Where does an image come from ?
In the previous section we discussed that a geophysical image is is a spatial representation of physical properties resulting from the processing of geophysical data. However, we did not provide any details on this processing. This processing is known as inversion. Inversion is a mathematical methodology with which we can estimate a distribution of subsurface physical properties from measured data.
If we know what the earth properties are, we can calculate what geophysical data we would obtain collect for a specific instrument placements and acquisition parameters). This is known as the so called forward problem .
The inverse problem is If we know what data we have, what are the earth properties ?. The cartoon on the right shows how this problem is solved: we take an initial guess on property distributions, calculate the data for these property distributions (so called synthetic data) and compare them with our field data. If there is a large difference we change our model and try again, until we have a good fit between synthetic and observed data
There are a lot of details that this description glosses over (specifically the hardest detail, which is how exactly do we change the distribution of properties), but these fall outside the scope of this primer. We suggest that interested readers should consult the free books on inversion available from e.g. the Samizdat Press at Colorado School of Mines for more specifics.
However, three of the key details in the inversion process which are important to remember are:
- We can use information to constrain our model: for instance, if we know where an interface is we can place this in our model;
- The model we end up with is non unique: there are many models which fit our data. These models will in many cases (but not always) look very similar, but this what geophysicists meant if they say that geophysical inversion is non unique;
- Inversion has finite resolving ability (associated with the data and physics): there are details on physical property distributions which we will never be able to see with geophysics.