Greens functions for wavefield equations

1 Green s funetions for the scalar wave equation and for the corresponding Helmholtz equation 

Green s functions appear as the solutions of seismic field equations (acoustic wave equation or equations of dynamic elasticity theory) in cases where the right-hand side of those equations represents the point pulse source. These solutions are often referred to as fundamental solutions. For example, in the case of the scalar wave equation (13.54), the density of the distribution of point pulse forces is given as a product, 

The fundamental solution or the scalar Green s function in this case satisfies the following equation  

The importance of studying Green s functions is dictated by the following considerations. 

First of all, according to the basic property of the 5-function (13.63), any source F (r,t) can be represented as a sum of point pulse sources appropriately distributed 

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