Signal and Traveltime Parameter Estimation Using Singular Value Decomposition

We have derived two new semblance coefficients based on singular value decomposition (SVD) of the data matrix. In the signal model the time signal is constant on each channel, but the amplitude changes. Then the optimal signal estimate is the first eigenimage, and the corresponding semblance coefficient is the square of the first singular value divided by the data energy. The normalized crosscorrelation coefficients derived from the first eigenimage can also be used as coherence measure. The multiple signal classification (MUSIC) coherence measure is also used to detect multiple signals in noise. Numerical examples with different coherence measures applied to seismic velocity analysis showed that the normalized crosscorrelation coefficients performed poorly. The log MUSIC coherence measure corresponding to the crosscorrelation between the first temporal singular vector and the average time signal gave good results on synthetic data with high and medium signal-to-noise ratio (SNR). For low SNR and on real data it performed poorly. The normalized eigenimage energy coherence measure performed poorly on synthetic data testing on velocity and time resolution, but gave by far the best result for a simulated reflection with a polarity reversal.