Multi-component autoregressive techniques for the analysis of seismograms

Autoregressive methods provide a very useful means of characterising a seismic record; calculating the power spectra of a seismic record and determining the onset time of different classes of arrivals. The representation of a time series with an autoregressive (AR) process of low order can be applied to both multi-component and single-component traces of broadband and short period seismograms. In three-component analysis the AR coefficients are represented as second-order tensors and include potential cross-coupling between the different components of the seismogram. Power spectrum estimation using autoregressive methods is demonstrated to be effective for both signal and noise and has the advantage over FFT methods in that it is smoother and less susceptible to statistical noise. The order of the AR process required to resolve the detail of the spectra is higher for a complex signal than for the preceding noise. This variation in the weighting of the AR coefficients provides an effective way to characterise data in a similar way to Spectragrams and Vespagrams and can be achieved with as few as five AR coefficients. For three-component analysis a display of the nine AR coefficients can be readily organised with three AR-grams for each of the original data components. The various elements of the AR tensor coefficients reflect different changes in the seismogram. The presence of secondary phases is often clearer on a cross-correlation AR-gram (NE or EN) than on the autocorrelation AR-gram (NN or NE). The variations in the weighting of the AR coefficients can be exploited in two different styles of approach to onset time estimation (phase picking). In the first method, two different AR representations are constructed for different portions of the record and the onset time is estimated from the point of transition. In the second method, a single AR representation is constructed and the onset time estimation is based on the growth of a component which is not represented by the AR process. Both methods can be applied to both single and three-component data. For large impulsive P phases, both methods picked the onset time within two samples of the manually estimated onset time. For S phases, where the energy is present on all three components, three-component AR onset time estimation is preferred to that using a single component. The approach is very robust with the three-component method picking the onset time of a very small S phase on a broad-band record to within 0.5 s of the best manual estimate