Techniques to enhance the accuracy and efficiency of finite-difference modelling for the propagation of elastic waves
Peter Malcolm Manning
New techniques are described to enhance the accuracy and efficiency of finite-difference modelling for the propagation of elastic waves.
The most important technique involves the active adjustment of the frequency content of each finite modelling step. This contrasts with most current finite- difference modelling practise, which uses frequency analysis only to evaluate the utility of various other processes within a step. In order to adjust frequency content with spatial operators of limited size, procedures combining Fourier analysis and optimization are developed. This is done first for one spatial dimension, and then for two. Tests show obvious improvements by use of this technique.
A second technique develops a mathematical definition of a transmitting edge for finite-difference models, often called an absorbing boundary. Tests indicate that this is a valid concept, and show some encouraging results.
Three case studies are also included where finite-difference modelling sheds some light on elastic propagation problems. The first shows how Rayleigh (surface) waves are transmitted and reflected at simple velocity boundaries. The second shows how near surface conditions affect the character of body and surface waves. The third shows where finite-difference modelling may add to the realism of AVO interpretations.