L1 norm is calculated by minimising the absolute differences and L2 is the square
of differences between observed data and calculated data in the electrical resistivity model.
Both are based on Gauss-Newton method. So it's not easy to say which one is better, but in Res2DInv, higher resisitivity contrasts can be obtained using the L1 norm, the L2 norm tends to smooth lateral contrasts.
L1 norm is used for areas that have high contrast the distribution of resistivities between their layers. in other words LI is suitable if there are high variation in resistivity of layers. this variations may, for example, occur due to fractures or cavities. the L2 works perfectly in areas that characteristic by low variations in resistivity between layers. horizontal layers or aquifers for instance.
Mohammed M. AL-Hameedawie
I am sorry to say, but neither of the above! L1 minimization is an effective method to downgrade the role of outliers in the measurements, because it uses a penalty function that minimizes the sum of absolute deviation (residuals) between the observed and theoretical response. On the other hand, L2 minimization works well only if there are no outliers; if there are, the square of the deviation between the theoretical and observed response weighs disproportionally in the penalty function and biases the outcome of the inversion toward the outlier. Now, if there are conductivity configurations that are more likely to produce outliers is another question and rather irrelevant in that matter! Just bear in mind that in the presence of noise, outliers can appear in ANY conductivity structure. In conclusion, one has to carefully inspect one's data prior to inversion and choose the more appropriate for the data penalty function, irrespective of one's preconception of the conductivity configuration.
All the best to everyone...
- Badges
- Science topic