Formulation of forward and inverse problems for different geophysical fields

1 Formulation of forward and inverse problems for different geophysical fields 

In this introductory section, I will give a mathematical formulation of several forward and inverse problems typical for geophysical methods. The definition of general forward and inverse problems can be described schematically by the following chart FORWARD PROBLEM model model parameters m data d. 

In studying the geophysical methods, we should also take into account that the field can be generated by some source. So wo have to correct our chart accordingly. FORWARD PROBLEM  

We will call the problem (1.2) an inverse model problem. Note that the problem (1.2), as applied to electromagnetic field or acoustic field propagation, is usually called an inverse scattering problem. 

In some geophysical applications the inverse problem is formulated with respect to the sources of the observed field only  

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