Reconstruction of seismic data using adaptive regularization

Abstract

In seismic data processing, we often need to interpolate/extrapolate missing spatial locations in a domain of interest. The reconstruction problem can be posed as an inverse problem where from inadequate and incomplete data one attempts to recover the complete band-limited seismic wavefield. However, the problem is often ill posed due to factors such as inaccurate knowledge of bandwidth and noise. In this case, regularization can be used to help to obtain a unique and stable solution. In this paper, we formulate band-limited data reconstruction as a minimum norm least squares type problem where an adaptive DFT-weighted norm regularization term is used to constrain solutions. In particular, the regularization term is updated iteratively through using the modified periodogram of the estimated data. The technique allows for adaptive incorporation of prior knowledge of the data such as the spectrum support and the shape of the spectrum. The adaptive regularization can be accelerated using FFTs and an iterative solver like preconditioned conjugate gradient algorithm. Examples on synthetic and real seismic data illustrate improvement of the new method over damped least squares estimation.