Translations:Wavefront for velocity linear with depth/1/en

From SEG Wiki
Jump to navigation Jump to search
ADVERTISEMENT

Our next task is to use the eikonal equation to find the wavefronts. The eikonal equation tells us that the wavefronts are orthogonal to the raypaths. We will use this orthogonal property to construct a wavefront (Figure 14). To this end, it is advantageous to make a one-to-one relationship between raypaths and wavefronts. For each point on the (x,y) plane, a raypath exists whose tangent at that point is horizontal. As we have seen, this is the point of maximum depth. By the eikonal equation, the tangent of the wavefront passing through that point must be vertical. The center C of the circular raypath lies vertically under this point. For the moment, we will assume that the wavefront is also circular. It follows that the center G of this circular wavefront must lie horizontally to the side of this point. But where does the center reside? Because everything is symmetric about the vertical axis, it follows that the center of this circular wavefront must lie on the vertical axis. Thus, the required wavefront is a circle with center and radius given, respectively, by