The Pointwise Double Constraint Methodology

This chapter deals with the basic elements of the double constraint methodology (DCM). Since the DCM is an imaging method, while most parameter estimation methods are calibration methods, the difference is introduced in Sect. 3.1 and worked out in much greater depths in Sect. 3.9. Section 3.2 introduces the DCM in its most simple, intuitive form. To avoid presentation of three times the same equation for the three conductivity components in anisotropic media, we introduce the “voxel notation” in Sect. 3.3. Sections 3.4 and 3.5 present the theoretical justifications for the “intuitive DCM” presented in Sect. 3.2, while Sect. 3.6 discusses convergence and termination of the iterations. Section 3.7 presents some different approaches to handling anisotropy. Since the DCM is based on two models—the flux model and the head model—the rules for posing the correct boundary conditions for the two models are dealt with in Sect. 3.8.