PITSA Demo Script

Introduction

This script demonstrates the use of various alogrythms to the problem of detection and parameter estimation of "hidden explosion" - that is, if a signal from explosion arrived during the coda phase of a strong earthquake. The input data is an artificially constructed example for the NORESS array. A presumed underground nuclear test at Novaya Zemlya ("NZE", October 24, 1990) was used as the explosion and placed in the coda of an earthquake in the Hindu Kush ("HKE", 25 Oct 1990) with a signal to noise ratio of approximately 0.5 RMS. Phases of signal detection is skipped because it uses a number of routine commands which realisation in PITSA are significantly interactive and thus cannot be reproduced at that time.

Selected traces of source signals

Data after mixture
Signal/noise ratio = 0.5 RMS

Adaptive filtration methods

Once a signal was detected, the explosion time signal may be extracted by the adaptive optimum group filtering (AOGF) (Kushnir et al., 1990,1995; Kusnir, 1996). The superiority of the AOGF over linear beamforming is evident as is the ability of AOGF to faithfully reproduce the signal. The coherence of the HKE coda that causes poor supp suppression for conventional beamforming actually helps the AOGF procedure because it uses the covariance properties of the noise (code) to design the filter. The filter design (adaptation) in the AOGF algorithm was made using the NZE+HKE NORESS seismogram mixture at time intervals (0-22) sec and (35-60) sec., that is, before and after the interval containing the NZE P-wave.

Traces were obtained by a filtering of a pure data (in the top, traces from 2 to 5) and mixed HK+NZ event (bottom, traces from 6 to 9)

(1) Original Hindu-Kush beam (not obtained from any procedure, given only for comparison with filtered one)
(6) NZ+HK Beam output - the trace after beamformingprocedure steered to Novaya Zemlya. The explosion signal is obscured by the coda of Hindu-Kush earthquake
(7) NZ+HK trace after rejection group filtering procedure (REJ), supressing the plane wave arriving from Hindu-Kush direction. The SNR here is larger in comparison with beam, but the HK coda is not supressed enough
(8) NZ+HK trace after undistoring adaptive optimal group filter (UGRF). The HK coda is strongly supressed and signal waveform is extraced without distortion.
(9) NZ+HK trace after noise whitening adaptive optimal group filter (WGRF). The HK coda is supressed and its residuals are subjected to whitening filtering. The signal to noise ration is maximal at this trace, but the shape of signal waveform is changed due to whitening of the noise residuals
(2) Beam output for pure NZ event
(3) REJ form pure NZ explosion
(4) UGRF for pure NZ explosion
(5) WGRF for pure NZ explosion

Novaya Zemlya Event Parameter Estimation

Low Resolution F-K analysis

The following pictures are spatial spectrum calculated from the NZE+HKE seismogram mixture over the time interval containing NZE P-wave using a conventional broad band F-K analysis algorythm. (Kushnir, 1996). The single spectrum maximum seen in this low-resolution estimate differs only slightly from the expected azimuth and apparent velocity of the HKE P-wave, no useful measure can be made of the NZE parameters.

WIDEBAND F-K ESTIMATION (dB)
Frequency band: 0.8 - 3.2 Hz

AVERAGED LOW RESOLUTION F-K MAP
Frequencies: 1.0, 3.1

High Resolution F-K Analysis

Application of high resolution spectral analysis which is a modified Capon algorith with estimation of a power spectrum by multidimensional autogressive-moving average modeling (Kushnir, 1996), separates the two waves in the HKE+NZE data mixture within the analyzed time interval. This method is rather widely used; the global maximum is due to the presence of HKE P-wave. Measuring the second maximum we get: azimuth=26.5 degrees, apparent velocity = 7.4 km/sec. They are similar to, but deviate somewhat from, the expected NZE P-wave parameters: azimuth = 32.9 degrees, apparent velocity = 10.4 km/sec.

HIGH RESOLUTION F-K ANALYSIS

Adaptive F-K Analysis

As you could see, two previous methods don't give precise values for NZE event. To improve those results an advanced algorithm is used to accurately estimate the NZE P-wave arrival direction in the NZE+HKE data. The method is adaptive maximum likelihood algorithm for direction estimation of a signal plane wave (NZE) arriving at a site together with coherent interfering wave(s) - HKE coda; it is important that the interfering wave(s) can be observed independently in a time interval which doesn't containtain the signal wave (Kushnir et al., 1995). The estimate contains a single strong peak whose maximum is located at azimuth = 31.0 degrees and apparent velocity = 8.6 km/sec. These values are significantly nearer to the expected values for the NZE P-wave (32.9 degrees, 10.4 km/sec) than those given by the high resolution F-K analysis conventionally used. (see previous example).

AVERAGED ADAPTIVE F-K MAP

AVERAGED BROAD BAND ADAPTIVE F-K MAP