Applications of median filtering to deconvolution, pulse estimation, and statistical editing of seismic data

Abstract

Seismic exploration problems frequently require analysis of noisy data. Traditional processing removes or reduces noise effects by linear statistical filtering. This filtering process can be viewed as a weighted averaging with coefficients chosen to enhance the data information content. When the signal and noise components occupy separate spectral windows, or when the statistical properties of the noise are sufficiently understood, linear statistical filtering is an effective tool for data enhancement. When the noise properties are not well understood, or when the noise and signal occupy the same spectral window, linear or weighted averaging performs poorly as a signal enhancement process. One must look for alternative procedures to extract the desired information. As a nonlinear operation which is statistically similar to averaging, median filtering represents one potential alternative. This paper investigates the application of median filtering to several seismic data enhancement problems. A methodology for using median filtering as one step in cepstral deconvolution or seismic signature estimation is presented. The median filtering process is applied to statistical editing of acoustic impedance data and the removal of noise bursts from reflection data. The most surprising conclusion obtained from the empirical studies on synthetic data is that, in high‐noise situations, cepstral‐based median filtering appears to perform exceptionally well as a deconvolver but poorly as a signature estimator. For real data, the process is stable and, to the extent that the data follow the convolutional model, does a reasonable job at both pulse estimation and deconvolution.