Lp normed spectral estimation residual analysis for sonic well logging

The authors describe how the complex kurtosis of the residual vector can be used as a test statistic for deciding if impulsive noise is present in sonic log data and consequently whether to incur the additional computational expense for calculating an L₁ normed solution. The robustness of the method is demonstrated by a Monte Carlo simulation. The FBLP (forward-backward linear prediction) spectral estimator has been found to be essentially unbiased in the presence of moderate amounts of additive Gaussian noise. The addition of an impulse to the data did not significantly increase the bias of the FBLP frequency estimator