Translations:Time-varying convolutional model/1/en

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Hubral et al. (1980)[1] introduced the sum autoregressive representation of a seismic trace. This representation displays the reflection response as the convolution of the reflectivity with a time-varying sequence of wavelets. In other words, the sum autoregressive representation is a time-varying convolutional model of the trace and includes all multiple reflections. Each time-varying wavelet in the sequence is associated with one and only one interface. Mathematically, a single interface is associated with each discrete instant on the trace. That is, each interface is associated with its own time-varying wavelet, which is called either the generalized primary or the interface wavelet. Each generalized primary (or interface wavelet) is autoregressive, with its denominator given by the product of two successively longer prediction-error operator Z-transforms so that the generalized primary is minimum phase. The interface wavelet of a layer depends only on the reflection coefficients at and above that layer. Further treatment is given in Robinson (1999)[2].

  1. Hubral, P., S. Treitel, and P. R. Gutowski, 1980, A sum autoregressive formula for the reflection response: Geophysics, 45, 1697-1705.
  2. Robinson, E. A., 1999, Seismic inversion and deconvolution, dual sensor technology: Elsevier.