These are all those numerical processes involved in the processing of geophysical data. Those used by the ICGC are: modeling, resolution of the inverse problem, integration of geophysical data based on exploratory statistical analysis techniques: "clusters" or fuzzy logic.

Modeling

Also known as direct problem, geophysical modeling or simulation is a numerical process that allows us to know the theoretical response of the subsoil.

This process is used:

• to know the influence of the subsoil structure under the effect of a certain stimulus (e.g., injection of electric current, propagation of seismic or electromagnetic waves).
• to optimize data acquisition (field campaign design, resolution capacity, economic costs).
• to improve the interpretation of the final model.
• in the investment process, to calculate the response of each new model iteratively.

Diagram of a 2D modeling process

Inverse problem

This process provides a description of the Earth's interior by fitting the data measured on the surface to a possible model of the Earth's subsoil.

This numerical process has disadvantages such as:

• non-existence.
• non-uniqueness: impossibility of determining a single solution due to the existence of a finite set of data; there is a wide range of models that are compatible with the measured data.
• instability of the solution: ill-conditioned problem, small variations in the data can cause large changes in the parameters that define the model.

To reduce these problems, all the information available a priori from geological studies and other geophysical methods is introduced into the inversion process.

Schematic of a 2D inversion process, which uses direct problem solving (2D modelling)

Geophysical data integration

It is the main line of work to reduce uncertainty and ambiguity in the interpretation of geophysical models.

This process can be carried out in different ways:

• Indirectly. By superimposing models from different methods, looking for common characteristics and making a joint interpretation of the results.

Example of an indirect integration of geophysical data (electrical and seismic refraction tomography)

• Directly through cluster analysis. It is an exploratory statistical data analysis technique to solve classification problems. Its objective is to order variables (physical parameters) so that their degree of association/similarity between members of the same group is stronger than the degree of association/similarity between members of different groups. Within this technique, different lines of analysis can be chosen such as: "fuzzy-logic", "k-means" and others.

Schematic of an interactive cluster analysis process (top) and application of the result to the description of the lithology of the area (bottom)