Differential operators 2: The second derivative
John C. Bancroft
Differential operators are used in many seismic data processes such as triangle filters to reduce aliasing, finite difference solutions to the wave equation, and wavelet correction when modelling with diffractions or migrating with Kirchhoff algorithms. Short operators may be quite accurate when the data are restricted to low order polynomials, but may be inaccurate in other applications.
This is the second of three papers on differential operators and deals specifically with the second derivative. The first paper deals with the first derivative and the third paper deals with the square-root derivative.
The purpose of this paper is to evaluate visually the short operators that approximate a second derivative.