LPA Smoothing

structure preserving spatial filter by local polynomial approximation

Script: ex_lpa_smooth.py

Description

This Python External Attribute script can be used to filter noise while preserving steep dips. A region of data around each sample location is approximated by a second order 3D polynomial using gaussian weighted least squares.

The approximation has the following form:

$$ r_0+ r_1 * x + r_2 * y + r_3 * z + r_4 * x^2 + r_5 * y^2 + r_6 * z^2 +r_7 * x * y + r_8 * x * z + r_9 * y * z $$

where x (inline), y (crossline) and z (time/depth) are relative to the analysis location, ie the analysis location has x=y=z=0.

This attribute calculates and outputs only the \(r_0\) term of the local polynomial approximation. This provides a smoother version of the input with relatively minor smearing of steep dips and fault cuts. Increasing either the Weight Factor or size of the analysis volume (StepOut or Z window) increases the amount of smoothing.

Examples

Input lpa 2x2x2 WF: 0.5

Input Parameters

LPA Smoothing external attribute input parameters

LPA Smoothing external attribute input parameters

NAME DESCRIPTION
Z window (+/-samples) Specifies the extent of the analysis cube in the Z direction. Number of Z samples in cube will be \(2 * Zwindow + 1\).
Stepout Specifies the inline and crossline extent of the analysis cube. Number of samples in each direction will be \(2 * Stepout + 1\).
Weight Factor Determines the extent of the gaussian weight function used in the weighted least squares approximation. The standard deviation of the gaussian weight function \((\sigma)\) is related to this value by:
\(\sigma = min(2*Stepout, 2*Zwindow)*WeightFactor\).
A value of 0.15 gives near zero weight for points at the smallest extent of the analysis cube.

References

Anisotropic Multidimensional Savitzky Golay kernels for Smoothing, Differentiation and Reconstruction

Polynomial Expansion for Orientation and Motion Estimation


Last modified April 17, 2022: First update (afe101d)