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DC2DInvRes - Resolution Analysis Menu

The SVD resolution analysis is an powerfull tool for estimating quality and confidence of inversion results as well as for experimental design and the optimization of model parameterization. For further information see here.
By means of an example is show, how the particular quantities can be interpreted.

Compute resolution

A generalized singular decomposition is carried out in order to compute the full resolution matrices. This might take a while for large data sets or couldn't even be possible. Once the calculation is done all options below are enabled.
Note that one single model resolution can also be asessed by solving an additional subproblem. This is possible also for large data sets.

Clear SVD

This option is used to clean any svd matrices from workspace and to force a new calculation, when resolution images are called.

Data Resolution

The "Data Resolution" is the main diagonal of the data resolution matrix. It shows, how well (and how independend from other data) the particular data points can be predicted and how much information of the data set comes from this measurement. The maximum of 1 is nearly reached for shallow electrode configurations with small errors. Data with large errors and (nearly) redundant data have small resolutions and contribute less information.

Data resolution of a pole-dipole survey with separation 1-8

Model Resolution

The "Model Resolution" is the main diagonal of the model resolution matrix. The value can be interpreted as reconstructability of the model cells. Shallow cells have high resolution (1), resulting in a good resistivity reconstruction in amplitude and shape. Deep cells and such outside of the center can't perfectly be reconstructed by the inversion process. A loss in amplitude is the result connected with smooth shapes.

Resolution radius

Under the assumption of approximately constant model resolution a cell can be seen as an equivalent circle with the same model information. The consideration of model dimensions leads to the resolution radius, which can be treated as uncertainty of boundary or bodies.

Model Cell Resolution

The columns of the model resolution matrix show for each model cell, how a change in resistivity is reproduced by the inversion. Shallow cells have sharp cell resolutions, whereas deep cells tend to give blurred images.
The model cells can be chosen by clicking on it or by controlling the slider.
Note, that the model cell resolutions can be calculated without singular value decomposition.

Single Data Resolution

The different columns of the data resolution matrix show for each datum point, how well they are connected with each other. Data with the same transmittor/receiver dipole usually correlate to a high degree.

Singular Values

Shows the singular values. Fast decreasing singular values show the ill-conditioning of the inverse problem.

Filter factors and transform function

Very small singular values tend to explode in the inversion, resulting in much high-frequency components in the solution. Filter factors are used to prevent this. Additionally, this plot shows the transform function, filter factors divided by singular values, which is the main diagonal in the generalized inverse. It can also be seen, how the information content is cumulated by the several singular vectors.