Nonstationary local slope estimation via forward-backward space derivative calculation

Abstract

The local slope estimated from seismic images has a variety of meaningful applications. Slope estimation based on the plane-wave destruction (PWD) method is a widely accepted technique in the seismic community. However, the PWD method suffers from sensitivity to noise in the seismic data. We have developed an improved slope estimation method based on the PWD theory that is more robust in the presence of strong random noise. The PWD operator derived in the Z-transform domain contains a phase-shift operator in space corresponding to the calculation of the first-order derivative of the wavefield in the space domain. The first-order derivative is discretized based on a forward finite difference in the traditional PWD method, which lacks the constraint from the backward direction. We have developed an improved method by discretizing the first-order space derivative based on an averaged forward-backward finite-difference calculation. The forward-backward space derivative calculation makes the space-domain first-order derivative more accurate and better at antinoise because it takes more space grids for the derivative calculation. In addition, we introduce nonstationary smoothing to regularize the slope estimation and to make it even more robust to noise. We determine the performance of the new slope estimation method with several synthetic and field data examples in different applications, including 2D/3D structural filtering, structure-oriented deblending, and horizon tracking.