Model fitting by least squares

Gulf of Mexico Salt Piercement Example (Jesse Lomask)

Figure 9 shows a 3-D seismic data cube from the Gulf of Mexico provided by Chevron. A volume of data cannot be displayed on the page of a book. The display here consists of three slices from the volume. Top is a $(t_0 , x , y )$ slice, also called a ``time slice.'' Beneath it is a $(t , x , y_0 )$ slice; aside that is a $(t , x_0 , y )$ slice, depth slices in orthogonal directions. Intersections of the slices within the cube are shown by the heavy black lines on the faces of the cube. The circle in the lower right corner of the top slice is an eruption of salt (which, like ice, under high pressure will flow like a liquid). Inside the salt there are no reflections so the data should be ignored there. Outside the salt we see layers, simple horizons of sedimentary rock. As the salt has pushed upward it has dragged bedding planes upward with it. Presuming the bedding to contain permeable sandstones and impermeable shales, the pushed up bedding around the salt is a prospective oil trap. The time slice in the top panel shows ancient river channels, some large, some small, that are now deeply buried. These may also contain sand. Being natural underground ``oil pipes'' they are of great interest. To see these pipes as they approach the salt dome we need a picture not at a constant $t$, but at a constant $t -\tau (x , y )$.

Figure 10 shows a time slice of the original cube and the flattened cube of Figure 9. The first thing to notice on the plane before flattening is that the panel drifts from dark to light in place to place. This is because the horizontal layers are not fully horizontal. Approaching the dome the change from dark to light and back again happens so rapidly that the dome appears surrounded by rings. After flattening, the drift and rings disappear. The reflection horizons are no longer cutting across the image. Channels no longer drift off (above or below) the viewable time slice. Carefully viewing the salt dome it seems smaller after flattening because the rings are replace by a bedding plane.

slicecomp22 Figure 10. Slices of constant time before and after flattening. Notice the rings surrounding the dome are gone giving the dome a reduced diameter. (Ignore the inside of the dome.)

Model fitting by least squares