Weighted Averaging for Calculating Azimuthal Angles and Filtering Love Waves Using S-transforms

Abstract:

The S-transform methodology is based on Stockwell transforms, which is a form of a short Fourier transform, with a time domain transform window defined by a Gaussian function. The Gaussian function has a standard deviation equal to the frequency of interest. Applying the transform to multiple frequencies of interest results in a time/frequency spectrogram, which has the advantage of being simply invertible back to the time domain. This allows for the calculation of instantaneous frequency/time phase and amplitude measurements, which makes 2D signal filtration of surface waves possible. By solving for the transverse angle of propagation of narrow band filtered Love waves at a range of periods (8-25s) we calculate a vector of possible azimuths, one at each period. We then average over all the bands of interest to determine the mean angle of propagation. To avoid using unreliable low signal-to-noise (SNR) azimuth estimates, we use a SNR weighted average to more accurately reflect the overall signal propagation azimuth. We then use the mean signal azimuth to design a 2D Love wave rejection filter that will reject off-azimuth noise and then invert this to the time domain for an improved signal on the propagation azimuth.

We apply this method to the 2009 Democratic People’s Republic of Korea nuclear test. After testing the weighted averaging approach, the SNR ratio increases by a factor of 2 overall, and a signal on the transverse component is identified as a Rayleigh wave that “leaked” into the transverse component. Without this method, there could have been improper Love wave signal identification for the event. Using this innovative SNR weighted averaging technique to calculate propagation angle indicates that S-transform filters can lower the noise level by a factor of 2 or more, helping with low SNR events, and remove Rayleigh “leakage” into the transverse channel.