Abstract
Differential methods have found wide applications in numerical modeling because of the ease with which they handle a very complicated model of the target. This approach to electromagnetic modeling and inversion has its own advantages and disadvantages over the integral equation method. The advantage is that one can apply a very flexible grid for discretization of the model parameters using differential methods. The disadvantage is that in the framework of the differential methods we have to discretize the entire modeling domain, while in the integral equation method one should discretize the domain with the anomalous conductivity distribution only. In this chapter, we will consider the most widely used differential techniques of forward electromagnetic modeling based on finite difference and finite element methods. We will also discuss the basic ideas of using differential methods in electromagnetic inversion.
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