Nonstationary signal and noise separation using adaptive prediction‐error filter

Abstract

Many natural phenomena, including geologic events and geophysical data, are fundamentally nonstationary. They might exhibit stationarity on a short timescale but eventually alter their behavior in space and time. We extend the application of adaptive prediction‐error filter (PEF) based on regularized nonstationary autoregression, which aims at signal and noise separation in t‐x domain. Instead of using patching, a popular method for handling nonstationarity, we obtain smoothly nonstationary PEF coefficients by solving a regularized least‐squares problem with shaping regularization. In the second step, we solve the other least‐square system tailored specifically to signal and noise separation. Using synthetic and real data examples, we successfully apply this method to the problem of nonstationary signal and two different noise separation.