Easy Inversion Processing Steps

What Is Inversion Processing?

When geophysical resistivity data is collected in the field, geophysicists try to relate that data to a resistivity model of the ground so they can create a “smooth” model of the ground. To do so, they solve a system of partial differential equations using finite element analysis.

 

Consider a question where the answer is “C.” The question could be any number of things, like:

  • What is the first letter in the word “cat”?

  • What letter comes after B?

  • What letter comes before D?

An infinite number of questions could be produced for that same answer.

 

In many ways, this is similar to what is happening with resistivity. When you interpret the data you have collected in the field, you have to ask what model in the ground could have caused that data. To answer this question, you will have to work backwards.

How Inversion Processing Works

 

When you conduct a geophysical electrical resistivity survey, you collect hundreds or thousands of data points that “show” you resistivity variations in the ground. These variations are measured from many different electrode locations, which is like looking at the same thing from many different directions.

 

Based on the field data, an initial raw resistivity model of the earth is created. Next, synthetic data which would theoretically be produced if the measurement was performed on the first raw model of the earth is calculated. That synthetic data is then compared to what was actually collected in the field. Finally, the misfit between the data that was collected in the field and the synthetic data that was calculated from the raw model is minimized by adjusting the raw start model. This procedure is called iteration, and is repeated typically three to four times but could be less or more. For each iteration a particular percentage known as RMS is assigned to the iteration. The RMS, root mean square, is a statistical measure on how well the field data fits the synthetic data.

 

Once you’ve gotten close enough to a particular RMS percentage, you know you’re fairly close to the real model. But since there are an infinite number of questions that satisfy the answer, geophysicists don’t try to find the “one question”—as it will undoubtedly be wrong due to noise and calculation errors. So the goal is to be in proximity with the real answer, which is known as “smoothness constraint inversion” (as it’s an average of many solutions, and thus, “smooth”).

Easy Inversion Processing Steps Using EarthImager Software

 

  • Read in the data: To do this, you’ll need to locate and start the EarthImager software and then read in the data text file. If data was collected with the SuperSting instrument, it will have the extension “.stg.” (If collected with another instrument it may have another extension like “.dat.”)

  • Select from default settings: You’ll then want to set some default settings, which are numbers that we know work really well with whatever type of application you need. The defaults are different if you’re laying out electrodes on the surface, or if you’re in a conductive area, or if you’re in water.

  • Begin the inversion: With AGI’s system, you simply push a button to begin the calculation. It can take anywhere from a few seconds to a few hours to finish the solution depending on the number of data points and computer used.

  • Remove poorly fit data using a histogram misfit graph: The misfit of the data is plotted in a histogram. Outliers in this diagram can simply be removed graphically from the calculation. Outliers can for example be data points which by some reason (noise) has been mis-measured.

  • Invert the data: Once the outliers are removed, you invert the data again.

  • Repeat: Continue this process until you are able to lower the RMF to below 10% (3% is excellent).

  • Create a convergence chart: Once you’ve brought the RMS down, you’ll need to decide which iteration of the inversion model to select. The default is eight iterations—the first being very smooth, and the eighth being the most detailed and complex. You’ll want to select the iteration where the inversion converges. To do that, you have to look at the convergence curve (i.e. the plot showing the misfit for each iteration). As the misfit improves, it becomes smaller (and thus fits better), until changing the model will not decrease the misfit. Once you’ve gotten to that point, that will be your best model. Hint: We’ve found this is typically iteration three or four of the final inversion.

 

By following these easy inversion processing steps, you can take all the complexity out of doing the inversion calculation and make the process far more automated.