ANALYSIS OF VARIABLE‐DENSITY SEISMOGRAMS BY MEANS OF OPTICAL DIFFRACTION

Abstract

Variable‐density seismograms were originally developed in exploration work to aid in the visualization of strata formations. They can also be directly analyzed by means of optical diffraction. When a plane wave of spatially coherent monochromatic light passes through a variable‐density seismogram, a diffraction pattern can be formed which defines the seismic frequencies. The seismogram is placed so that it affects the incident light in the same manner as a diffraction grating in a conventional spectroscopic apparatus. Resulting diffraction patterns reveal continuous energy‐density spectra over a range of about nine octaves. The spectra are normally two‐dimensional. When variable‐density profiles are used, the second dimension of the spectra is wavenumber, which is expressed as the diffraction caused by density variations across the data channels. The spectra can be made one‐dimensional by inserting a cylindrical lens so that an image of the seismograms is formed in one direction in the same plane that Fraunhofer diffraction occurs in a perpendicular direction. By this means multichannel spectral analysis is performed. An additional lens is used to image the seismogram after the light has passed through the diffraction plane. The image can be filtered as to frequency, wavenumber, or propagation velocity when suitable obstructions are placed in the diffraction plane. By properly combining optical diffraction and imaging, one can obtain or perform the following: energy‐density spectra, time‐varying spectra, constant apparent wavenumber spectra, dispersion measurements, apparent velocity of narrow‐band energy, frequency filtering, wavenumber filtering, wideband velocity filtering, and correlations.