Abstract
The Earth's filter response to seismic wave propagation can be approximated by constant Q attenuation and is dispersive or minimum phase. A finite-length autoregressive (AR) filter model is a good representation for constant Q attenuation with minimum phase. Coefficients of the AR filter are the Wiener-Levinson inverse filter coefficients for the sampled constant Q autocorrelation. Conventional spike deconvolution approximates fairly well the inverse filter on this ground if the minimum-phase attenuation law holds true.Wavelet response to attenuation was analyzed using the AR filter model. The amplitude of the filtered impulse response decreases at nearly 1/t, where t is traveltime, and is sensitive to the loss of low frequencies. The wavelets' peak amplitude is fractionally time delayed with .92/Q. Velocity dispersion of seismic waves should not contribute to the mis-tie observed between the conventional check shot and the borehole sonic log when the first arrivals are picked the same way.
