Preliminary Maps

Figures 2 and 3 display the best merged map using the Laplacian, ${\nabla^2}$, and 2D gradient, (${\nabla_x},{\nabla_y}$), as regulators.

 

laplac
Figure 2 Dense and sparse tracks combined using the 2D Laplacian as regularization, EW roughened by gradient.

 

igrad2
Figure 3 Dense and sparse tracks combined using the 2D gradient as regularization, EW roughened by gradient.

As expected, the northern half is too smooth, but the major trends are captured in both examples. The general shapes of the major ridge and the western dome features continue into the northern half.

It is possible that this model with two different data densities needs two different regularization parameters, $\epsilon$. In Figure 2, the southern half is clearly being blurred by the regularization fitting goal. The $\epsilon$ used in this case was the $\epsilon$ that created a reasonable image in the northern half. In the southern half, the best $\epsilon$ to use would actually be 0, because on this grid there is no missing data in the southern half.