Criteria for the resolution and reconstruction of acoustic impedance

We derive approximate quantitative criteria for the resolution and reconstruction of the acoustic impedance for horizontally stratified media calculated from band‐limited seismic data both without and with noise. The first criterion, for noise‐free data, relates the calculated acoustic impedance to the true acoustic impedance using only the DC (zero frequency) level of the seismic source or wavelet. The second criterion, for noisy data, predicts the band of uncertainty of the calculated impedance. The third criterion is the combination of the first two. One of the most important results of this paper is that the average shape of the acoustic impedance can be estimated from data without wavelet deconvolution, if the D.C. component of the wavelet function is not zero.