SEISMIC DATA PROCESSING WITH THE WAVE （与波地震资料处理）.pdfVIP

SEISMIC DATA PROCESSING WITH THE WAVE EQUATION The coordinate frames used by theoreticians to describe wave propagation do not include frames in common use by geophysical prospectors to describe observations. Whereas the theoretician generally considers a single source (or shot) location at a time, the experimentalist deals simultaneously with waves which have been gener- ated separately by many shots. Our task in this section is to put the wave equation into some prospectors coordinate frames. 11-1 DOWNWARD CONTINUATION OF GATHERS AND SECTIONS Suboceanic prospecting is generally carried out by a ship which carries a repetitive energy source and which trails a cable that is 2 to 3 kilometers long and packed with sonic receivers. Ideally, the ships course is a straight line which we can take to be the x axis. Ideally, all the seismic waves of interest propagate in a vertical plane through the line of the ships course. This plane is called the plane of the seismic section. Despite the fact that it is no great problem to describe waves in three dimensions once difference techniques have been mastered for two dimensions, we will restrict the theory to two dimensions in order to keep it compatible with the bulk of present-day surveying practice and the capability of most present-day computing machines. An impulsive wave from a point source spreading out in three dimensions will decay in amplitude in inverse proportion to the travel time. (The area of a spherical wavefront increases as t 2, so the energy per unit area decreases as t2, and so the wave amplitude is proportional to t-l.) An impulsive wave from a line source (the line would be on the oceans surface perpendicular to the ships course) has an amplitude decay propo