The L-DVV method for the seismic signal extraction

Abstract The delay vector variance (DVV) method enables analyzing the nonlinearity of a time series by the so-called scatter diagram, where the original time series is compared to the linearized version, the so-called surrogate. The surrogate is often constructed by the iterative amplitude adjusted Fourier transformation (iAAFT) method, so a linear signal in the DVV method can be generated by a linear time-invariant system in a white Gaussian noise environment. Owing to the iAAFT method and the linearity criterion, the DVV method is not sensitive to stochastic noise and the results are unstable, which may cause some confusion between the desired signal and the stochastic noise when processing the seismic signal. The now proposed method, the delay vector variance based on the straight line sequence (L-DVV) method, is essentially an extension of the DVV method, so that the straight line sequence is selected from the original signal and defined as the surrogate time series, which is used to construct the L-DVV scatter diagram based on the target variances calculated from both time series. This new scatter diagram is taken as criterion for testing the linearity of the analyzed time series. The analyses as to the stability of the method and its sensitivity to the stochastic noise are based on the quantification of the delay vector variance (QDV) or deviation with respect to bisector in the scatter diagram. These are the two key points – L-DVV scatter diagram and QVD – that we bear in mind when studying some examples of synthetic seismic signals contaminated by different noise levels and also real field data. The L-DVV method has high stability and strong sensitivity to the stochastic noise, and is able to discriminate accurately the seismic signal masked by stochastic noise, thus being a useful tool for the seismic signal processing in the exploratory practice.