overlap in the distributions of earthquakes and nuelear tests. All 75 events in the data set were correctly classified with the method. The testing was performed with a jack knife method to create an independent test data base

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