Saltar al contenido principal

Calibration

The calibration aims to adjust the inputs parameters (P32P_{32} and diameter mainly) so the DFN reflects the data. In order to do it, the DFNs generated are sampled as the data are collected (i.e. same scanline dimensions, orientation, minimum trace length mapped, etc.). Then, the same biases apply for the collected data and the sampled DFN data. The calibration is also a way to better defined inputs parameters; the better are the input parameters, the quicker the calibration will be made / obtained.

In mXrap - The steps to calibrate are:

  1. Generation: Estimate the Mean diameter and P32 inputs
    1. To generate multiple DFN to ‘compare’ the data: open the ‘Controls/Sampling Control Panel’ and change the ‘Number of DFNs To Sample’
  2. Validation: Compare DFN samples ‘as scanline; vs actual scanline data: by verifying the fit of the DFN with the data in the ‘CDF chart’. The Chi square test and the KS-test both quantifies the similarity of the DFN and the original data (from mapping). For both, the question answered by the test is “are the two data samples different”? The KS test performs usually better for small data set than Chi-square test.
    • KS-Test: A confidence at which we can say that these two datasets are different. Outliers have a strong effect on the reported value for alpha (because K-S is a measure of maximum deviation).
      • KS-value: Numerical value related to the difference between A and B’s cumulative distribution functions (CDF).
      • Rejection alpha: The reject level for the hypothesis that the fitted data follow same distribution. A high value (max = 1 or 100%) occurs when the fit is good and a low value (min = 0) occurs when fit is not good. When the rejection alpha goes below 0.05, the lack of fit is significant.
    • Chi-square Test: The Chi-square test is meant to test the probability of independence of a distribution of data. The larger the sample size, the more reliable the results.
      • Chi-square value: The Chi-square value serves as input for the more interesting piece of information: the p-value
      • P-value: Calculated from the chi-square value and the degree of freedom (dependant on the number of data). A low p-value indicates that we can say with high confidence that the two data samples (DFN sampled and data from mapping) are different. By convention, the “cutoff” point for a p—value is 0.05 (5%)

3. Calibration: In order to help achieve a good fit (step 2); adjust the input parameters (P32 and mean diameter) – To help you in decide which value, look at the proposed ‘optimal input values’ in the calibration chart. The graph shows the relation between the P32 input vs the resulting true spacing sampled of the DFN. The fit is not important (don’t bother with the ks-value of that chart), it is just to give us an indication of what the relation looks like

For each set, an input P32P_{32} and Mean Diameter must be defined

  • For Trace length / mean diameter: The calibration curve is more accurate for diameter < surveys dimensions (i.e. tunnel, around 5 meters). More ‘weight’ is set for the dimensions for <5meters for this reason at the first iteration, because of the biases regarding trace length higher than 5 meters. After the first iteration, can press ‘set optimal value as input value’ and ‘initiliaze diameter values samples’: that will sample the diameter value input around the optimal diameter (0.5x – 1.5x). That will help to focus the calibration in the interval that’s suits better the data.
  • Many iterations could be required to obtain a satisfying fit of the DFN to the data
  • Both P32P_{32} and Mean Diameter could need to be adjust simultaneously in order to do so.
Última actualización el