Low-frequency components of reflection seismic data are of paramount importance for acoustic impedance (AI) inversion, but they typically suffer from a poor signal-to-noise ratio. The estimation of the low frequencies of AI can benefit from the combination of a harmonic reconstruction method (based on autoregressive [AR] models) and a seismic-derived interval velocity field. We have developed the construction of a convex cost function that accounts for the velocity field, together with geologic a priori information on AI and its uncertainty, during the AR reconstruction of the low frequencies. The minimization of this function allows one to reconstruct sensible estimates of low-frequency components of the subsurface reflectivity, which lead to an estimation of AI model via a recursive formulation. In particular, the method is suited for an initial and computationally inexpensive assessment of the absolute value of AI even when no well-log data are available. We first tested the method on layered synthetic models, then we analyzed its applicability and limitations on a real marine seismic data set that included tomographic velocity information. Despite a strong trace-to-trace variability in the results, which could partially be mitigated by multitrace inversion, the method demonstrates its capability to highlight lateral variations of AI that cannot be detected when the low frequencies only come from well-log information.

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