# Damping Tests

### July 17th, 2013

Sadly, my mentor and I have not yet cracked the out of bounds entry point error that has been plaguing the tomography process since day one. I have been running some debugging tests this week however and found out where exactly the error is generated from. Unfortunately, because the level of coding is way beyond my current knowledge, I don't know how to fix the problem. But identifying it will hopefully help my mentor streamline the process of getting rid of the errors once and for all!

In the mean time, I've been working with my model constructed from the fragmented data. Tomography models solved via a least squares method include a parameter known as "damping". Essentially, damping varies how "smooth" a model looks. Depending on what you set your damping parameter to be, you are minimizing different parameters. If your damping is high, your result minimizes error, but doesn't necessarily reflect the complexities of the undetermined parameters in the solution. If your damping is low, your results will attempt to best represent the undetermined parameters in the problem, but won't ensure small degrees of error. To display this visually, I've included three images below with different degrees of damping. The images are of the same slice through an identical model. The only difference between them is the damping parameter.

1. Damping: 200

2. Damping: 20

3. Damping: 2

As you can see, the three images show varying degrees of similarity. Features that are evident in one image, are completely missing in another. After seeing these images, you may be wondering how you know which one is most accurate! Well, the answer to that question is actually fairly simple. You can create what is known as a "damping trade-off curve" to analyze how the damping levels compare to each other. This graph plots the amount of variance in your data versus the amount of variance in the model. In general, you want to pick the smoothest model that fits your data. Ideally, you test all the models on multiple iterations as well. I will hopefully be producing a damping trade-off curve for my model before the end of the summer!

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