Lp Normed Spectral Estimation Residual Analysis

Seismic sonic log data is characterized by a relatively high signal-to-noise ratio with the possible presence of one or more impulses arising from the data acquisition environment. Frequently, in order to completely analyze sonic log data, a high resolution frequency estimation technique is required that is resistant to the possible presence of impulsive noise. Previous work has shown that increased frequency resolution is possible fo r multiple sinusoids contaminated by impulsive noise utilizing an L1 normed solution to a set of linear prediction equations. In an actual data analysis scenario, however, the interpreter is uncertain whether impulsive noise is present. This paper outlines how the complex kurtosis of the residual vector may be conveniently used as a test statistic for deciding if impulsive noise is present and consequently to decide whether to incur the additional computational expense of calculating an L1 normed solution.