Currently, I am working on 2-D nonlinear joint inversion of VLF and VLF-R data. Since VLF_R data which I am taking in log scale ranging from (0-5) and sensitivity matrix has been calculated by considering log of both model and data.. but VLF data which I'm considering is on linear scale ranging ( -40 to 40) and the sensitivity matrix has been calculated by considering model (log) and data (linear ).How should I give different weight to different data sets in this joint inversion problem ?
You can introduce a weighting matrix with the reciprocals of the standard deviation of the data as diagonal elements. Your data contains the VLF_R data in log scale so you should take the standard deviation of the log of the data for VLF_R data and the standard deviation of the VLF data in linear scale.
Not sure if I understood properly.
if you want to mix the different scalings, you have to standardise before inversion as Benjamin said. So that the weight of the 2 measures is 0.5 * 2.
If you want to give different weights you have to give different proportions from the results according to your parameters (QC signal or amplitude, etc) then I would use a weighting matrix affecting the standardised result.
I'd always recommend (in individual or joint inversion) to scale data by their errors (you should have a rough idea of how accurately to predict them from independent inversion if there is no other information). If you apply any transformation you have to do this also for the errors (e.g. log(1+e_i/d_i) for log). Consequently the misfit function should ideally become a standard Gaussian distribution. If you then add two methods, the two distributions are just added and do not need further weighting.
Dear Thomas, Thank you very much .i need more explanation in that context if you have any paper regarding that plz suggest me .
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