Analysis and design of filters for differentiation
John C. Bancroft, Hugh D. Geiger
Differential equations are an "integral" part of seismic processing. In the discrete computer world they are solved using finite difference equations. Derivatives are also used in the integral forms of DMO and migration algorithms.
This paper looks at some commonly used convolutional and recursive filters that are used to approximate the derivative. Traditionally, the convolutional methods are the easiest to design, but the recursive methods run faster.
The main motivation is to find fast and accurate filters that represent the first derivative, the second derivative and the square root derivative.