Run Inversion
By clicking with the right mouse button on the main node of the “ERT Data” and selecting “Run Inversion” will open the window shown in Figure 332.
Figure 331 Run Inversion
Figure 332 Run Inversion Panel
Simple view
Data Error
In a good model the difference (misfit) between the acquired data and modelled data is sufficiently small (it solves the inversion problem). However, field data are affected by errors (noise). For this reason, the inversion processing does not search for the models that exactly reproduce the field data, but for the model which reproduces the filed data without a certain noise. In this window all the mathematical parameters to estimate this error can be set before running the inversion. In this window the user can set the Error of the Rho and IP in terms of percent error or constant value (suggestions are: 1 for very clean data, 3-5 for data with medium signal/noise ratio, 10 or more for very noisy data).
Figure 333 Data error panel
Data Percent Errors [%]: This parameter controls the acceptable percent difference between the data and the model (the inversion will converge to this error level). The value entered here should reflect the estimated degree of data repeatability (i.e. the actual noise in the field data), which is easily obtained if reciprocal data were collected. This term works in conjunction with the constant error term to determine convergence.
Data Constant Error Term [V/I]-[mV/V]: This parameter indicates the acceptable absolute difference between the data and the model that is acceptable (the inversion will converge to this error level). The value entered here should reflect the estimated lower noise threshold of the instrument used to collect the data. This term works in conjunction with the percent error term to determine convergence.
IP Modelling
ERTLab Studio can simultaneously process Electrical Resistivity (Rho) and Induced Polarization (IP) data. To include the IP data in the inversion, check the box behind IP.
Figure 334 IP Modelling panel
Iterations
The inversion process computes “trials”, to determine the optimal roughness parameters to use each iteration. This operation can take a long time, so the user can choose the number of trials to run on each iteration. Left clicking on the Inversion Type drop down box exposes three possible selections:
Simple (4 1): it performs 4 trials at the first iteration and 1 trial from the second iteration onwards.
Full (4): it performs 4 trials at each iteration, from the first to the last.
Balanced (4 1 1 1 4 1 1 1 … ): it performs 4 trials only at specified iterations, else only 1 trial will be performed.
Stabilized (4 1 1 1 1 4): it is similar to the Simple configuration for the first 5 trials, then it proceeds with 4 trials up to the end.
Custom: it lets the user choose the number of trials at each iteration, writing the desired numbers in the dedicated box.
In Maximum number of Inversion Iterations the user can set the number of iterations to compute the Rho and the IP separately. The complete sequence of the trials iterations resulting from the set values is shown in the Rough Trials Iter box (Figure 335). In the example a custom inversion is shown, where a maximum of 15 iterations are to be performed. At the first iteration 4 trials are performed, 2 at the second, and 1 from the third to the last iteration (maximum 15).
Figure 335 Custom iteration
CPU Core Numbers
This value depends on the hardware features of the computer used to run ERTLab Studio. The more threads can be used for the inversion the faster the processing will be running. An estimation of the maximum number of thread can make automatically enabling the “Max Value” flag.
Figure 336 CPU setting
Advanced view
Clicking on the Show Advanced button will expose additional options (Figure 337).
Figure 337 Advanced inversion panel
The window has three tabs: Inversion, Noise and Forward Solver Setup. Some options are the same as already explained in this User Guide. In addition, it is possible to set the following parameters.
Inversion Tab
PCG Iterative Solver Parameters:
Maximum internal Inverse PCG Iterations: this is the maximum number of “inner” iterations in the conjugate gradient inversion solver at each iteration. The higher the number of iterations the more the solution of the system of equations will approach the analytical solution, but the slower the inversion. A value of 15 is usually enough. For simple 2D inversions this value can be increased to 30.
Tolerance for Inverse PCG iterations: this is the requested tolerance for the conjugate gradient inversion solver.
Roughness parameters:
Initial Roughness Factor: lets the user set the value to use as Roughness Factor at the beginning of inversion process. Almost always the default (10) is the best choice.
Multiplier for changing Roughness Factor: when it the simple inversion type is used (trials 4 1), the roughness parameter uses results from the previous roughness divided by the multiplication factor set through this tool.
Factor < 1 for choosing optimal Roughness Factor: the optimal roughness factor is chosen based on the minimum data residual with a given tolerance, which is defined by this factor. Typically, users can ignore this parameter.
Constant value for parameters weight: these weights of the roughness parameters allow to control the roughness trend in the three directions, x, y and z. By default, they are the same in the three directions.
Other parameters:
Smoothness Constrain: when selected, the smoothness constrain of adjacent cells will be applied to both model blocks variations and model blocks values. If not selected the smoothness constrain of adjacent cells will only be applied at the model blocks variations “dmi” at each iteration “i”.
Constrain to reference model: selecting this command will constrain the solution to the starting model at each iteration. If during the model setting one or more anomalies have been inserted (section Anomalies). Users have to check this box to take them into account during the inversion.
Noise Tab
Figure 338 Advanced noise panel
Use Robust inversion (data errors reweighted): generally, the model does not constitute exactly the real distribution of data but just an approximation of it, so it is advisable to adopt a Robust Inversion. In this case, the results are relatively insensitive to changes in assumptions of the statistical model. At the contrary, in case of not robust inversion there will be abrupt variations even in correspondence to small changes of data distribution. If “Use Robust Inversion” is selected, the noise is appropriately modified during the inversion after each iteration, to reduce the “weight” to those measures which are heavily affected by errors (outliers) and therefore are not relevant to the model.
It is possible to set even the number to reweight iteration for Rho and for IP separately.
Forward Solver Setup Tab
This tab is the same as already explained in section Run Forward Model.
Figure 339 Forward Solver Setup panel
Progress Window
When all the parameters in all three tabs are set, click on the Run Inversion button to start the inversion. Chose and select a project folder where the inversion files will be automatically saved. A progress window will appear on the screen and it will be completed automatically as the calculation proceeds. When the processing ends, a message will alert the user (Figure 340).
Figure 340 Run Inversion progress
The inversion summary chart is automatically saved in the project folder (chosen when the inversion was started) with the name “RES Iter n Trial m.png” (where n is the number of iteration and m the number of trial). A good inversion gives a diagram where:
The bar height decreases as iterations proceed (as a consequence of the residual decreasing);
The last bar of the bar chart corresponds in height to the red line (Data residual, ideal inversion target = number of measurements to process).
There is a low number (7 in the example) of iterations (easy convergence).
Figure 341 Histogram chart of a reliable inversion
At the end of the inversion, the plot between field data and calculated data is near to 1:1 ratio, and data are distributed along the diagonal;
Abnormal values (outliers, yellow dots, where the absolute difference between modelled data and measured data is high) are in the minority.
Figure 342 Cross-plot of a reliable inversion
Figure 343 shows an example summary chart of a not successful inversion.
The histograms remain at a constant height from iteration 6 to 12 (no progresses at the proceed of inversion) and at the last 2 iterations they are opposite to the trend, reaching very high residual values;
The last bar in the bar chart does not match the red target line;
High number of iterations (14 iterations) (difficulty in convergence).
Figure 343 Histogram chart of a not reliable inversion
At the end of the inversion, the plot between field data and calculated data is far from the diagonal (in this case they are align along 0 of calculated V/I);
Outliers (yellow dots, where the absolute difference between modelled data and measured data is high) are the most common values and they are distributed almost evenly throughout the cross-plot.
Figure 344 Cross-plot of a not reliable inversion
In this case it is necessary to check and eventually further clean the field data, edit the noise, and/or the starting model before proceeding to run the inversion again.