Accounting for limited spatial aperture in the waveform inversion of p-τ seismograms

The finite length of seismic arrays results in smeared estimates of the plane‐wave decomposition of the recorded wave field. The smearing is a fundamental property of plane‐wave decomposition; it can be reduced but not eliminated. If not accounted for, this smearing can have a significant effect upon the waveform inversion of plane‐wave seismograms. This paper illustrates the effects of limited spatial aperture on the plane‐wave decomposition and demonstrates that these truncation artifacts can be described by a linear ray parameter‐dependent filter. Experiments with synthetic data indicate that including the effects of limited aperture in the forward model of an iterative inversion produces a stable inversion result without significantly reducing the information content of the data. The method is illustrated with synthetic data derived for an earth consisting of elastic, isotropic, flat layers.