Generalized iterative deconvolution for receiver function estimation

This paper describes a generalization of the iterative deconvolution method commonly used as a component of passive array wavefield imaging. We show that the iterative method should be thought of as a sparse output deconvolution method with the number of terms retained dependent on the convergence criteria. The generalized method we introduce uses an inverse operator to shape the assumed wavelet to a peaked function at zero lag. We show that the conventional method is equivalent to using a damped least-squares spiking filter with extremely large damping and proper scaling. In that case, the inverse operator used in the generalized method reduces to the cross-correlation operator. The theoretical insight of realizing the output is a sparse series provides a basis for the second important addition of the generalized method-an output shaping wavelet. A constant output shaping wavelet is a critical component in scattered wave imaging to avoid mixing data of variable bandwidth. We demonstrate the new approach can improve resolution by using an inverse operator tuned to maximize resolution. We also show that the signal-to-noise ratio of the result can be improved by applying a different convergence criterion than the standard method, which measures the energy left after each iteration. The efficacy of the approach was evaluated with synthetic experiment in various signal and noise conditions. We further validated the approach with real data from the USArray. We compared our results with data from the EarthScope Automated Receiver Survey and found that our results show modest improvements in consistency measured by correlation coefficients with station stacks and a reduced number of outliers.