Generalized Seismic Information Visualization and Isosurfaces Synthesis Technique Based on Spline Decomposition

A new approach especially actual in seismic data processing and interpretation is performed. The essence of the method is continuous analytical function restoration from the initial discrete samples on the base of finite spline functions. It provides classical mathematical methods utilization possibility in digital data processing (differentiation, integrals calculation etc). Particularly precise interpolation becomes accessible (in 3D graphics it always was one of the main problem). The method is a new efficient generalization of known theoretical approach to discrete‐continuous data restoring - so called Kotelnikov theorem or Nyquist criterion. The main difference is in initial discrete samples replacement by their decomposition coefficients (it’s amount may be even less). Finally signal may be restored in any point as convolution with spline function. In seismic data processing this method appeared to be the most simple and efficient due to sufficient data spectrum top border stability. The most simple and convenient spline functions on the base of short Fourier series were synthesized. One of the most important results is a new algorithm of horizon correlation based on phase extraction alternative to Gilbert transform. Along with it basic mathematical algorithms frequently used in such implementations were also greatly improved (FFT, linear systems resolution, cubical polynomial roots extraction). Due to the noticeable increase of the whole computations amount the necessity of additional hardware support also proportionally arises. New parallel processing techniques may be successfully utilized.