diego domenzain September 2020 @ Colorado School of Mines

Two (or more) physical parameters can share structure. Here, the parameters are two-dimensional matrices.

The question is then, how can we transfer the structure of one parameter onto the other?

This script is an example of cross-gradient inversion.

Here, they are called a and b. They do not represent any physical parameters. However, they do emulate the mathematical description of a physical parameter.

There are three possibilities,

• a and b get to be like each other,
• a gets to be like b (and b is fixed),
• b gets to be like a (and a is fixed).

These inversions are done with gradient descent.

• xgrad_ex_circs.m perform these inversions on two discs for a and b.
• xgrad_ex_circ_box.m performs these inversions on a disc and a square for a and b.

This is the result of making both a and b look like each other. Note how both shapes are deformed:

• the New a and the New b agree in shape on a weird shape.

This is the result of making a look like b. Note how a changes and b remains constant:

• the New a now looks more like b and the shape is not deformed.

This is the result of making b look like a. Note how b changes and a remains constant:

• the New b now looks more like a and the shape is not deformed.

Finally, lets look at these last two results together.