Lecture 6c Inverting Resistivity Data

Inverted resistivity model outputs are represented as colorful resistivity images.
It's critical to remember the limitations involved and not get drawn into over interpretations.
Data for a two dimensional resistivity image are acquired by surveys which combine the elements of profiling and sounding.
Measurements collected using different electrode central positions and different electrode separations.
Different central positions provide information on lateral changes, and the different electrode separations provide different effective depths of measurement.
Pseudosections are a way of simply visualizing the measurement arrangements of apparent resistivity.
To derive a resistivity image, the apparent resistivity measurements need to be inverted to derive a model of subsurface resistivity.
Pseudosections are not themselves resistivity images, but they can be used to derive the initial parameter estimates for inversion model.

Apparent resistivity measurements may vary with electrode configuration.
Example: A pseudosection representing a two dimensional survey collected using a Vennar array.
The vertical level has been converted into an estimated equivalent depth in meters.
The deeper measurements require a wider array separation.
Colors represent the apparent resistivity on a log scale.
If minimum values are around 2.13, resistivity values are $10^{2.13}$ , which is about $30$ ohm meters.
If the maximum on the scale is 2.37, the value is $234$ ohm meters.
The Vennar and the dipole dipolar array give different pseudosections.
Processing these data into a resistivity image should reconcile these differences because the processing accounts for the array geometry used to collect the measurements.

The inverse model represents the best view of the subsurface acquired from the resistivity survey.
The inversion process is an iterative process.
At each iteration, a forward model is used to assess the misfit between the model and the data.
If the misfit is too large, the model parameters are adjusted, and another iteration is run.
In two d resistivity inversion, the model parameters are all the estimates of subsurface resistivity that make up that resistivity image.
The inversion stops when the iterations no longer decrease the misfit or the decreases are sufficiently small to be negligible.
The two dimensional inversion process is equivalent to the one dimensional process to invert the sounding curve.

Resistivity images derived from different electrode arrangements should all be similar.
Arrays have different measurement sensitivities, causing differences in subsurface models.
Example: the high resistivity anomaly in the Vennet image appears to be slightly larger, but maybe with a slightly lower maximum magnitude than in the image from the dipole dipole survey.
The difference between the inverted images and the true model give you some insight into how the resistivity, just like any other geophysical techniques, gives you only some sort of fuzzy view of the subsurface.
The region of anomalously high resistivity is not actually circular at all as potentially suggested by inverted resistivity images.
The dipole dipole array gives a slightly better representation of the true model.

Vennar array: potential electrodes are located inside the current electrodes, providing higher signal strength.
Allows use of cheaper, less sensitive equipment.
Safety considerations: injecting tens to hundreds of thousands of volts into the ground; not desirable to be located inside those current electrodes.
Array selection can be critical due to different sensitivities.
Example: Simulation by Andy to assess the suitability of resistivity measurements for detecting narrow vertical resistivity anomalies, such as mine shafts.
The Vennar survey is unable to resolve this narrow anomaly, but the dipole dipole array is much more successful.
Simulating synthetic scenarios such as this is an excellent approach for assessing any proposed survey design.

Measurement sensitivity deteriorates with increasing depth and with increasing distance from the electrodes.
The inversion method allows some insight into the sensitivity of the results.
Sensitivity maps can be directly produced.
Highest sensitivity is nearest the electrodes at the surface.
Low measurement sensitivity implies greater uncertainty in the results.
Uncertainty varies spatially across the image.
A more honest visualization would vary transparency using sensitivity.

The inversion process can be used for three-dimensional data.
The computational burden is much greater.
Three d imaging much manageable over smaller spatial areas than the larger ones.
Example: Andy's work in China, looking at agricultural practices and their impact on soil and soil thicknesses.

Pseudosections provide useful visualizations of apparent resistivity measurements, but they're not direct representations of subsurface resistivity.
Inverting the data accounts for most of this variability, but differences between models will remain due to different measurement sensitivities from different electrode arrays.
It's important to have in mind what you're trying to look for when deciding on the type of array to be used.
It's critical to remember that a colorful image is the results of a modeling process and based on data which have inherent limitations.
Care must be taken not to over interpret apparently otherwise clear features.