Multichannel Autoregressive Data Models

Abstract

Autoregressive (AR) data models are implied in many analytical procedures used in the description and interpretation of geophysical measurements. Predictive deconvolution, prediction filtering, and spectral estimation based upon the maximum entropy and maximum likelihood criteria are among those procedures which imply AR models. Predictive deconvolution as a method for determining a seismic reflection series or for targetting an anomaly in profile potential field data has been broadly applied. Maximum entropy spectral analysis has been found particularly useful in searching for the presence of harmonics in short segments of geophysical data. We describe a new recursive procedure for estimating, directly from a data set, the matrix coefficients representing a multichannel or η-vector stationary time series. An AR data model which considers all possible inter-relationships between the component channels is obtained. In several examples, multichannel geophysical data sets are modeled for deconvolution and maximum entropy multispectral analysis.