Gaussian scaling noise model of seismic reflection sequences; evidence from well logs

Abstract A simple model for reflection series is desirable for two reasons: first, to have a means of generating model reflection sequences on which to test geophysical data processing techniques, specifically methods of predictive deconvolution, and second, to suggest a way of parameterizing real reflection sequences for classification and further geologic study. In this note we wish to discuss a model suggested by Hosken (1980); our discussion is founded upon the powerful ideas of self-similarity and scaling developed by Mandelbrot (1983) and on the paucity of typical lengths in geology. Typical lengths are common in physics problems; for example, the length of an organ pipe governs the wavelengths of the notes played. When taking photographs, geologists include some manmade object to give scale to the photo. Otherwise it is very hard to tell if, say, folds are of centimeter size or form whole mountains.