8: Inversion of Controlled-Source Electromagnetic Data
Given a set of geophysical measurements, we want to determine all information possible about the geologic structure that gave rise to the data. There are two aspects. First, because we use electrical and electromagnetic (EM) methods of exploration we want to determine the geoelectric structure of the earth; i.e., the conductivity and/or the permittivity as a function of depth and lateral distance. If we can do this, then the second aspect will relate the geoelectric structure to the geologic structure. In some cases, a one-to-one relationship exists between the two; in others, there may be only a partial but useful overlap. This chapter addresses the first aspect–determining the geoelectrical structure based on controlled-source electromagnetic (CSEM) data.
The earliest inversion methods can be described as trial-and-error exercises. Starting with a general model, such as a layered earth or a thin dike, and then adjusting the parameters of the model we achieve a best-fit to the data. The parameters in this case are the physical dimensions and conductivities of the structures. Basically the exercise consists of running a number of forward models, and systematically adjusting the important parameters until the response matches the observed data within the noise level of the measurements.
Model-fitting by trial-and-error is still the most common interpretation technique for multidimensional models, but there are problems with the approach:
1. There is an a priori restriction to classes of models for which a relatively fast forward solution exists.
2. Because relatively simple models can have several parameters, some of which may be strongly correlated, the trial-and-error process may involve a prohibitive amount of time.
3. Fitting an assumed physical model to observed data involves a high degree of subjectivity. It is important to estimate confidence intervals for the various parameters and for other statistical measures that provide insight into how appropriate the model is. The trial-and- error approach does not provide this information.