Iterative trace deconvolution and noncausal transform for processing band‐limited data

Abstract

In 1983, Carrion and Patton showed that if recorded seismic data do not have low frequencies in their spectrum, inversion for acoustic impedance is unstable. This concept is commonly accepted. Here, we infer acoustic impedance from band‐limited data without low frequencies using iterative trace deconvolution with the so‐called “noncausal projection” which moves initial data samples corresponding to small eigenvalues to negative times. We show that this procedure can solve ill‐posed problems by migrating large residuals (uncertainties in the trend of the recovered impedance) to the bottom of the model. An important property of the proposed method is that it converges to the true solution independently of the chosen initial model. Another advantage of the proposed algorithm is that, unlike conventional dynamic deconvolution (characteristic‐integration schemes), it increases neither errors nor the condition number with depth. The method is illustrated on synthetic and real data.