Appraisal of broadband acoustic impedances from first principles and band-limited seismic reflection data

Abstract:

Seismic derived acoustic impedance is an essential output for the quantitative interpretation of seismic data. However, the band limitation of seismic data leads to a nonunique estimate of the acoustic impedance profile. The prevalent 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. Making a nominal assumption of a homogeneous layered earth model, we formulate a set of linear equations where the reflection coefficients are the unknowns and the recursively integrated seismic trace constitutes the data. The approach makes a frontal assault on the problem of reconstructing reflection coefficients from band-limited data and stems from first principles, i.e., Zöppritz’s equation in this case. Nonuniqueness is countered in part by the layercake assumption, and in part by the adoption of the singular value decomposition (SVD) method of finding an optimal solution to the set of linear equations, provided the objective is to reconstruct a smoothed version of the impedance profile that includes only its coarser structures. The efficacy of the method has been tested with synthetic data added with significant noise and generated from rudimentary earth models as well as from measured logs of acoustic impedance. Emergence of consistent estimates of impedance from synthetic data generated for several frequency bands increases the confidence in the method. The study also proves the successfulness of the method for (a) an accurate estimate of the impedance mean, (b) an accurate reconstruction of the direct-current (dc) frequency of the reflectivity, and (c) an acceptable reconstruction of the broad trend of the original impedance profile. All these outputs can serve as significant constraints for either more refined inversions or geological interpretations.

(Keywords: Reflection data, Acoustic impedance, Broadband, Linear equations, Singular Value Decomposition, Inversion)