SYNTHESIS OF ADDITIVE AMBIENT SEISMIC NOISE WITH A GAUSSIAN MARKOV MODEL
Seismic data laboratory rept.
TELEDYNE INDUSTRIES INC ALEXANDRIA VA EARTH SCIENCES DIV
Pagination or Media Count:
The ambient seismic noise is modeled by a single Gaussian population from which independent realizations or states are taken as input to tuned filters with spectral peaks matched to those observed in noise samples, for example at .2 cps and 2. cps. For each spectral noise peak, the realization on channel i 1 is equal to a constant times the realization on channel i plus another constant times a new realization on channel i 1. The constants defining the Markov process can be used to theoretically derive the associated power spectral matrix of the noise model. The model can be extended to dispersive systems by using a set of constants and time lags to relate the noise on channel i to that on channel i 1. A vertical array signal model is also given. The purpose is to efficiently generate noise andor signals at prescribed SN ratios. The noise covariance structure is close to that observed naturally and is known exactly for the noise model realizations. Thus the spectral covariance of the noise is given exactly subject only to roundoff error, and conditions of stationarity and equilibrium are satisfied by the data generated for testing and designing multichannel filters.
- Statistics and Probability