Abstract

Estimation of acoustic impedance from reflection data is an essential step for quantitative interpretation of seismic data. However, the band limitation of reflection seismic data (in particular the absence of low frequencies) hinders a direct interpretation in terms of rock properties owing to nonuniqueness of the solution. The existing methods counter the nonuniqueness either by stabilizing the answer with respect to an initial model or by resorting to an assumption of certain criterion such as sparsity of the reflection coefficients. Using a layered earth model and the basic amplitude equation we formulate a set of linear equations where the recursively integrated reflection trace amplitudes constitute the data and reflection coefficients are the unknowns. The local layercake assumption and the strategy of seeking singular value decomposition (SVD) solution of the formulated linear equations counter the nonuniqueness by aiming only for the low frequency part of the impedance profile. The efficacy of the proposed approach has been tested with synthetic data containing significant noise for a simple earth model as well as the real earth represented by well log impedance data. Additional advantages of the method include accurate estimates of the impedance mean, and approximate reconstruction of the trend of the impedance profile. All of these can serve as important constraints for an effective earth modeling.