Article,
Multi-component autoregressive techniques for the analysis of seismograms
Physics of the Earth and Planetary Interiors, 113 (1-4): 247--263 (June 1999)
DOI: 10.1016/S0031-9201(99)00054-0
Abstract
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.
