Density imaging of the Cheops pyramid. A 3D view

Figure 1 : A 3D view of the surface density.

Figure 2. The SE view. Houdin's theory of internal tunnel ramp and theories of degrees.

The surface density is a mean value of the surface finite element of the pyramid, through 10m depth at the bottom and 3m at the top. The density imaging is obtained by discretizing the pyramid into 2000 elements and using 750 measurements inside and outside the pyramid. Methods of inverse problems for the gravitation equation were used with constraints on the density (see our 1988 paper). The vertical projection can be raised up to the four faces. Then we can display a 3D view of the pyramid in different angles, Figure 1.

We select the SE view and make a comparison with Houdin's theory of internal tunnel ramp Fig. 2d and theories which involve degrees. The cornices of these degrees may be filled of stones with many void so that the density can be low (green colour), Figure 2. With degrees theories (Holscher, Borchart, Guerrier etc) the image patterns of degrees are horizontal Fig. 2c.