Seminar

# Signal and travel-time parameter estimation using singular value decomposition

#### Inverse Problems and Applications

#### 08 April 15:30 - 16:30

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For a given type of travel time function and travel time parameters, a data matrix is generated for a time window centered around this travel time for each spatial data channel. We normally compute a coherence measure from the data matrix corresponding to these travel time parameters. There are two main classes of normalized coherence measures. Generalized semblance which is normalized between zero and one, and so-called high-resolution coherence measures which are bounded from below. The multiple signal classification (MUSIC) coherence measure is greater than one, and a new signal-to-noise energy ration is greater than zero. A generalized MUSIC measure is equal to the inverse of one minus a generalized semblance co- efficient, and the signal-to-noise energy ratio is equal to semblance divided by one minus semblance. Both coherence measures can take on a large range of values, so we prefer to use the logarithm of MUSIC, which is greater than zero. For a signal in the data window with the correct travel time, and for a large value of semblance, these coherence measures take on large values. They also have larger curvature than semblance at the maximum of the coherence function corresponding to the optimal estimate of the travel time parameters. However, for small values of semblance, they are equivalent to semblance, and there is no high-resolution effect. Singular value decomposition (SVD) of the data matrix results in several new types of generalized semblance. The first SVD subspace or eigenimage gives three different generalized semblance coefficients which take into account the main signal energy for a signal with the travel time corresponding to the parameters which were used to generate the data window. They can all be efficiently computed by the power method. Velocity analysis was performed on synthetic data with various noise levels and with and without amplitude-versus-offset (AV0) effects and on marine seismic data. The new semblance functions all gave better results than the classical one.