Autoregressive recovery of the acoustic impedance

Abstract

This paper presents a method of recovering the acoustic impedance from reflection seismograms using autoregressive (AR) modeling, an approach originally applied to deconvolution by Lines and Clayton (1977). The algorithm which we describe is novel both in the manner in which the missing low‐ and high‐frequency information is predicted, and in the fact that the prediction may be constrained if acoustic impedance information is available. The prediction of the low frequencies treats the missing data as a gap which extends from the low‐frequency cut‐off in the negative frequency band to the corresponding frequency in the positive frequency band. The conjugate symmetry which governs the behavior of the spectrum in the band is taken into account in the prediction. The missing high frequencies are predicted using a modified minimum entropy norm in the frequency domain. Both synthetic and field examples are presented and illustrate the robustness of the new AR algorithm under a variety of conditions. The field example also compares the results obtained using the AR algorithm with the linear programming method of Oldenburg et al (1983). The agreement in results is particularly gratifying in view of the differences in the two inversion schemes.