Extended Resolution by 3-D Holographic Seismic Imaging

Abstract

Abstract Holography represents a method of recording on a plane (the hologram) a pattern due to the interference of a reference beam with light diffracted from an object. When the hologram is illuminated, the entire picture of the object in three dimensional space is obtained as a virtual image. An essential principle is that a seismogram is a hologram. The understanding of this principle opens up new vistas in seismic exploration, and in particular justifies important cost saving measures in acquisition and processing methods. When a hologram is illuminated or a seismic section is migrated, each depicts the entire image of the unattainable object. Moreover, any part of the hologram also depicts the entire image of the object. The same is true in the seismic case if conventional migration is replaced by holographic seismic imaging, also known as holistic migration. Holistic migration is a process in which any part of the seismic section produces the entire image of the subsurface. Holistic methods allow wavefield images to achieve resolution beyond that predicted by conventional digital processing techniques. The image might not be quite as clear, but the same fine structure will be present. The implication is that in a seismic survey the number of shot points and detectors can be greatly reduced without adversely affecting the results. Holographic seismic imaging provides the extended resolution needed to attain a better image of the subsurface. Introduction The reflection seismic method is an instrument to find the structure of an inaccessible body, the subsurface geology. Because the rock layers are transparent to seismic waves, the recorded seismic time sections contain not only the primary reflections from the geologic interfaces, but the multiple reflections as well. The purpose of deconvolution, stacking, and related seismic processing methods is to produce multiplefree time sections and also to obtain a velocity function of the subsurface. The purpose of migration is to find a threedimensional (3-D) picture or image of the subsurface from the multiple-free time sections according to the velocity function. Cost is a major factor in the design of 3-D surveys. Neidell (Ref. 1) has challenged traditionally views, and has introduced methods that allow extended resolution in seismic imaging as compared to conventional methods. The purpose of this paper is to give a theoretical basis for the new methods of imaging known as holographic seismic imaging, or simply as holistic migration. They are addressed from the viewpoint of imaging technology, and in particular the theory of holography. Holography is the doorway that leads to better methods of seismic imaging. This doorway gives access to the fulfillment of the imaginative methods required to obtain the best possible images of the subsurface. Holography involves the recording and the illumination of a hologram in order to produce a 3-D image of a body. In shifting our seismic guidelines and paradigms to the point of view of holography, many of the unnecessary restrictions and limitations that have been accepted as essentially insurmountable barriers can be removed. Holographic seismic imaging can achieve resolution beyond that given byconventional methods of migration.